Section 2 Bridge Engineering

**References**

[1] Romão T.G. Evolução do Sector da Construção em Portugal - Aplicação do Engineering and Management, vol. 136,

n° 9, pp. 1028-1036, 2010. DOI: 10.1061/(ASCE)CO.1943-7862.

[10] Wang H, Deng X, Zhang Z, Jiang W. A New Failure Mode and Effects Analysis Method. IEEE Acess ISSN 2169-3536*,* vol. 7, p. 12, 2019. DOI:

10.1109/ACCESS.2019.2923064.

[12] Huang J, You J-X, Liu H-C, Song M-S. Failure mode and effect analysis improvement: A systematic literature. Reliability Engineering and System Safety ISSN 0951-8320*,* vol. 199,

p. 12, 2020. DOI: 10.1016/j.

[13] Chen J. K. Utility Priority Number Evaluation for FMEA. Journal of Failure

[14] Oliveira M.R. Planos de Controlo,

Procedimento. ISEP Moodle, Porto,

Analysis and Prevention*,* vol. 7, pp. 321-328, 2007. DOI: 10.1007/

Medição e Monitorização –

ress.2020.106885.

s11668-007-9060-2.

2018.

QIC2006, Lisboa, 2006.

[11] Silva S.R.C, Fonseca M, Brito J. Metodologia FMEA e sua Aplicação à Construção de Edificios. LNEC,

0000210.

Performance [Dissertação]. Instituto Superior Técnico-IST. Lisboa, 2015.

[2] Oliveira M.R. Plans of Control, Measurement and Monitoring with Risk

Integrity Procedia*.* vol. 5, pp. 1129-1135, 2017. DOI: 10.1016/j.prostr.2017.07.016.

[3] Ali M.C. Exploring the Potential of Integration Quality Assessment System in Construction (QLASSIC) With ISO 9001 Quality Management System (QMS). International Journal for

Quality Research*,* vol. 8, n° 1, pp. 73-86,

[4] Oliveira M.R. A Gestão da Qualidade na Construção e a Gestão do Risco. ISEP

[5] NP EN ISO 9001:2015 - Sistemas de Gestão da Qualidade - Requisitos (ISO 9001:2015). Instituto Português da Qualidade (IPQ), Caparica, 2015.

[6] DNP ISO Guia 73:2011 - Gestão do risco - Vocabulário (ISO Guide 73: 2009). Instituto Português da Qualidade

[7] NP EN 31010:2016 - Gestão do risco - Técnicas de apreciação do risco (ISO/ IEC 31010:2009). Instituto Português da Qualidade (IPQ), Caparica, 2016.

Pongpullponsak A. Risk Assessment in the Organization by Using FMEA Innovation: A Literature Review. King Mongkut's University Technology

[9] M. Abdelgawad M, Fayek A.R. Risk Management in the Construction Industry Using Combined Fuzzi FMEA and Fuzzy AHP. Journal of Construction

Modelo Structure-Conduct-

*Structural Integrity and Failure*

Assessment Application to Rehabilitation works. Structural

2014. ISSN 1800-6450.

Moodle, Porto, 2016.

(IPQ), Caparica, 2011.

[8] Nuchpho P, Nansaarng S,

Thonburi, Thailand, 2014.

**74**

**Chapter 5**

*Louay S. Yousuf*

varied between 60*C*<sup>∘</sup> and�15*C*<sup>∘</sup>

combined loading

**1. Introduction**

**77**

**Abstract**

Composite Plate

Analytic and Numerical Results of

Bending Deflection of Rectangular

In this chapter, the derivation of analytic formulation of bending deflection has been

the y-direction and in-plane force (*Nxx*) in the x-direction. The in-plane force (*Nxx*) has a

. The combined loading are the bending moment (*Mo*) in

done using the theory of classical laminate plate. The method of Navier and Levy solutions are used in the calculation. The composite laminate plate is exposed to out-off plane temperatures and combined loading. The temperature gradient of thermal shock is

great effect on the bending deflection value within a 95 ð Þ *:*842% , but the bending moment (*Mo*) has a small effect on the bending deflection value in the rate of 4ð Þ *:*101% .

**Keywords:** classical plate theory, composite laminate plate, temperature affect,

The effect of temperature and combined loading on composite plate is one of the primary life limiting factors of a bridge engineering application. This chapter will consider the structural evaluation of the localized effect in the bridge engineering. The application of bridge engineering can be found in a structural bridge deck panel. Ray studied the fiber-matrix debonding by applying the thermal shock of thermal fatigue, taking into account the conditioning time. He performed a three-point bending test on glass fiber reinforced with unsaturated polyester and epoxy resin composites in which it exposed to 75 *C*° of the temperature gradient [1]. Hussein and Alasadi used a numerical analysis of stress and strain values of angle-ply with fourlayered symmetric laminated plate under the effect of force resultant ð Þ *Nxx* and bending moment ð Þ *Mxx* graphically. He predicted the material properties of the multilayered plate of the reinforcement fibers of E-glass and epoxy resin [2]. Yousuf et al. evaluated the dynamic analysis of normal deflection, taking into consideration the effect of thermal fatigue beside the effect of bending moment (*Mo*) and in-plane force (*Nxx*). The composite laminate plate of woven roving fiber glass and polyester were exposed to 75 *C*° of the temperature gradient. A composite laminate plate with fiber volume fraction (*v <sup>f</sup>* ¼ 25*:*076 %) was selected [3]. Wang et al. applied the thermal cycles in the temperature range between (80 *C*° and �40 *C*°) on different plys of glass fiber/epoxy matrix composites. Scanning electron microscopy (SEM) images showed that after 180 of thermal cycles, the bonding effect of glass fiber and epoxy matrix became worse, leading to the decrease in mechanical properties [4].

The results are compared and verified for central normal deflection.

### **Chapter 5**

## Analytic and Numerical Results of Bending Deflection of Rectangular Composite Plate

*Louay S. Yousuf*

### **Abstract**

In this chapter, the derivation of analytic formulation of bending deflection has been done using the theory of classical laminate plate. The method of Navier and Levy solutions are used in the calculation. The composite laminate plate is exposed to out-off plane temperatures and combined loading. The temperature gradient of thermal shock is varied between 60*C*<sup>∘</sup> and �15*C*<sup>∘</sup> . The combined loading are the bending moment (*Mo*) in the y-direction and in-plane force (*Nxx*) in the x-direction. The in-plane force (*Nxx*) has a great effect on the bending deflection value within a 95 ð Þ *:*842% , but the bending moment (*Mo*) has a small effect on the bending deflection value in the rate of 4ð Þ *:*101% . The results are compared and verified for central normal deflection.

**Keywords:** classical plate theory, composite laminate plate, temperature affect, combined loading

### **1. Introduction**

The effect of temperature and combined loading on composite plate is one of the primary life limiting factors of a bridge engineering application. This chapter will consider the structural evaluation of the localized effect in the bridge engineering. The application of bridge engineering can be found in a structural bridge deck panel. Ray studied the fiber-matrix debonding by applying the thermal shock of thermal fatigue, taking into account the conditioning time. He performed a three-point bending test on glass fiber reinforced with unsaturated polyester and epoxy resin composites in which it exposed to 75 *C*° of the temperature gradient [1]. Hussein and Alasadi used a numerical analysis of stress and strain values of angle-ply with fourlayered symmetric laminated plate under the effect of force resultant ð Þ *Nxx* and bending moment ð Þ *Mxx* graphically. He predicted the material properties of the multilayered plate of the reinforcement fibers of E-glass and epoxy resin [2]. Yousuf et al. evaluated the dynamic analysis of normal deflection, taking into consideration the effect of thermal fatigue beside the effect of bending moment (*Mo*) and in-plane force (*Nxx*). The composite laminate plate of woven roving fiber glass and polyester were exposed to 75 *C*° of the temperature gradient. A composite laminate plate with fiber volume fraction (*v <sup>f</sup>* ¼ 25*:*076 %) was selected [3]. Wang et al. applied the thermal cycles in the temperature range between (80 *C*° and �40 *C*°) on different plys of glass fiber/epoxy matrix composites. Scanning electron microscopy (SEM) images showed that after 180 of thermal cycles, the bonding effect of glass fiber and epoxy matrix became worse, leading to the decrease in mechanical properties [4].

Khashaba et al. investigated the mechanical properties of 0½ �<sup>8</sup> of woven glass fiber reinforced polyester (GFRP) composites under monotonic and combined tension/ bending loading [5, 6]. Yousuf reduced the vibration properties of composite material under the variation of combined temperatures (60 *C*° to �15 *C*°) using three types of boundary conditions. The free vibration test was carried out for (5, 10, 15, 20, 25, and 30) minutes [7]. Moufari proposed several numerical simulations to describe the interaction between thermal and mechanical stresses. The estimation damage modes of carbon/epoxy laminate plate has been achieved due to thermal cyclic loading. Zhen and Xiaohui proposed an analytic model of Reddy-type higher-order plate theory for simply supported plates based on thermal and mechanical combined loading [8]. In this work, the analytic derivation of bending deflection has been done by using the theory of classical laminate plate. Levy and Navier solutions are used to describe the theory of bending deflection by taking into consideration the use of simply supported boundary condition from all edges. In our point of view, the analytic derivation of normal deflection under the effect of temperature and combined loading has not been studied.

### **2. Equations of motion in terms of displacements**

The stress and strain relationship is varied through the laminate thickness, as indicated in Eq. (1):

$$
\begin{bmatrix}
\sigma\_{\rm xx} \\
\sigma\_{\rm yy} \\
\sigma\_{\rm xy}
\end{bmatrix} = \begin{bmatrix}
\mathbf{Q}\_{11} & \mathbf{Q}\_{12} & \mathbf{0} \\
\mathbf{Q}\_{12} & \mathbf{Q}\_{22} & \mathbf{0} \\
\mathbf{0} & \mathbf{0} & \mathbf{Q}\_{66} \\
\end{bmatrix} \ast \begin{bmatrix}
\begin{bmatrix}
\varepsilon\_{\rm xx} \\
\varepsilon\_{\rm yy} \\
\gamma\_{\rm xy}
\end{bmatrix} - \begin{bmatrix}
a\_1 \\
a\_2 \\
\mathbf{0}
\end{bmatrix} \ast \Delta T \\
\end{bmatrix} \tag{1}
$$

The general bending equation of rectangular plate is as below:

$$\frac{\partial^2 M\_{\infty}}{\partial \mathbf{x}^2} + 2 \frac{\partial^2 M\_{\infty}}{\partial \mathbf{x} \partial \mathbf{y}} + \frac{\partial^2 M\_{\text{yy}}}{\partial \mathbf{y}^2} = \mathbf{0} \tag{2}$$

By taking into account the temperature effect, the mechanical and thermal bending moments are:

$$
\begin{bmatrix} M\_{\text{xx}} \\ M\_{\text{yy}} \\ M\_{\text{xy}} \end{bmatrix} = \begin{bmatrix} M\_{\text{xx}}^{\text{Mech.}} \\ M\_{\text{yy}}^{\text{Mech.}} \\ M\_{\text{xy}}^{\text{Mech.}} \end{bmatrix} - \begin{bmatrix} M\_{\text{xx}}^{\text{Ther.}} \\ M\_{\text{yy}}^{\text{Ther.}} \\ M\_{\text{xy}}^{\text{Ther.}} \end{bmatrix} \tag{3}
$$

where

$$
\begin{bmatrix} M\_{\text{xx}}^{\text{Mech.}}\\ M\_{\text{yy}}^{\text{Mech.}}\\ M\_{\text{xy}}^{\text{Mech.}} \end{bmatrix} = \begin{bmatrix} B\_{11} & B\_{12} & 0\\ B\_{12} & B\_{22} & 0\\ 0 & 0 & B\_{66} \end{bmatrix} \ast \begin{bmatrix} \frac{\partial u\_{o}}{\partial x}\\ \frac{\partial v\_{o}}{\partial y}\\ \frac{\partial v\_{o}}{\partial y}\\ \frac{\partial u\_{o}}{\partial y} + \frac{\partial v\_{o}}{\partial x} \end{bmatrix} - \begin{bmatrix} D\_{11} & D\_{12} & 0\\ D\_{12} & D\_{22} & 0\\ 0 & 0 & D\_{66} \end{bmatrix} \ast \begin{bmatrix} \frac{\partial^{2}w\_{o}}{\partial x^{2}}\\ \frac{\partial^{2}w\_{o}}{\partial y^{2}}\\ \frac{\partial^{2}w\_{o}}{\partial x \partial y} \end{bmatrix}
$$

(4)

And,

**Figure 1.**

*D*<sup>11</sup>

where.

**79**

through the plate thickness.

*∂*<sup>4</sup>*wo ∂x*<sup>4</sup> � � *MTher: xx*

*Lamina of arbitrary of principal material direction.*

*DOI: http://dx.doi.org/10.5772/intechopen.93592*

3 <sup>5</sup> <sup>¼</sup> <sup>X</sup> *N*

þ 2ð Þ *D*<sup>12</sup> þ 2*D*<sup>66</sup>

*k*¼1

¼ � *<sup>∂</sup>*<sup>2</sup>

varied linearly through the plate thickness, as in below:

4 *ab* ð*a* 0 ð*b* 0

*Tmn*ð Þ¼ *z*

*Q*<sup>11</sup> *Q*<sup>12</sup>

*Analytic and Numerical Results of Bending Deflection of Rectangular Composite Plate*

" #*<sup>k</sup>*

∗ *α*1

It can be assumed that all layers have ð Þ <sup>Θ</sup> <sup>¼</sup> <sup>0</sup> , and the same thickness *Bij* <sup>¼</sup> <sup>0</sup> � �,

þ *D*<sup>22</sup>

*∂*2 *MTher: yy ∂y*<sup>2</sup>

**3. Formulation of bending deflection distribution using Navier solution**

The normal deflection distribution is derived based on the solution of classical laminate plate theory using Navier equation. Navier solution assumed that the boundary condition is simply supported from all edges under the effect of temperature ð Þ Δ*T* and in-plane force ð Þ *Nxx* . It can be assumed that the temperature is

*T*<sup>1</sup> is the out-off plane uniform temperature when the heat source is applied

*α*2

*∂*<sup>4</sup>*wo ∂y*<sup>4</sup> � �

! (6)

Δ*T x*ð Þ , *y*, *z sin* ð Þ *αmx sin β<sup>n</sup>* ð Þ*y dxdy* (7)

þ *Nxx*

*∂*2 *wo ∂x*<sup>2</sup> � �

" #*<sup>k</sup>*

∗ ð*zk*þ<sup>1</sup> *zk*

Δ*Tzdz* (5)

*Q*<sup>12</sup> *Q*<sup>22</sup>

as indicated in **Figure 1**. Substitute Eq. (4) and into Eq. (3), it can be obtained:

*∂*<sup>4</sup>*wo ∂x*<sup>2</sup>*∂y*<sup>2</sup> � �

> *MTher: xx ∂x*<sup>2</sup> þ

2 4

*MTher: yy*

*Analytic and Numerical Results of Bending Deflection of Rectangular Composite Plate DOI: http://dx.doi.org/10.5772/intechopen.93592*

**Figure 1.** *Lamina of arbitrary of principal material direction.*

And,

Khashaba et al. investigated the mechanical properties of 0½ �<sup>8</sup> of woven glass fiber reinforced polyester (GFRP) composites under monotonic and combined tension/ bending loading [5, 6]. Yousuf reduced the vibration properties of composite material under the variation of combined temperatures (60 *C*° to �15 *C*°) using three types of boundary conditions. The free vibration test was carried out for (5, 10, 15, 20, 25, and 30) minutes [7]. Moufari proposed several numerical simulations to describe the interaction between thermal and mechanical stresses. The estimation damage modes of carbon/epoxy laminate plate has been achieved due to thermal cyclic loading. Zhen and Xiaohui proposed an analytic model of Reddy-type higher-order plate theory for simply supported plates based on thermal and mechanical combined loading [8]. In this work, the analytic derivation of bending deflection has been done by using the theory of classical laminate plate. Levy and Navier solutions are used to describe the theory of bending deflection by taking into consideration the use of simply supported boundary condition from all edges. In our point of view, the analytic derivation of normal deflection under the effect of temperature and combined loading has not been

The stress and strain relationship is varied through the laminate thickness, as

*εxx εyy γxy*

*MTher: xx MTher: yy*

*D*<sup>11</sup> *D*<sup>12</sup> 0 *D*<sup>12</sup> *D*<sup>22</sup> 0 0 0 *D*<sup>66</sup>

*∂*2 *wo ∂x*<sup>2</sup> *∂*2 *wo ∂y*<sup>2</sup>

2 *∂*2 *wo ∂x∂y*

*MTher: xy*

*α*1 *α*2 0

3 7 <sup>5</sup><sup>∗</sup> <sup>Δ</sup>*<sup>T</sup>*

*<sup>∂</sup>y*<sup>2</sup> <sup>¼</sup> <sup>0</sup> (2)

3 7

<sup>5</sup> (1)

(3)

(4)

2 6 4

2 6 4

2 6 4

**2. Equations of motion in terms of displacements**

*Q*<sup>11</sup> *Q*<sup>12</sup> 0 *Q*<sup>12</sup> *Q*<sup>22</sup> 0 0 0 *Q*<sup>66</sup>

The general bending equation of rectangular plate is as below:

*∂*2 *Mxy ∂x∂y* þ *∂*2 *Myy*

By taking into account the temperature effect, the mechanical and thermal

*MMech: xx MMech: yy*

*MMech: xy*

*∂uo ∂x ∂vo ∂y*

�

*∂uo ∂y* þ *∂vo ∂x*

*∂*2 *Mxx <sup>∂</sup>x*<sup>2</sup> <sup>þ</sup> <sup>2</sup>

*Mxx Myy Mxy*

*B*<sup>11</sup> *B*<sup>12</sup> 0 *B*<sup>12</sup> *B*<sup>22</sup> 0 0 0 *B*<sup>66</sup>

studied.

indicated in Eq. (1):

bending moments are:

where

*MMech: xx MMech: yy*

**78**

*MMech: xy*

*σxx σyy σxy*

2 6 4

*Structural Integrity and Failure*

$$
\begin{bmatrix} M\_{\text{xx}}^{\text{Therr.}} \\ \\ M\_{\text{yy}}^{\text{Therr.}} \end{bmatrix} = \sum\_{k=1}^{N} \begin{bmatrix} Q\_{11} & Q\_{12} \\ \\ Q\_{12} & Q\_{22} \end{bmatrix}^{k} \* \begin{bmatrix} a\_{1} \\ a\_{2} \end{bmatrix}^{k} \* \int\_{x\_{k}}^{x\_{k+1}} \Delta T z dz \tag{5}
$$

It can be assumed that all layers have ð Þ <sup>Θ</sup> <sup>¼</sup> <sup>0</sup> , and the same thickness *Bij* <sup>¼</sup> <sup>0</sup> � �, as indicated in **Figure 1**. Substitute Eq. (4) and into Eq. (3), it can be obtained:

$$\begin{split} D\_{11} \left( \frac{\partial^4 w\_o}{\partial \mathbf{x}^4} \right) &+ 2(D\_{12} + 2D\_{66}) \left( \frac{\partial^4 w\_o}{\partial \mathbf{x}^2 \partial \mathbf{y}^2} \right) + D\_{22} \left( \frac{\partial^4 w\_o}{\partial \mathbf{y}^4} \right) + N\_{\text{xx}} \left( \frac{\partial^2 w\_o}{\partial \mathbf{x}^2} \right) \\ &= -\left( \frac{\partial^2 M\_{\text{xx}}^{\text{Ther}}}{\partial \mathbf{x}^2} + \frac{\partial^2 M\_{\text{yy}}^{\text{Ther}}}{\partial \mathbf{y}^2} \right) \end{split} \tag{6}$$

### **3. Formulation of bending deflection distribution using Navier solution**

The normal deflection distribution is derived based on the solution of classical laminate plate theory using Navier equation. Navier solution assumed that the boundary condition is simply supported from all edges under the effect of temperature ð Þ Δ*T* and in-plane force ð Þ *Nxx* . It can be assumed that the temperature is varied linearly through the plate thickness, as in below:

$$T\_{mn}(\mathbf{z}) = \frac{4}{ab} \int\_0^a \int\_0^b \Delta T(\mathbf{x}, \mathbf{y}, \mathbf{z}) \sin \left(\alpha\_m \mathbf{x}\right) \sin \left(\beta\_n \mathbf{y}\right) d\mathbf{x} d\mathbf{y} \tag{7}$$

where.

*T*<sup>1</sup> is the out-off plane uniform temperature when the heat source is applied through the plate thickness.

And,

$$a\_m = \frac{m\pi}{a}, m = 1, 2, 3, \dots, \infty \tag{8a}$$

bending deflection should be along the x-axis. Levy solution can be used on any type of boundary condition which gives flexibility on any type of loading such as ð Þ Δ*T* , in-plane force ð Þ *Nxx* , and bending moment (*Mo*). As mentioned in the previous section that the temperature is varied linearly through the plate thickness, as below:

By integrating Eq. (15) with respect to (x), the temperature distribution through

4*T*1*z*

*∂*2 *wo ∂x*<sup>2</sup> � �

¼

*Tm*ð Þ¼ *z*

Ignore the variation of thermal bending moment and normal deflection along

þ *Nxx*

*MTher: xx ∂x*<sup>2</sup>

As mentioned earlier, the thermal bending moment is varied along x-axis, as

*M*ð Þ<sup>1</sup> *m*

*m*¼1

ð*zk*þ<sup>1</sup> *zk*

� *∂*2

Δ*T x*ð Þ , *z sin* ð Þ *αmx dx* (15)

*<sup>a</sup>* , *<sup>m</sup>* <sup>¼</sup> 1, 2, 3, … , <sup>∞</sup> (16)

*<sup>m</sup><sup>π</sup>* (17)

� � *sin* ð Þ *<sup>α</sup>mx* (19)

ð Þ *Q*11*α*<sup>1</sup> *Tm*ð Þ*z zdz* (20)

*wm sin* ð Þ *αmx* (22)

*wo*ð Þ¼ *x*, *y wo*ð Þ *x*, *y <sup>H</sup>* þ *wo*ð Þ *x <sup>P</sup>* (21)

(18)

*Tm*ð Þ¼ *z*

*DOI: http://dx.doi.org/10.5772/intechopen.93592*

*D*<sup>11</sup>

*M*ð Þ<sup>1</sup> *<sup>m</sup>* <sup>¼</sup> <sup>X</sup> *N*

The solution of normal bending deflection is as below:

*wo*ð Þ *<sup>x</sup> <sup>p</sup>* <sup>¼</sup> <sup>4</sup>*T*1*A*<sup>1</sup>

*∂*<sup>4</sup>*wo ∂x*<sup>4</sup> � �

*<sup>M</sup>Ther: xx* � � <sup>¼</sup> <sup>X</sup><sup>∞</sup>

*k*¼1

*wo*ð Þ *<sup>x</sup>*, *<sup>t</sup> <sup>p</sup>* <sup>¼</sup> <sup>X</sup><sup>∞</sup>

3*π*

*m*¼1

X∞ *m*¼1

Substitute Eq. (19) and Eq. (22) into Eq. (18) to obtain the particular solution of

*α*2

*m D*11*α*<sup>4</sup>

*<sup>m</sup> sin* ð Þ *αmx*

*<sup>m</sup>* � *Nxxα*<sup>2</sup>

*m* � � (23)

where

the plate thickness is:

y-axis, Eq. (6) will be:

below:

where

To find *wo*ð Þ *x <sup>P</sup>*:

**81**

bending deflection along x-axis, *wo*ð Þ *x <sup>P</sup>*:

2 *a* ð*a* 0

*Analytic and Numerical Results of Bending Deflection of Rectangular Composite Plate*

*<sup>α</sup><sup>m</sup>* <sup>¼</sup> *<sup>m</sup><sup>π</sup>*

$$
\beta\_n = \frac{n\pi}{b}, n = 1, 2, 3, \dots, \infty \tag{8b}
$$

By integrating Eq. (7) with respect to (x) and (y), the temperature distribution through the plate thickness is:

$$T\_{mn}(z) = \frac{16T\_1z}{mn\pi^2} \tag{9}$$

The thermal bending moment is defined as in the following:

$$
\begin{bmatrix} M\_{\text{xx}}^{\text{Therr.}}\\ M\_{\text{yy}}^{\text{Therr.}} \end{bmatrix} = \sum\_{m=1}^{\infty} \sum\_{n=1}^{\infty} \begin{bmatrix} M\_{mn}^{(1)}\\ M\_{mn}^{(2)} \end{bmatrix} \sin \left(a\_m \omega \right) \sin \left(\beta\_n \mathbf{y} \right) \tag{10}
$$

where

$$\mathcal{M}\_{mn}^{(1)} = \sum\_{k=1}^{N} \int\_{x\_k}^{x\_{k+1}} (Q\_{11}a\_1 + Q\_{12}a\_2)T\_{mn}(z)zdz\tag{11a}$$

$$\mathbf{M}\_{mn}^{(2)} = \sum\_{k=1}^{N} \int\_{x\_k}^{x\_{k+1}} (\mathbf{Q}\_{12}a\_1 + \mathbf{Q}\_{22}a\_2) T\_{mn}(\mathbf{z}) \mathbf{z} d\mathbf{z} \tag{11b}$$

The general solution of normal deflection for simply supported boundary condition from all edges is:

$$\omega\_{\sigma} = \sum\_{m=1}^{\infty} \sum\_{n=1}^{\infty} w\_{mn} \sin \left( a\_m \mathbf{x} \right) \sin \left( \beta\_n \mathbf{y} \right) \tag{12}$$

Substitute Eq. (12) and Eq. (10) into Eq. (6), the solution of bending deflection is illustrated in the following equation:

$$w\_o(\mathbf{x}, \mathbf{y}) = \frac{16T\_1}{3\pi^2} \sum\_{m=1}^{\infty} \sum\_{n=1}^{\infty} \frac{\left(A\_1 a\_m^2 + A\_2 \theta\_n^2\right) \sin\left(a\_m \mathbf{x}\right) \sin\left(\beta\_n \mathbf{y}\right)}{mn\left(D\_{11} a\_m^4 + 2(D\_{12} + 2D\_{66}) a\_m^2 \theta\_n^2 + D\_{22} \theta\_n^4 - N\_{\infty} a\_m^2\right)} \tag{13}$$

where

$$A\_1 = \sum\_{k=1}^{N} (Q\_{11}a\_1 + Q\_{12}a\_2) \left(z\_{k+1}^3 - z\_k^3\right) \tag{14a}$$

$$A\_2 = \sum\_{k=1}^{N} (Q\_{12}a\_1 + Q\_{22}a\_2) \left(x\_{k+1}^3 - x\_k^3\right) \tag{14b}$$

### **4. Formulation of bending deflection distribution using levy solution**

The theory of classical laminate plate of Levy solution is used to derive the solution of normal deflection. The Levy solution assumed that the variation of the *Analytic and Numerical Results of Bending Deflection of Rectangular Composite Plate DOI: http://dx.doi.org/10.5772/intechopen.93592*

bending deflection should be along the x-axis. Levy solution can be used on any type of boundary condition which gives flexibility on any type of loading such as ð Þ Δ*T* , in-plane force ð Þ *Nxx* , and bending moment (*Mo*). As mentioned in the previous section that the temperature is varied linearly through the plate thickness, as below:

$$T\_m(z) = \frac{2}{a} \int\_0^a \Delta T(\varkappa, z) \sin \left(\alpha\_m \varkappa \right) d\varkappa \tag{15}$$

where

And,

where

*wo*ð Þ¼ *x*, *y*

where

**80**

through the plate thickness is:

*Structural Integrity and Failure*

*<sup>α</sup><sup>m</sup>* <sup>¼</sup> *<sup>m</sup><sup>π</sup>*

*<sup>β</sup><sup>n</sup>* <sup>¼</sup> *<sup>n</sup><sup>π</sup>*

The thermal bending moment is defined as in the following:

<sup>¼</sup> <sup>X</sup><sup>∞</sup> *m*¼1

> ð*zk*þ<sup>1</sup> *zk*

> ð*zk*þ<sup>1</sup> *zk*

> > X∞ *n*¼1

> > > *A*1*α*<sup>2</sup>

The general solution of normal deflection for simply supported boundary

Substitute Eq. (12) and Eq. (10) into Eq. (6), the solution of bending deflection

*<sup>m</sup>* <sup>þ</sup> *<sup>A</sup>*2*β*<sup>2</sup> *n* � � *sin* ð Þ *<sup>α</sup>mx sin <sup>β</sup><sup>n</sup>* ð Þ*<sup>y</sup>*

*<sup>m</sup>* þ 2ð Þ *D*<sup>12</sup> þ 2*D*<sup>66</sup> *α*<sup>2</sup>

ð Þ *<sup>Q</sup>*11*α*<sup>1</sup> <sup>þ</sup> *<sup>Q</sup>*12*α*<sup>2</sup> *<sup>z</sup>*<sup>3</sup>

ð Þ *<sup>Q</sup>*12*α*<sup>1</sup> <sup>þ</sup> *<sup>Q</sup>*22*α*<sup>2</sup> *<sup>z</sup>*<sup>3</sup>

**4. Formulation of bending deflection distribution using levy solution**

The theory of classical laminate plate of Levy solution is used to derive the solution of normal deflection. The Levy solution assumed that the variation of the

*k*¼1

*k*¼1

*wo* <sup>¼</sup> <sup>X</sup><sup>∞</sup> *m*¼1

*mn D*11*α*<sup>4</sup>

*<sup>A</sup>*<sup>1</sup> <sup>¼</sup> <sup>X</sup> *N*

*<sup>A</sup>*<sup>2</sup> <sup>¼</sup> <sup>X</sup> *N*

*k*¼1

*k*¼1

*MTher: xx MTher: yy* " #

> *M*ð Þ<sup>1</sup> *mn* <sup>¼</sup> <sup>X</sup> *N*

> *M*ð Þ<sup>2</sup> *mn* <sup>¼</sup> <sup>X</sup> *N*

condition from all edges is:

is illustrated in the following equation:

X∞ *m*¼1 X∞ *n*¼1

16*T*<sup>1</sup> 3*π*<sup>2</sup>

By integrating Eq. (7) with respect to (x) and (y), the temperature distribution

*M*ð Þ<sup>1</sup> *mn M*ð Þ<sup>2</sup> *mn*

" #

16*T*1*z*

*Tmn*ð Þ¼ *z*

X∞ *n*¼1

*<sup>a</sup>* , *<sup>m</sup>* <sup>¼</sup> 1, 2, 3, … , <sup>∞</sup> (8a)

*<sup>b</sup>* , *<sup>n</sup>* <sup>¼</sup> 1, 2, 3, … , <sup>∞</sup> (8b)

*mnπ*<sup>2</sup> (9)

*sin* ð Þ *αmx sin β<sup>n</sup>* ð Þ*y* (10)

ð Þ *Q*11*α*<sup>1</sup> þ *Q*12*α*<sup>2</sup> *Tmn*ð Þ*z zdz* (11a)

ð Þ *Q*12*α*<sup>1</sup> þ *Q*22*α*<sup>2</sup> *Tmn*ð Þ*z zdz* (11b)

*wmn sin* ð Þ *αmx sin β<sup>n</sup>* ð Þ*y* (12)

*<sup>n</sup>* <sup>þ</sup> *<sup>D</sup>*22*β*<sup>4</sup>

*<sup>n</sup>* � *Nxxα*<sup>2</sup>

� � (14a)

� � (14b)

*m*

*mβ*<sup>2</sup>

*<sup>k</sup>*þ<sup>1</sup> � *<sup>z</sup>*<sup>3</sup> *k*

*<sup>k</sup>*þ<sup>1</sup> � *<sup>z</sup>*<sup>3</sup> *k*

� � (13)

$$a\_m = \frac{m\pi}{a}, m = 1, 2, 3, \dots, \infty \tag{16}$$

By integrating Eq. (15) with respect to (x), the temperature distribution through the plate thickness is:

$$T\_m(z) = \frac{4T\_{1Z}}{m\pi} \tag{17}$$

Ignore the variation of thermal bending moment and normal deflection along y-axis, Eq. (6) will be:

$$\begin{split} D\_{11} \left( \frac{\partial^4 w\_o}{\partial \mathbf{x}^4} \right) + N\_{\text{xx}} \left( \frac{\partial^2 w\_o}{\partial \mathbf{x}^2} \right) &= \\ -\frac{\partial^2 M\_{\text{xx}}^{\text{Ther}.} }{\partial \mathbf{x}^2} \end{split} \tag{18}$$

As mentioned earlier, the thermal bending moment is varied along x-axis, as below:

$$\mathbb{E}\left[M\_{\text{xx}}^{\text{Ther.}}\right] = \sum\_{m=1}^{\infty} \left[M\_m^{(1)}\right] \sin\left(a\_m \mathbf{x}\right) \tag{19}$$

where

$$M\_m^{(1)} = \sum\_{k=1}^N \int\_{x\_k}^{x\_{k+1}} (Q\_{11}\alpha\_1) T\_m(z) z dz \tag{20}$$

The solution of normal bending deflection is as below:

$$
\omega\_o(\mathbf{x}, \mathbf{y}) = \omega\_o(\mathbf{x}, \mathbf{y})\_H + \omega\_o(\mathbf{x})\_P \tag{21}
$$

To find *wo*ð Þ *x <sup>P</sup>*:

$$\left(w\_{\theta}(\mathbf{x},t)\right)\_{p} = \sum\_{m=1}^{\infty} w\_{m} \sin\left(a\_{m}\mathbf{x}\right) \tag{22}$$

Substitute Eq. (19) and Eq. (22) into Eq. (18) to obtain the particular solution of bending deflection along x-axis, *wo*ð Þ *x <sup>P</sup>*:

$$\left(w\_o(\mathbf{x})\_p = \frac{4T\_1A\_1}{3\pi} \sum\_{m=1}^{\infty} \frac{a\_m^2 \sin\left(\alpha\_m \mathbf{x}\right)}{m \left(D\_{11}a\_m^4 - N\_{\infty}a\_m^2\right)}\tag{23}$$

where

$$A\_1 = \sum\_{k=1}^{N} (Q\_{11} a\_1) \left( x\_{k+1}^3 - x\_k^3 \right) \tag{24}$$

To find *wo*ð Þ *x*, *y <sup>H</sup>*, Eq. (6) will be:

$$D\_{11} \frac{\partial^4 w\_o}{\partial \mathbf{x}^4} + 2(D\_{12} + 2D\_{66}) \frac{\partial^4 w\_o}{\partial \mathbf{x}^2 \partial \mathbf{y}^2} + D\_{22} \frac{\partial^4 w\_o}{\partial \mathbf{y}^4} + N\_{\text{xx}} \frac{\partial^2 w\_o}{\partial \mathbf{x}^2} = \mathbf{0} \tag{25}$$

The solution of Eq. (25) is as below:

$$\left(w\_o(\mathbf{x}, \mathbf{y})\_H = \sum\_{m=1}^{\infty} Y\_m \sin \left(a\_m \mathbf{x}\right)\right) \tag{26}$$

Substitute Eq. (26) into Eq. (25), to obtain the homogeneous solution of Eq. (25) along x- and y-directions:

$$\left[w\_o(\mathbf{x}, \boldsymbol{y})\_H = \sum\_{m=1}^{\infty} \left[N\_1 \cosh\left(ay\right) + N\_2 \sinh\left(ay\right) + N\_3 \cos\left(\beta \boldsymbol{y}\right) + N\_4 \sin\left(\beta \boldsymbol{y}\right)\right] \tag{27}$$

$$\sin\left(a\_m \mathbf{x}\right)$$

Substitute Eq. (27) and Eq. (23) into Eq. (21) to obtain the general solution of normal bending deflection, as indicated below:

$$\begin{aligned} w\_o(\mathbf{x}, \mathbf{y}) &= \sum\_{m=1}^{\infty} [N\_1 \cosh \left( a \mathbf{y} \right) + N\_2 \sinh \left( a \mathbf{y} \right) + N\_3 \cos \left( \beta \mathbf{y} \right) + N\_4 \sin \left( \beta \mathbf{y} \right)] \\ &\quad \sin \left( a\_m \mathbf{x} \right) + \frac{4T\_1 A\_1}{3\pi} \sum\_{m=1}^{\infty} \frac{a\_m^2 \sin \left( a\_m \mathbf{x} \right)}{m \left[ D\_{11} a\_m^4 - N\_{\infty} a\_m^2 \right]} \end{aligned} \tag{28}$$

The simply supported boundary conditions from all edges are assumed and the constants ð Þ *N*1, *N*2, *N*3, *and N*<sup>4</sup> are as below:

$$N\_1 = -\frac{\beta^2 H}{\left(a^2 + \beta^2\right)} - \frac{4M\_o}{\left(a^2 + \beta^2\right)m\pi D\_{22}}\tag{29}$$

$$\begin{aligned} N\_2 &= \frac{\cosh\left(ab\right)\beta^2 H}{\left(a^2 + \beta^2\right)\sinh\left(ab\right)} + \frac{4\cosh\left(ab\right)M\_o}{\left(a^2 + \beta^2\right)\sinh\left(ab\right)m\pi D\_{22}} - \frac{\left(D\_{12}a\_m^2 + \beta^2 D\_{22}\right)H}{\left(a^2 + \beta^2\right)\sinh\left(ab\right)D\_{22}} \\ &- \frac{\left(\frac{4M\_o}{m\pi} - D\_{12}a\_m^2 H\right)}{\left(a^2 + \beta^2\right)\sinh\left(ab\right)D\_{22}} \end{aligned}$$

$$N\_3 = -\frac{a^2 H}{(a^2 + \beta^2)} + \frac{4M\_o}{(a^2 + \beta^2)m\pi D\_{22}}\tag{31}$$

(30)

where

*Ec*

*Ec*

*Ec*

*αc*

*αc*

*αc*

*kc*

*kc*

*kc*

*Cc*

**Table 1.**

**83**

**5. Numerical simulation procedure**

*DOI: http://dx.doi.org/10.5772/intechopen.93592*

properties of the simulated materials.

**6. Results and discussions**

*Mechanical and thermal properties of the simulated materials.*

*<sup>H</sup>* <sup>¼</sup> <sup>4</sup>*T*1*A*1*α*<sup>2</sup>

*Analytic and Numerical Results of Bending Deflection of Rectangular Composite Plate*

3*πm D*11*α*<sup>4</sup>

Ver. 18.2. (SHELL 132) element is used to mesh the composite laminate plate. SHELL 132 is defined by eight nodes having six degrees of freedom at each node to calculate the central normal deflection. In the simulation analysis, the central point of laminate plate is used to calculate the normal deflection. Always the convergence test is needed to determine the size of elements in which the value of normal bending deflection settles down. Finite element analysis of convergence curve defines the relationship between the grid interval and the analysis accuracy. Four types of combined loading is used such as: (temperature affect only ð Þ Δ*T* ),

In this chapter, the finite element discretization is carried out by using ANSYS

(temperature affect ð Þ Δ*T* + Mo), (temperature affect ð Þ Δ*T* + Nxx), and (temperature affect ð Þ Δ*T* + Mo + Nxx). Multiple values of fiber volume fraction is used such as (25, 40, 50, 60, 70, and 80)%. **Table 1** shows the mechanical and thermal

*ν <sup>f</sup>* **25.07% 40% 50% 60% 70% 80%**

*<sup>x</sup>*ð Þ *GPa:* 19.933 30.4038 37.41988 44.435 51.452 58.468

*<sup>y</sup>*ð Þ *GPa:* 19.933 30.4038 37.41988 44.435 51.452 58.468

*<sup>z</sup>*ð Þ *GPa:* 3.0896 3.81746 4.53322 5.5793 7.25302 10.3612 *ν*<sup>12</sup> 0.3835 0.35098 0.32915 0.30732 0.2855 0.26366 *G*12ð Þ *GPa:* 1.07675 1.33379 1.5878 1.9614 2.5648 3.70468 *<sup>ρ</sup><sup>c</sup> kg=m*<sup>3</sup> ð Þ 1464.18 1686.48 1835.4 1984.32 2133.24 2282.16

*<sup>x</sup>* <sup>1</sup>*=C*<sup>∘</sup> ð Þ 25.746 E-6 21.6044 E-6 18.5098 E-6 15.3005 E-6 12.0234 E-6 8.70307 E-6

*<sup>y</sup>* <sup>1</sup>*=C*<sup>∘</sup> ð Þ 25.746 E-6 21.6044 E-6 18.5098 E-6 15.3005 E-6 12.0234 E-6 8.70307 E-6

*<sup>z</sup>* <sup>1</sup>*=C*<sup>∘</sup> ð Þ 10.5844 E-6 7.932 E-6 6.9852 E-6 6.3374 E-6 5.8663 E-6 5.5082 E-6

*<sup>x</sup> <sup>W</sup>=mC*<sup>∘</sup> ð Þ 0.4533 0.622 0.735 0.848 0.961 1.074

*<sup>y</sup> <sup>W</sup>=mC*<sup>∘</sup> ð Þ 0.4533 0.622 0.735 0.848 0.961 1.074

*<sup>z</sup> <sup>W</sup>=mC*<sup>∘</sup> ð Þ 0.2174 0.2626 0.30068 0.3553 0.43418 0.55808

*<sup>p</sup> <sup>J</sup>=kgC*<sup>∘</sup> ð Þ 768.139 780.8944 787.7133 793.5087 798.495 802.8304

**Figures 2** and **3** show the verification test of normal bending deflection using Levy and Navier solutions, taking into consideration ANSYS 18.2 results. The normal bending deflection decreased with the increasing of plate aspect ratio because of the increasing in plate bending stiffness under the temperature effect 60*C*<sup>∘</sup> ð Þ and �15*C*<sup>∘</sup> ð Þ for fiber volume fraction (25*:*076%). The bending deflection value when

*m*

*<sup>m</sup>* � *Nxxα*<sup>2</sup>

*m*

(33)

$$\begin{split} N\_{4} &= \frac{\cos\left(\beta b\right)a^{2}H}{\left(a^{2} + \beta^{2}\right)\sin\left(\beta b\right)} - \frac{4\cos\left(\beta b\right)M\_{o}}{\left(a^{2} + \beta^{2}\right)\sin\left(\beta b\right)m\pi D\_{22}} - \frac{\left(a^{2}D\Omega - D\_{12}a\_{m}^{2}\right)H}{\left(a^{2} + \beta^{2}\right)D\_{22}\sin\left(\beta b\right)} \\ &+ \frac{\left(\frac{4M\_{o}}{mx} - D\_{12}a\_{m}^{2}H\right)}{\left(a^{2} + \beta^{2}\right)\sin\left(\beta b\right)D\_{22}} \end{split} \tag{32}$$

*Analytic and Numerical Results of Bending Deflection of Rectangular Composite Plate DOI: http://dx.doi.org/10.5772/intechopen.93592*

where

where

*D*<sup>11</sup>

along x- and y-directions:

*m*¼1

*m*¼1

*<sup>N</sup>*<sup>2</sup> <sup>¼</sup> *cosh* ð Þ *<sup>α</sup><sup>b</sup> <sup>β</sup>*<sup>2</sup>

�

*<sup>N</sup>*<sup>4</sup> <sup>¼</sup> *cos*ð Þ *<sup>β</sup><sup>b</sup> <sup>α</sup>*<sup>2</sup>*<sup>H</sup>*

4*Mo <sup>m</sup><sup>π</sup>* � *<sup>D</sup>*12*α*<sup>2</sup> *mH* � � *<sup>α</sup>*<sup>2</sup> <sup>þ</sup> *<sup>β</sup>*<sup>2</sup> � � *sin* ð Þ *<sup>β</sup><sup>b</sup> <sup>D</sup>*<sup>22</sup>

þ

**82**

normal bending deflection, as indicated below:

constants ð Þ *N*1, *N*2, *N*3, *and N*<sup>4</sup> are as below:

*H*

*<sup>α</sup>*<sup>2</sup> <sup>þ</sup> *<sup>β</sup>*<sup>2</sup> � � *sinh* ð Þ *<sup>α</sup><sup>b</sup>* <sup>þ</sup>

4*Mo <sup>m</sup><sup>π</sup>* � *<sup>D</sup>*12*α*<sup>2</sup> *mH* � � *<sup>α</sup>*<sup>2</sup> <sup>þ</sup> *<sup>β</sup>*<sup>2</sup> � � *sinh* ð Þ *<sup>α</sup><sup>b</sup> <sup>D</sup>*<sup>22</sup>

*sin* ð Þþ *αmx*

*<sup>N</sup>*<sup>1</sup> ¼ � *<sup>β</sup>*<sup>2</sup>

*<sup>N</sup>*<sup>3</sup> ¼ � *<sup>α</sup>*<sup>2</sup>*<sup>H</sup>*

*<sup>α</sup>*<sup>2</sup> <sup>þ</sup> *<sup>β</sup>*<sup>2</sup> � � *sin* ð Þ *<sup>β</sup><sup>b</sup>* � <sup>4</sup> *cos*ð Þ *<sup>β</sup><sup>b</sup> Mo*

*wo*ð Þ *<sup>x</sup>*, *<sup>y</sup> <sup>H</sup>* <sup>¼</sup> <sup>X</sup><sup>∞</sup>

*wo*ð Þ¼ *<sup>x</sup>*, *<sup>y</sup>* <sup>X</sup><sup>∞</sup>

*∂*<sup>4</sup>*wo*

*Structural Integrity and Failure*

*<sup>A</sup>*<sup>1</sup> <sup>¼</sup> <sup>X</sup> *N*

To find *wo*ð Þ *x*, *y <sup>H</sup>*, Eq. (6) will be:

*<sup>∂</sup>x*<sup>4</sup> <sup>þ</sup> <sup>2</sup>ð Þ *<sup>D</sup>*<sup>12</sup> <sup>þ</sup> <sup>2</sup>*D*<sup>66</sup>

The solution of Eq. (25) is as below:

*k*¼1

*wo*ð Þ *<sup>x</sup>*, *<sup>y</sup> <sup>H</sup>* <sup>¼</sup> <sup>X</sup><sup>∞</sup>

*m*¼1

Substitute Eq. (26) into Eq. (25), to obtain the homogeneous solution of Eq. (25)

½ � *N*<sup>1</sup> *cosh* ð Þþ *αy N*<sup>2</sup> *sinh* ð Þþ *αy N*<sup>3</sup> *cos*ð Þþ *βy N*<sup>4</sup> *sin* ð Þ *βy*

*sin* ð Þ *αmx*

½ � *N*<sup>1</sup> *cosh* ð Þþ *αy N*<sup>2</sup> *sinh* ð Þþ *αy N*<sup>3</sup> *cos*ð Þþ *βy N*<sup>4</sup> *sin* ð Þ *βy*

*α*2

*m D*11*α*<sup>4</sup>

*<sup>m</sup> sin* ð Þ *αmx*

� �

*<sup>α</sup>*<sup>2</sup> <sup>þ</sup> *<sup>β</sup>*<sup>2</sup> � �*mπD*<sup>22</sup>

4*Mo <sup>α</sup>*<sup>2</sup> <sup>þ</sup> *<sup>β</sup>*<sup>2</sup> � �*mπD*<sup>22</sup>

*<sup>m</sup>* � *Nxxα*<sup>2</sup>

*m*

� *<sup>D</sup>*12*α*<sup>2</sup>

� *<sup>α</sup>*<sup>2</sup>*D*<sup>22</sup> � *<sup>D</sup>*12*α*<sup>2</sup>

� �*H <sup>α</sup>*<sup>2</sup> <sup>þ</sup> *<sup>β</sup>*<sup>2</sup> � �*D*<sup>22</sup> *sin* ð Þ *<sup>β</sup><sup>b</sup>*

*<sup>m</sup>* <sup>þ</sup> *<sup>β</sup>*<sup>2</sup>

*m*

*D*<sup>22</sup> � �*H <sup>α</sup>*<sup>2</sup> <sup>þ</sup> *<sup>β</sup>*<sup>2</sup> � � *sinh* ð Þ *<sup>α</sup><sup>b</sup> <sup>D</sup>*<sup>22</sup>

Substitute Eq. (27) and Eq. (23) into Eq. (21) to obtain the general solution of

X∞ *m*¼1

The simply supported boundary conditions from all edges are assumed and the

*<sup>α</sup>*<sup>2</sup> <sup>þ</sup> *<sup>β</sup>*<sup>2</sup> � � � <sup>4</sup>*Mo*

4 *cosh* ð Þ *αb Mo <sup>α</sup>*<sup>2</sup> <sup>þ</sup> *<sup>β</sup>*<sup>2</sup> � � *sinh* ð Þ *<sup>α</sup><sup>b</sup> <sup>m</sup>πD*<sup>22</sup>

4*T*1*A*<sup>1</sup> 3*π*

*H*

*<sup>α</sup>*<sup>2</sup> <sup>þ</sup> *<sup>β</sup>*<sup>2</sup> � � <sup>þ</sup>

*<sup>α</sup>*<sup>2</sup> <sup>þ</sup> *<sup>β</sup>*<sup>2</sup> � � *sin* ð Þ *<sup>β</sup><sup>b</sup> <sup>m</sup>πD*<sup>22</sup>

*∂*<sup>4</sup>*wo <sup>∂</sup>x*<sup>2</sup>*∂y*<sup>2</sup> <sup>þ</sup> *<sup>D</sup>*<sup>22</sup>

ð Þ *<sup>Q</sup>*11*α*<sup>1</sup> *<sup>z</sup>*<sup>3</sup>

*<sup>k</sup>*þ<sup>1</sup> � *<sup>z</sup>*<sup>3</sup> *k*

> *∂*<sup>4</sup>*wo <sup>∂</sup>y*<sup>4</sup> <sup>þ</sup> *Nxx*

� � (24)

*<sup>∂</sup>x*<sup>2</sup> <sup>¼</sup> <sup>0</sup> (25)

(27)

(28)

(29)

(30)

(31)

(32)

*∂*2 *wo*

*Ym sin* ð Þ *αmx* (26)

$$H = \frac{4T\_1 A\_1 a\_m^2}{3\pi m \left(D\_{11} a\_m^4 - N\_{\infty} a\_m^2\right)}\tag{33}$$

### **5. Numerical simulation procedure**

In this chapter, the finite element discretization is carried out by using ANSYS Ver. 18.2. (SHELL 132) element is used to mesh the composite laminate plate. SHELL 132 is defined by eight nodes having six degrees of freedom at each node to calculate the central normal deflection. In the simulation analysis, the central point of laminate plate is used to calculate the normal deflection. Always the convergence test is needed to determine the size of elements in which the value of normal bending deflection settles down. Finite element analysis of convergence curve defines the relationship between the grid interval and the analysis accuracy. Four types of combined loading is used such as: (temperature affect only ð Þ Δ*T* ), (temperature affect ð Þ Δ*T* + Mo), (temperature affect ð Þ Δ*T* + Nxx), and (temperature affect ð Þ Δ*T* + Mo + Nxx). Multiple values of fiber volume fraction is used such as (25, 40, 50, 60, 70, and 80)%. **Table 1** shows the mechanical and thermal properties of the simulated materials.


**Table 1.**

*Mechanical and thermal properties of the simulated materials.*

### **6. Results and discussions**

**Figures 2** and **3** show the verification test of normal bending deflection using Levy and Navier solutions, taking into consideration ANSYS 18.2 results. The normal bending deflection decreased with the increasing of plate aspect ratio because of the increasing in plate bending stiffness under the temperature effect 60*C*<sup>∘</sup> ð Þ and �15*C*<sup>∘</sup> ð Þ for fiber volume fraction (25*:*076%). The bending deflection value when

*<sup>T</sup>* <sup>¼</sup> <sup>60</sup>*C*<sup>∘</sup> ð Þ is higher than the value of bending deflection when *<sup>T</sup>* ¼ �15*C*<sup>∘</sup> ð Þ because of the expansion and contraction through the plate laminate thickness. **Figure 4** shows the convergence test of normal bending deflection with total degrees of freedom for different fiber volume fractions using ANSYS software. The normal central deflection decrease with the increasing of fiber volume fraction under the effect of temperature ð Þ Δ*T* , bending moment ð Þ *Mo* , and in-plane force ð Þ *Nxx* . **Table 2** shows the analytic and simulation verification results of bending deflection under combined loadings for fiber volume fraction *υ <sup>f</sup>* ¼ 25*:*076% and plate aspect ratio (1.8). The value of central deflection of the system with combined loading (Δ*T*) is higher than the others of combined loading. The deflection of system with combined loading (Δ*T* + *Mo* + *Nxx*) and the system with loading (Δ*T* + *Nxx*) is almost the same and in the opposite direction because bending

*Analytic and simulation verification of bending deflection under combined loading.*

**Deflection Levy method results ANSYS 18.2 results Percentage error (%)**

ð Þ Δ*T* 0.1853e-3 0.1880e-3 1.748 ð Þ Δ*T* + ð Þ *Mo* �0.1777e-3 �0.1882e-3 5.536 ð Þ Δ*T* + ð Þ *Nxx* 0.7704e-5 0.7108 e-5 7.736 ð Þ Δ*T* + ð Þ *Mo* +ðÞ � *Nxx* 0.9859e-5 �0.9365e-5 5.010

*Analytic and Numerical Results of Bending Deflection of Rectangular Composite Plate*

*DOI: http://dx.doi.org/10.5772/intechopen.93592*

As mentioned in Introduction section, Levy and Navier solutions are used to describe the theory of bending deflection by taking into consideration the use of simply supported boundary condition from all edges. ANSYS software is used in the convergence test. The bending deflection value when *<sup>T</sup>* <sup>¼</sup> <sup>60</sup>*C*<sup>∘</sup> ð Þ is higher than the value of bending deflection when *<sup>T</sup>* ¼ �15*C*<sup>∘</sup> ð Þ because of the expansion and contraction through the plate laminate thickness. The in-plane force (*Nxx*) has a great effect on the bending deflection value of composite laminate plate, but the bending moment (*Mo*) has a small effect on the bending deflection value. The normal deflection is decreased with the increasing of fiber volume fraction from 25*:*07% to 80% under the effect of ð Þ Δ*T* and combined loading ð Þ *Mo* + ð Þ *Nxx* . Moreover, the normal bending deflection is decreased with the increasing of aspect ratio from 0.8

to 2.4 under the effect of *<sup>T</sup>* <sup>¼</sup> <sup>60</sup>*C*<sup>∘</sup> ð Þ and *<sup>T</sup>* ¼ �15*C*<sup>∘</sup> ð Þ, respectively.

directions, 1/*C*<sup>∘</sup>

z-direction, m.

*A*1, *A*<sup>2</sup> bending moment due to temperature, N.m/*C*<sup>∘</sup>

*zk*, *zk*þ<sup>1</sup> upper and lower lamina surface coordinates along

Δ*T* gradient uniform temperature, *C*<sup>∘</sup>

*Mxx*, *Myy*, and *Mxy* bending and twist moments, N.m. *Qij* reduced stiffness elements, *N=m*2. *w*<sup>0</sup> midplane deflection along z-direction.

*α*1, *α*<sup>2</sup> thermal expansion coefficient in longitudinal and lateral

.

.

.

moment has a small effect.

**7. Conclusions**

**Table 2.**

**Nomenclature**

**85**

**Figure 2.** *Normal bending deflection varying with laminate plate aspect ratio under temperature effect* <sup>60</sup>*C*<sup>∘</sup> ð Þ*.*

**Figure 3.** *Normal bending deflection varying with laminate plate aspect ratio under temperature effect* �15*C*<sup>∘</sup> ð Þ*.*

### **Figure 4.**

*Convergence test of normal deflection and total degrees of freedom under the effect of temperature* ð Þ ΔT *, bending moment* ð Þ Mo *, and in-plane force* ð Þ Nxx *.*

*Analytic and Numerical Results of Bending Deflection of Rectangular Composite Plate DOI: http://dx.doi.org/10.5772/intechopen.93592*


**Table 2.**

*Analytic and simulation verification of bending deflection under combined loading.*

*<sup>T</sup>* <sup>¼</sup> <sup>60</sup>*C*<sup>∘</sup> ð Þ is higher than the value of bending deflection when *<sup>T</sup>* ¼ �15*C*<sup>∘</sup> ð Þ because of the expansion and contraction through the plate laminate thickness.

**Figure 4** shows the convergence test of normal bending deflection with total degrees of freedom for different fiber volume fractions using ANSYS software. The normal central deflection decrease with the increasing of fiber volume fraction under the effect of temperature ð Þ Δ*T* , bending moment ð Þ *Mo* , and in-plane force ð Þ *Nxx* .

**Table 2** shows the analytic and simulation verification results of bending deflection under combined loadings for fiber volume fraction *υ <sup>f</sup>* ¼ 25*:*076% and plate aspect ratio (1.8). The value of central deflection of the system with combined loading (Δ*T*) is higher than the others of combined loading. The deflection of system with combined loading (Δ*T* + *Mo* + *Nxx*) and the system with loading (Δ*T* + *Nxx*) is almost the same and in the opposite direction because bending moment has a small effect.

### **7. Conclusions**

**Figure 3.**

**Figure 2.**

*Structural Integrity and Failure*

**Figure 4.**

**84**

*moment* ð Þ Mo *, and in-plane force* ð Þ Nxx *.*

*Normal bending deflection varying with laminate plate aspect ratio under temperature effect* �15*C*<sup>∘</sup> ð Þ*.*

*Normal bending deflection varying with laminate plate aspect ratio under temperature effect* <sup>60</sup>*C*<sup>∘</sup> ð Þ*.*

*Convergence test of normal deflection and total degrees of freedom under the effect of temperature* ð Þ ΔT *, bending*

As mentioned in Introduction section, Levy and Navier solutions are used to describe the theory of bending deflection by taking into consideration the use of simply supported boundary condition from all edges. ANSYS software is used in the convergence test. The bending deflection value when *<sup>T</sup>* <sup>¼</sup> <sup>60</sup>*C*<sup>∘</sup> ð Þ is higher than the value of bending deflection when *<sup>T</sup>* ¼ �15*C*<sup>∘</sup> ð Þ because of the expansion and contraction through the plate laminate thickness. The in-plane force (*Nxx*) has a great effect on the bending deflection value of composite laminate plate, but the bending moment (*Mo*) has a small effect on the bending deflection value. The normal deflection is decreased with the increasing of fiber volume fraction from 25*:*07% to 80% under the effect of ð Þ Δ*T* and combined loading ð Þ *Mo* + ð Þ *Nxx* . Moreover, the normal bending deflection is decreased with the increasing of aspect ratio from 0.8 to 2.4 under the effect of *<sup>T</sup>* <sup>¼</sup> <sup>60</sup>*C*<sup>∘</sup> ð Þ and *<sup>T</sup>* ¼ �15*C*<sup>∘</sup> ð Þ, respectively.

### **Nomenclature**



**References**

(1):129-140

6123-6142

[1] Ray B. Thermal shock and thermal fatigue on delamination of glass-fiberreinforced polymeric composites. Journal of Reinforced Plastics and Composites. 2005;**24**(1):111-116

*DOI: http://dx.doi.org/10.5772/intechopen.93592*

multilayered plates in terms of Reddytype higher-order theory. Journal of Advanced Materials and Structures. Taylor & Francis Publisher; 2017;**24**(14):

1196-1205

*Analytic and Numerical Results of Bending Deflection of Rectangular Composite Plate*

[2] Hussein EQ, Alasadi SJ.

Experimental and theoretical stress analysis for composite plate under combined load. Journal of University of Babylon. Babylon University; 2018;**26**

[3] Yousuf LS, Jameel AN, AL-Sahib NKA. Verification of laminate composite plate simulation under combined loadings thermal stresses. Journal of Engineering. 2010;**16**(4):

[4] Wang D, Zhou X, Ge H, Liu Z, Liu H, Sun K. The influence of thermal fatigue on the properties of glass fiber/epoxy composites. Polymers & Polymer Composites. 2012;**20**(1-2):129-132

[5] Khashaba U, Aldousari S, Najjar I. Behavior of [0]8 woven composites under combined bending and tension loading: Part-i experimental and analytical. Journal of Composite Materials. 2012;**46**(11):1345-1355

[6] Onyechi PC, Asiegbu KO, Chinenye AL. Effect of volume fraction on the mechanical properties of Periwinkle shell reinforced polyester composite (PRPC). American Journal of Mechanical Engineering and

Automation. Open Science Publisher;

[7] Yousuf LS. Time prediction of dynamic behavior of glass fiber reinforced polyester composites subjected to fluctuating varied temperatures. Al-Khwarizmi

Engineering Journal. 2018;**5**(3):28-37

[8] Zhen W, Xiaohui R. Thermomechanical analysis of

**87**

2015;**2**(1):1-15

### **Author details**

Louay S. Yousuf Department of Mechanical Engineering, San Diego State University, San Diego, CA, USA

\*Address all correspondence to: louaysabah79@yahoo.com

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Analytic and Numerical Results of Bending Deflection of Rectangular Composite Plate DOI: http://dx.doi.org/10.5772/intechopen.93592*

### **References**

a, b length of large and small spans of rectangular plate (m).

Department of Mechanical Engineering, San Diego State University, San Diego, CA,

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\*Address all correspondence to: louaysabah79@yahoo.com

provided the original work is properly cited.

m, n double trigonometric of Furrier series.

N total number of layers.

*Structural Integrity and Failure*

**Author details**

Louay S. Yousuf

USA

**86**

[1] Ray B. Thermal shock and thermal fatigue on delamination of glass-fiberreinforced polymeric composites. Journal of Reinforced Plastics and Composites. 2005;**24**(1):111-116

[2] Hussein EQ, Alasadi SJ. Experimental and theoretical stress analysis for composite plate under combined load. Journal of University of Babylon. Babylon University; 2018;**26** (1):129-140

[3] Yousuf LS, Jameel AN, AL-Sahib NKA. Verification of laminate composite plate simulation under combined loadings thermal stresses. Journal of Engineering. 2010;**16**(4): 6123-6142

[4] Wang D, Zhou X, Ge H, Liu Z, Liu H, Sun K. The influence of thermal fatigue on the properties of glass fiber/epoxy composites. Polymers & Polymer Composites. 2012;**20**(1-2):129-132

[5] Khashaba U, Aldousari S, Najjar I. Behavior of [0]8 woven composites under combined bending and tension loading: Part-i experimental and analytical. Journal of Composite Materials. 2012;**46**(11):1345-1355

[6] Onyechi PC, Asiegbu KO, Chinenye AL. Effect of volume fraction on the mechanical properties of Periwinkle shell reinforced polyester composite (PRPC). American Journal of Mechanical Engineering and Automation. Open Science Publisher; 2015;**2**(1):1-15

[7] Yousuf LS. Time prediction of dynamic behavior of glass fiber reinforced polyester composites subjected to fluctuating varied temperatures. Al-Khwarizmi Engineering Journal. 2018;**5**(3):28-37

[8] Zhen W, Xiaohui R. Thermomechanical analysis of multilayered plates in terms of Reddytype higher-order theory. Journal of Advanced Materials and Structures. Taylor & Francis Publisher; 2017;**24**(14): 1196-1205

**89**

**Chapter 6**

**Abstract**

*Ganga Kasi V. Prakhya*

Temporary Works in Construction

of Bridges Near Third Party Assets

This paper gives a summary of the temporary works and methods applied to enable the construction of bridges near third party assets. The temporary structures have a significant impact on the cost, construction method and construction safety of the supported permanent structures. In the literature, there are many examples of how the temporary works could fail catastrophically and could endanger public life if hazard identification, risk assessment and quality checks are not carried out by competent people or organisations. A brief literature survey of the construction techniques is outlined here. This paper looks at more recent failures and draws some more lessons with a re-emphasis on the use of industry established processes, guidelines for preventing catastrophic events. The paper also describes case histories, where mitigation measures are implemented in order to ensure safety by

means of independent checks, monitoring and back analysis.

statements, risk assessment, back analysis

permanent design at the early stages.

**1. Introduction**

**Keywords:** temporary works, monitoring, safety in construction, method

Most forms of bridge construction, whether preassembled or cast in-situ will require temporary works on site. These may include, depending on the type of bridge, temporary supports for precast girders or beams, box structures, and temporary staging for cast in-situ construction of the deck, and may also involve specialist operations for complex forms of bridge, e.g., post-tensioning. Many projects focus on optimising the concrete volumes and steel tonnage but a very few focus on how best to integrate temporary works and buildability concepts into the

Temporary works (TW) are the parts of a construction project that are needed to enable the permanent works to be built. Usually the TW are removed after use—e.g. access scaffolds, props, shoring, excavation support, falsework, and formwork, etc. It may be possible that sometimes the TW an integral part of the permanent works e.g. props for excavation can be used as part of permanent steelworks, haul road foundations and crane or piling platforms may be used for hard standing or road foundations. In view of safety, it is very important that the same degree of care and attention is given to the design and construction of temporary works (TW) as to the design and construction of the permanent works. As TW may be in place for only a short during the construction phase of the project, there is a tendency to assume they are less important. Lack of care with design, selection, assembly, etc. leaves TW liable to fail or collapse [1]. This places people at risk of injury and can cause the project to be

### **Chapter 6**

## Temporary Works in Construction of Bridges Near Third Party Assets

*Ganga Kasi V. Prakhya*

### **Abstract**

This paper gives a summary of the temporary works and methods applied to enable the construction of bridges near third party assets. The temporary structures have a significant impact on the cost, construction method and construction safety of the supported permanent structures. In the literature, there are many examples of how the temporary works could fail catastrophically and could endanger public life if hazard identification, risk assessment and quality checks are not carried out by competent people or organisations. A brief literature survey of the construction techniques is outlined here. This paper looks at more recent failures and draws some more lessons with a re-emphasis on the use of industry established processes, guidelines for preventing catastrophic events. The paper also describes case histories, where mitigation measures are implemented in order to ensure safety by means of independent checks, monitoring and back analysis.

**Keywords:** temporary works, monitoring, safety in construction, method statements, risk assessment, back analysis

### **1. Introduction**

Most forms of bridge construction, whether preassembled or cast in-situ will require temporary works on site. These may include, depending on the type of bridge, temporary supports for precast girders or beams, box structures, and temporary staging for cast in-situ construction of the deck, and may also involve specialist operations for complex forms of bridge, e.g., post-tensioning. Many projects focus on optimising the concrete volumes and steel tonnage but a very few focus on how best to integrate temporary works and buildability concepts into the permanent design at the early stages.

Temporary works (TW) are the parts of a construction project that are needed to enable the permanent works to be built. Usually the TW are removed after use—e.g. access scaffolds, props, shoring, excavation support, falsework, and formwork, etc. It may be possible that sometimes the TW an integral part of the permanent works e.g. props for excavation can be used as part of permanent steelworks, haul road foundations and crane or piling platforms may be used for hard standing or road foundations. In view of safety, it is very important that the same degree of care and attention is given to the design and construction of temporary works (TW) as to the design and construction of the permanent works. As TW may be in place for only a short during the construction phase of the project, there is a tendency to assume they are less important. Lack of care with design, selection, assembly, etc. leaves TW liable to fail or collapse [1]. This places people at risk of injury and can cause the project to be delayed. Therefore it is important to ensure that the methods, materials, and sequence of construction is thought through with the construction team during early stages and that the risks to the structure as well as the third-party asset owners are resolved.

Where bridges form features of modern infrastructure in densely populated cities and urban areas, the designers will be challenged with site logistics, narrow and busy streets, and third party assets such as railways, underground tunnels, and buried services and it is extremely important in these cases to be more diligent about designing for safety of the temporary works. While the principles can be applied to all bridges, this paper does not cover large suspension bridges on water.

### **2. Background and UK scenario**

Although there were bridge failures in 1950s in USA, Canada and other parts of the world, much of the development in temporary works design in UK was improved when Barton Bridge, Lodden Bridge [2–4] in 1960s and 1970s collapsed during construction and the government was moved to determine whether the industry was in a fit state to manage falsework. Following these major failures in the UK, Professor Stephen Bragg report [4], helped to set the standard for temporary works design and management in the UK. Major failures of UK temporary works have almost disappeared since BS 5975 [5] was published in 1982, following the Bragg report in 1975 into recent falsework disasters in which many lost their lives. In the UK, the design of temporary support trestles would normally comply with the requirements of BS 5975 [6] unless the use of Eurocode 12811 [6] and EN 12812 [7], is stipulated as a contractual requirement. More recently, a Temporary Works forum (TWf) was formed in 2009 [8] in the UK as an independent, non-profit company that operates on a limited cost base. Useful guidance and toolkit and guidance documents are produced by TWf that address the issues of temporary works and applicability of Eurocodes for safer construction in the UK [9]. The general principles of these tool kits generated by the TWf are applicable worldwide.

More recently, the Institutions of Civil Engineers and Institution of Structural Engineers (UK) formed an independent body called SCOSS/CROSS [10] Structural Safety Body in 2005. This Structural-Safety Body is a body devoted to evaluating, and anticipating where possible, trends in the construction industry and issuing warnings where necessary. A confidential (anonymous) reporting system called 'CROSS [10]' broadcasts events which it believes should be more widely known.

While UK standards are developed to a fuller extent to eliminate the catastrophic events in temporary work through the introduction codes, guidance documents [11, 12] we still see that failures occur for various reasons. A publication in ICE Forensic Engineering summarised failures in bridges until 2012 [13] and more than 60 major catastrophic failures across the world have been reported since 2012 to date [14] including the most recent failure in Florida. A few more recent failures are reviewed from the literature survey in this paper to highlight the importance of temporary works.

This paper describes briefly the existing construction techniques of bridges, and reviews more recent failures. There are many types of bridges and but this paper summarises a brief literature survey of current construction methods for precast, prefabricated, and cast-in-situ bridges.

This paper summarises typical scenarios in urban and rural environments and considers a few case histories with a view on how to safely manage the risks associated with the construction of bridges in an urban environment. Most forms of bridge construction, whether preassembled or cast-in-situ will require temporary works on site. These may include, depending on the type of bridge, temporary

**91**

**Figure 1.**

*Precast girders with GRP deck panels for in situ deck.*

*Temporary Works in Construction of Bridges Near Third Party Assets*

**3. Bridge construction techniques: a brief survey**

cost significant sums and involve extensive working at height.

tion of load, accidental load and out-of-tolerance assembly.

supports for precast girders or beams, box structures, and temporary staging for cast-in-situ construction of the deck, and may also involve specialist operations for complex forms of bridge, e.g. post-tensioning. Many projects focus on optimising the concrete volumes and steel tonnage but a very few focus on how best to integrate temporary works and buildability concepts into the permanent design at the

Precast concrete members in bridge systems are appealing because they lend themselves well to incorporating Accelerated Bridge Construction (ABC) methods. In some cases, ABC also includes integral column and cap beam systems for bridges utilising precast concrete girders which have several advantages over structures consisting of steel girders or cast-in-place concrete alternatives as shown in

For single-span bridge decks, temporary support is normally undertaken directly from the abutment bearing shelf or equivalent and this is relatively straightforward. Beams to multi-span bridge decks may require a more complex temporary support system. If the beams are designed in short lengths until they stitched, they will require a temporary support. A common solution is to provide a temporary trestle support either on a temporary foundation or on the permanent foundation of the piers. Beams are landed on the trestle that supports the bridge deck structure until such time that it becomes self-supporting. These trestles can

Given the consequences of failure and the difficulty of correcting issues that manifest themselves following landing of bridge beams, a robust temporary support structure is a necessity. Factors of safety (as per permissible stress design, e.g. BS 5975) and design factors (as per limit state design, e.g. Eurocodes [17, 18]) can be used amended by the designer to reflect the above. Safety can also be enhanced by building redundancy into the structure. Unless reasonable calculations are made of the specifics, there should be reasonable margins in the design for uneven distribu-

*DOI: http://dx.doi.org/10.5772/intechopen.92364*

early stages.

**3.1 Precast bridges**

**Figure 1** [15, 16].

### *Temporary Works in Construction of Bridges Near Third Party Assets DOI: http://dx.doi.org/10.5772/intechopen.92364*

supports for precast girders or beams, box structures, and temporary staging for cast-in-situ construction of the deck, and may also involve specialist operations for complex forms of bridge, e.g. post-tensioning. Many projects focus on optimising the concrete volumes and steel tonnage but a very few focus on how best to integrate temporary works and buildability concepts into the permanent design at the early stages.

### **3. Bridge construction techniques: a brief survey**

### **3.1 Precast bridges**

*Structural Integrity and Failure*

**2. Background and UK scenario**

delayed. Therefore it is important to ensure that the methods, materials, and sequence of construction is thought through with the construction team during early stages and that the risks to the structure as well as the third-party asset owners are resolved. Where bridges form features of modern infrastructure in densely populated cities and urban areas, the designers will be challenged with site logistics, narrow and busy streets, and third party assets such as railways, underground tunnels, and buried services and it is extremely important in these cases to be more diligent about designing for safety of the temporary works. While the principles can be applied to all bridges, this paper does not cover large suspension bridges on water.

Although there were bridge failures in 1950s in USA, Canada and other parts of the world, much of the development in temporary works design in UK was improved when Barton Bridge, Lodden Bridge [2–4] in 1960s and 1970s collapsed during construction and the government was moved to determine whether the industry was in a fit state to manage falsework. Following these major failures in the UK, Professor Stephen Bragg report [4], helped to set the standard for temporary works design and management in the UK. Major failures of UK temporary works have almost disappeared since BS 5975 [5] was published in 1982, following the Bragg report in 1975 into recent falsework disasters in which many lost their lives. In the UK, the design of temporary support trestles would normally comply with the requirements of BS 5975 [6] unless the use of Eurocode 12811 [6] and EN 12812 [7], is stipulated as a contractual requirement. More recently, a Temporary Works forum (TWf) was formed in 2009 [8] in the UK as an independent, non-profit company that operates on a limited cost base. Useful guidance and toolkit and guidance documents are produced by TWf that address the issues of temporary works and applicability of Eurocodes for safer construction in the UK [9]. The general principles of these tool kits generated by the TWf are applicable worldwide.

More recently, the Institutions of Civil Engineers and Institution of Structural Engineers (UK) formed an independent body called SCOSS/CROSS [10] Structural Safety Body in 2005. This Structural-Safety Body is a body devoted to evaluating, and anticipating where possible, trends in the construction industry and issuing warnings where necessary. A confidential (anonymous) reporting system called 'CROSS [10]' broadcasts events which it believes should be more widely known.

While UK standards are developed to a fuller extent to eliminate the catastrophic

This paper describes briefly the existing construction techniques of bridges, and reviews more recent failures. There are many types of bridges and but this paper summarises a brief literature survey of current construction methods for precast,

This paper summarises typical scenarios in urban and rural environments and considers a few case histories with a view on how to safely manage the risks associated with the construction of bridges in an urban environment. Most forms of bridge construction, whether preassembled or cast-in-situ will require temporary works on site. These may include, depending on the type of bridge, temporary

events in temporary work through the introduction codes, guidance documents [11, 12] we still see that failures occur for various reasons. A publication in ICE Forensic Engineering summarised failures in bridges until 2012 [13] and more than 60 major catastrophic failures across the world have been reported since 2012 to date [14] including the most recent failure in Florida. A few more recent failures are reviewed from the literature survey in this paper to highlight the importance of

**90**

temporary works.

prefabricated, and cast-in-situ bridges.

Precast concrete members in bridge systems are appealing because they lend themselves well to incorporating Accelerated Bridge Construction (ABC) methods. In some cases, ABC also includes integral column and cap beam systems for bridges utilising precast concrete girders which have several advantages over structures consisting of steel girders or cast-in-place concrete alternatives as shown in **Figure 1** [15, 16].

For single-span bridge decks, temporary support is normally undertaken directly from the abutment bearing shelf or equivalent and this is relatively straightforward. Beams to multi-span bridge decks may require a more complex temporary support system. If the beams are designed in short lengths until they stitched, they will require a temporary support. A common solution is to provide a temporary trestle support either on a temporary foundation or on the permanent foundation of the piers. Beams are landed on the trestle that supports the bridge deck structure until such time that it becomes self-supporting. These trestles can cost significant sums and involve extensive working at height.

Given the consequences of failure and the difficulty of correcting issues that manifest themselves following landing of bridge beams, a robust temporary support structure is a necessity. Factors of safety (as per permissible stress design, e.g. BS 5975) and design factors (as per limit state design, e.g. Eurocodes [17, 18]) can be used amended by the designer to reflect the above. Safety can also be enhanced by building redundancy into the structure. Unless reasonable calculations are made of the specifics, there should be reasonable margins in the design for uneven distribution of load, accidental load and out-of-tolerance assembly.

**Figure 1.** *Precast girders with GRP deck panels for in situ deck.*

In the case of steel structures, and launching steel bridge girders, we may need temporary trestles on temporary foundations. These trestles will require careful consideration due to the launching operations as their stability under dynamic conditions is of utmost importance.

The trestles are generally designed for dead loads, live loads, moving dynamic loads, notional horizontal loads, secondary forces from mis-alignment and will in some cases have impact loads if they are near a live highway.

### **3.2 Segmental**

Segmental construction is one of the most important developments in construction in the last century and is a very well proven method for delivering durable, long span, and repetitive structures that are both cost-effective and visually appealing.

Segmental concrete construction can be executed in two ways: using precast elements or through cast-in-place construction.

The advantages offered by precast elements are mainly related to fabrication, conducted in a plant that produces more consistency in quality products and where segments can be fabricated in parallel with early field construction activities, thus improving scheduling. The main challenges involved with precast segmental construction lie in the logistics and the setup process between the casting yard and the construction site. This includes a large temporary work system involving specialist materials and jacks, and large movable gantry parts.

Alternatively, cast-in-place construction requires that a substructure be completed prior to fabrication of the superstructure. Cast-in-place segmental construction is used when precast segments are too heavy to be shipped or access to the site is too restrictive, which can occur as spans get longer or bridges get wider.

Construction time is a key factor for projects in urban areas which require lane closures, detours, and traffic interruptions to be minimised. Precast concrete segments are often optimal as they can be built and stored until needed for erection, thus reducing the on-site time of large equipment and construction activities, thus increasing the pace of construction. **Figure 2** shows a multi span bridge over a busy highway built using precast and GRP panels for deck.

The choice between precast or cast-in-place primarily depends upon project size, construction schedule, weight of segments, and site access.

**93**

design life [19].

*Temporary Works in Construction of Bridges Near Third Party Assets*

segments, or to support a form traveller for cast-in-place segments.

• Failure of the lifting equipment, or temporary bearings

• Insufficient design capacity of a cantilevered arm of the cantilevered

If the temporary structures are located close to third party assets, there are further risks that are very expensive to correct there are explained in the following section. The paper covers bridges on land and in populated areas and will not cover

At bridge construction sites in the urban environment, it is not uncommon to come across: party walls, railways, existing grade listed buildings, existing underground utilities and live highways and riverways. The bridge design and construction will have to address how these asset owners can be protected including the safety of public road and railway users where applicable. The requirements of the asset owners may vary but the fundamental aspect of the construction logistics is to ensure that all assets and owners are protected and public safety is ensured. As per the CDM regulations in UK [18], the design and construction should also address life cycle management and also demolition at the end of

The balanced cantilever construction method is used when several spans ranging from 50 to 250 m exist. Bridges using this method can be either precast or castin-place. Once the piers are built, they are used as an erection platform for precast

This method can also be easily adapted to irregular and long span lengths, congested project sites, rough and water terrain, rail crossings, and environmentally

The cantilever method is the preferred method for building cable-stayed bridges. Once segments are installed, they are supported by new cable-stays in each erection stage. Since no auxiliary supports are required, it is both an economical and

As can be seen from the above, all of the techniques will require sophisticated forms of temporary works to enable safe construction. Despite much regulation and improvement in methods/processes in temporary works design, we are still, unfortunately, experiencing catastrophic accidents in bridges (examples include Barton bridge in Manchester in 2016 failure of lifting systems revealed and a 2019 failure in Norway failure of bolts). The failures of temporary works can be grouped into the

*DOI: http://dx.doi.org/10.5772/intechopen.92364*

practical solution for long cable-stayed bridges.

**3.3 Balanced cantilever construction**

sensitive areas.

following main areas;

• Scaffold collapse

construction

• Girder and connection failures

• Incorrect construction sequence

• Negligence and construction errors

**4. Hazards from and to third party assets**

• Design and detailing errors

large suspension bridges on water.

### **3.3 Balanced cantilever construction**

*Structural Integrity and Failure*

**3.2 Segmental**

visually appealing.

conditions is of utmost importance.

In the case of steel structures, and launching steel bridge girders, we may need temporary trestles on temporary foundations. These trestles will require careful consideration due to the launching operations as their stability under dynamic

The trestles are generally designed for dead loads, live loads, moving dynamic loads, notional horizontal loads, secondary forces from mis-alignment and will in

Segmental construction is one of the most important developments in construction in the last century and is a very well proven method for delivering durable, long span, and repetitive structures that are both cost-effective and

Segmental concrete construction can be executed in two ways: using precast

The advantages offered by precast elements are mainly related to fabrication, conducted in a plant that produces more consistency in quality products and where segments can be fabricated in parallel with early field construction activities, thus improving scheduling. The main challenges involved with precast segmental construction lie in the logistics and the setup process between the casting yard and the construction site. This includes a large temporary work system involving specialist

Alternatively, cast-in-place construction requires that a substructure be completed prior to fabrication of the superstructure. Cast-in-place segmental construction is used when precast segments are too heavy to be shipped or access to the site

Construction time is a key factor for projects in urban areas which require lane closures, detours, and traffic interruptions to be minimised. Precast concrete segments are often optimal as they can be built and stored until needed for erection, thus reducing the on-site time of large equipment and construction activities, thus increasing the pace of construction. **Figure 2** shows a multi span bridge over a busy

The choice between precast or cast-in-place primarily depends upon project

*Precast beams and cats in situ deck with GRP panels for formwork over existing highway–4 span bridge.*

is too restrictive, which can occur as spans get longer or bridges get wider.

some cases have impact loads if they are near a live highway.

elements or through cast-in-place construction.

materials and jacks, and large movable gantry parts.

highway built using precast and GRP panels for deck.

size, construction schedule, weight of segments, and site access.

**92**

**Figure 2.**

The balanced cantilever construction method is used when several spans ranging from 50 to 250 m exist. Bridges using this method can be either precast or castin-place. Once the piers are built, they are used as an erection platform for precast segments, or to support a form traveller for cast-in-place segments.

This method can also be easily adapted to irregular and long span lengths, congested project sites, rough and water terrain, rail crossings, and environmentally sensitive areas.

The cantilever method is the preferred method for building cable-stayed bridges. Once segments are installed, they are supported by new cable-stays in each erection stage. Since no auxiliary supports are required, it is both an economical and practical solution for long cable-stayed bridges.

As can be seen from the above, all of the techniques will require sophisticated forms of temporary works to enable safe construction. Despite much regulation and improvement in methods/processes in temporary works design, we are still, unfortunately, experiencing catastrophic accidents in bridges (examples include Barton bridge in Manchester in 2016 failure of lifting systems revealed and a 2019 failure in Norway failure of bolts). The failures of temporary works can be grouped into the following main areas;


If the temporary structures are located close to third party assets, there are further risks that are very expensive to correct there are explained in the following section. The paper covers bridges on land and in populated areas and will not cover large suspension bridges on water.

### **4. Hazards from and to third party assets**

At bridge construction sites in the urban environment, it is not uncommon to come across: party walls, railways, existing grade listed buildings, existing underground utilities and live highways and riverways. The bridge design and construction will have to address how these asset owners can be protected including the safety of public road and railway users where applicable. The requirements of the asset owners may vary but the fundamental aspect of the construction logistics is to ensure that all assets and owners are protected and public safety is ensured. As per the CDM regulations in UK [18], the design and construction should also address life cycle management and also demolition at the end of design life [19].

### **4.1 Electricity cables and overhead lines**

Injuries are usually caused by the explosive effects of arcing current, and by any associated fire or flames that may result, when a live cable is penetrated by a sharp object such as the point of a tool. Such effects can also occur when a cable is crushed severely enough to cause internal contact between the conductors. Injuries are typically severe, potentially fatal, burns to the hands, face and body. There is also a risk of electric shock.

Inadvertent contact or being in close proximity to overhead electricity lines with equipment such as scaffold tubes, irrigation pipes, metal ladders or vehicles, such as cranes, poses a risk of electric shock. Direct contact with overhead lines is not necessary as electrical current can arc or flashover any gap between the overhead lines and the object. It is therefore important to ensure sufficient clearances for overhead lines are maintained and plant/surcharge loading is restricted from trestle foundations.

### **4.2 Gas pipes**

Damage to underground gas pipes can cause leaks that immediate or time related that may lead to fire or explosion. The ground pressure from trestles or crane mats or outrigger could pose a risk to the stability of the gas pipes and therefore a risk assessment is required from the surcharge loading.

### **4.3 Water pipes, sewers and drains**

Although damage to water pipes is less likely to result in injury, the following may occur;


The type of materials for these water/sewage pipes, will include brick, cast iron, ductile iron, clay or concrete. Some asset owners, will give limitations on the surcharge loading and acceptance criterion for ground settlements or strain, an example of which is shown below from Thames water UK [20]. Current regulations in UK will require a risk assessment before placing any temporary foundations or surcharge on these assets (**Tables 1** and **2**).

### **4.4 Telecommunications cables, broadband and fibre optics**

Damage to telecommunication and TV cables may require expensive repairs and can cause considerable disruption to those relying on the system, especially emergency or essential services. The risks of direct personal injury are normally low, but claims for consequential losses may be substantial.

**95**

buried cables is limited.

*Maximum rotation for vitrified clay and concrete pipes.*

**Table 1.**

**Table 2.**

*Temporary Works in Construction of Bridges Near Third Party Assets*

It is important to ensure that surcharge loading from temporary foundation on

*Assessment criteria for existing Thames Water pipeline and sewer assets (reproduced from Ref. [20]).*

In addition to the above utility services, the presence of other pipes and cables should be anticipated. These include fuel oil pipes at States housing developments and private/security electricity and telecommunications cables. Risk assessment

Any movement of tunnels if they are underground or above ground (cut and cover) is very critical for the performance and therefore the asset owners will have very stringent requirements for the movement temporary works plant around these structures. Generally clearances need to be maintained between the plant and the assets and this will vary depending on the depth of the asset below the ground. No plant can operate within these zones while constructing the bridges. An example of

will be required on a case by case basis to suit to owners' requirement.

**4.5 Underground or above ground railway or cable tunnels**

the Cross Rail exclusion zone in London [20] is shown in **Figure 3**.

*DOI: http://dx.doi.org/10.5772/intechopen.92364*

*Temporary Works in Construction of Bridges Near Third Party Assets DOI: http://dx.doi.org/10.5772/intechopen.92364*


### **Table 1.**

*Structural Integrity and Failure*

of electric shock.

foundations.

**4.2 Gas pipes**

may occur;

**4.1 Electricity cables and overhead lines**

assessment is required from the surcharge loading.

• A jet of water from a main can injure a person.

possibilities of contamination and subsidence.

**4.4 Telecommunications cables, broadband and fibre optics**

**4.3 Water pipes, sewers and drains**

support for other structures.

surcharge on these assets (**Tables 1** and **2**).

claims for consequential losses may be substantial.

Injuries are usually caused by the explosive effects of arcing current, and by any associated fire or flames that may result, when a live cable is penetrated by a sharp object such as the point of a tool. Such effects can also occur when a cable is crushed severely enough to cause internal contact between the conductors. Injuries are typically severe, potentially fatal, burns to the hands, face and body. There is also a risk

Inadvertent contact or being in close proximity to overhead electricity lines with equipment such as scaffold tubes, irrigation pipes, metal ladders or vehicles, such as cranes, poses a risk of electric shock. Direct contact with overhead lines is not necessary as electrical current can arc or flashover any gap between the overhead lines and the object. It is therefore important to ensure sufficient clearances for overhead lines are maintained and plant/surcharge loading is restricted from trestle

Damage to underground gas pipes can cause leaks that immediate or time related that may lead to fire or explosion. The ground pressure from trestles or crane mats or outrigger could pose a risk to the stability of the gas pipes and therefore a risk

Although damage to water pipes is less likely to result in injury, the following

• Leaks of water from underground pipes can affect adjacent services and reduce

• Damage to, or removal of thrust blocks can result in sudden loss of containment and the movement of pipe fittings that may travel some distance or cause impact damage. While some sewage is pumped at pressure, sewers are generally gravity-fed, and the main hazards from damage to a sewer are the

The type of materials for these water/sewage pipes, will include brick, cast iron, ductile iron, clay or concrete. Some asset owners, will give limitations on the surcharge loading and acceptance criterion for ground settlements or strain, an example of which is shown below from Thames water UK [20]. Current regulations in UK will require a risk assessment before placing any temporary foundations or

Damage to telecommunication and TV cables may require expensive repairs and can cause considerable disruption to those relying on the system, especially emergency or essential services. The risks of direct personal injury are normally low, but

**94**

*Assessment criteria for existing Thames Water pipeline and sewer assets (reproduced from Ref. [20]).*


### **Table 2.**

*Maximum rotation for vitrified clay and concrete pipes.*

It is important to ensure that surcharge loading from temporary foundation on buried cables is limited.

In addition to the above utility services, the presence of other pipes and cables should be anticipated. These include fuel oil pipes at States housing developments and private/security electricity and telecommunications cables. Risk assessment will be required on a case by case basis to suit to owners' requirement.

### **4.5 Underground or above ground railway or cable tunnels**

Any movement of tunnels if they are underground or above ground (cut and cover) is very critical for the performance and therefore the asset owners will have very stringent requirements for the movement temporary works plant around these structures. Generally clearances need to be maintained between the plant and the assets and this will vary depending on the depth of the asset below the ground. No plant can operate within these zones while constructing the bridges. An example of the Cross Rail exclusion zone in London [20] is shown in **Figure 3**.

**Figure 3.** *Exclusion zone limits for crossrail underground lines (figure reproduced from Ref. [21]).*

### **4.6 Party walls or other grade listed buildings**

These include third party buildings, existing walls of private owners, and grade listed buildings. Generally, if the temporary works for bridge construction works are carried out by the contractor near these assets, he will have to ensure that the damage to either Partywalls or nearby listed grade buildings is minimal. In UK, there are party wall agreements on movements and crackwidths as per Boscardin guidelines [22].

In order to manage the risks from bridge construction operations, it is necessary to prepare a carefully coordinated construction method statement with all the supply chain involved and which includes the sequence, hazard identification, and a risk assessment. A management procedure is required to manage the residual risks on site and contingency measures to mitigate or control the risks.

### **5. Dealing with hazards: construction method statements, and risk assessments**

Catastrophic events in construction are real issues which require proper consideration by all stakeholders, led by directors and senior staff.

These potentially catastrophic events are sometimes referred to as 'Top Events'. It is appreciated that they can have a disastrous impact on a company's reputation and well-being and upon society. The process of examining the risk of a catastrophic event requires that a 'safety case' is prepared, based upon a safety risk assessment.

**97**

*Temporary Works in Construction of Bridges Near Third Party Assets*

• Where the UK construction industry could improve

The key issues proposed in this reports are as follows:

• Issue 7: Independent reviews should be employed

• Issue 8: The industry should learn from experience.

appropriate monitoring at all levels.

Statements and Risk Assessments

**5.1 Risk assessments**

CIRIA and HSE UK reports [23, 24] have looked at the risks of 'Catastrophic Events' in the UK construction industry and summarised its findings in the report. This report identified the types of events, reason for occurrence, and control

• The types of catastrophic event which have occurred or which might occur

• The controls which would contribute to an avoidance of a catastrophic event

It was clear that there have been Catastrophic Events with major consequences. Their importance was recognised by the industry, although it is considered that in their day-to-day work few people realised the severity of what might happen if

• Issue 1: The industry should recognise that catastrophic events need further

• Issue 3: Knowledge, skills and experience of safety risk management should be

Method statements and drawings need to fully detail all aspects of the works. All

• Low likelihood/high severity items are to be given careful consideration with

• More invasive questioning and understanding of sub-contractor's Method

The terms used in risk assessment vary considerably in the literature. In this report, a harm is defined as an adverse effect on a person. It might be, for example,

• Issue 4: Communication and interface management should be improved

• Issue 6: Effective management of temporary works is crucial to success

safety critical items and hold points/permits to load should be identified.

• Issue 2: Corporate risk management systems should be improved

• The reasons for occurrence when there have been (or could have been) catastrophic events during construction, including an examination of the

*DOI: http://dx.doi.org/10.5772/intechopen.92364*

measures and included:

during construction

underlying factors

things went seriously wrong.

• Issue 5: Competence is key

attention

raised

*Structural Integrity and Failure*

**4.6 Party walls or other grade listed buildings**

These include third party buildings, existing walls of private owners, and grade listed buildings. Generally, if the temporary works for bridge construction works are carried out by the contractor near these assets, he will have to ensure that the damage to either Partywalls or nearby listed grade buildings is minimal. In UK, there are party wall agreements on movements and crackwidths as per Boscardin

In order to manage the risks from bridge construction operations, it is necessary to prepare a carefully coordinated construction method statement with all the supply chain involved and which includes the sequence, hazard identification, and a risk assessment. A management procedure is required to manage the residual risks

**5. Dealing with hazards: construction method statements, and risk** 

Catastrophic events in construction are real issues which require proper consid-

These potentially catastrophic events are sometimes referred to as 'Top Events'. It is appreciated that they can have a disastrous impact on a company's reputation and well-being and upon society. The process of examining the risk of a catastrophic event requires that a 'safety case' is prepared, based upon a safety risk assessment.

on site and contingency measures to mitigate or control the risks.

*Exclusion zone limits for crossrail underground lines (figure reproduced from Ref. [21]).*

eration by all stakeholders, led by directors and senior staff.

**96**

guidelines [22].

**Figure 3.**

**assessments**

CIRIA and HSE UK reports [23, 24] have looked at the risks of 'Catastrophic Events' in the UK construction industry and summarised its findings in the report. This report identified the types of events, reason for occurrence, and control measures and included:


It was clear that there have been Catastrophic Events with major consequences. Their importance was recognised by the industry, although it is considered that in their day-to-day work few people realised the severity of what might happen if things went seriously wrong.

The key issues proposed in this reports are as follows:


Method statements and drawings need to fully detail all aspects of the works. All safety critical items and hold points/permits to load should be identified.


### **5.1 Risk assessments**

The terms used in risk assessment vary considerably in the literature. In this report, a harm is defined as an adverse effect on a person. It might be, for example,

### *Structural Integrity and Failure*

a serious illness or injury, but effects on well-being are also taken into account. A hazard is a potential cause of harm to a person, for example a faulty staircase. A hazardous situation exists when a person is exposed to a hazard, for example by using a faulty staircase. The risk associated with a hazard is a function of (a) the likelihood of the hazard causing harm and (b) the severity of the harms or their consequences.

Safe systems of work shall comprise:


The assessment of risk should be considered at all stages of the work, from planning through to final reinstatement. This may be accomplished by the use of formal risk assessments coupled, where necessary, with a work permit system. Risk assessment should include all related work activities and identify training and competency needs as well as the level of supervision required for the risks involved [10].

### **6. Need for construction: pre trials, tests and other monitoring**

Sometimes, it is necessary to carry out trials on site before the bridge structure construction begins. This may take include some mock structures to be built on site to validate all the assumptions in the design. The purpose is to ensure that the sequence of construction can be carried out safely. Examples include test loading on the trestles or surcharge loading, and monitoring of displacements etc. and mock assembly in case of structural steel joints. Eurocodes can be implemented to optimise the temporary works design if suitable testing is carried out.

In the following section, we give more recent literature survey of failures in the temporary works that involved public and third party asset owners and give additional examples of how we have managed the risks (as explained in Sections 3 and 4) during the construction for the projects in which Sir Robert McAlpine and their joint partners were involved. Our recent project also demonstrate how we have used trials on site for back analysis and how monitoring was carried out to improve the confidence in predictions and stakeholder assurances.

### **7. Survey of lessons learnt from recent failures**

### **7.1 Barton Bridge, Eccles, Feb 1959 & 2016**

In the UK the First Barton bridge collapsed in 1959 whilst erecting 4 No, 200 ton steel girders, 80 ft. above the ground [3, 14]. The supporting scaffolding collapsed bringing down the girders and killing 4 men. Sixty men, that would normally have been on the girders, were lining up for their pay at the time. Ironically after 57 years, at the same location in 2016, temporary lifting system failed collapsing a major chunk of the new bridge span across the river as shown in **Figure 4a** and **b**.

**99**

**Figure 5.** *Temporary bearing.*

**Figure 4.**

*reproduced from Refs. [3, 14]).*

*Temporary Works in Construction of Bridges Near Third Party Assets*

GE19 is an 84 m long, single span Warren truss girder bridge on a 3.3% gradient from East to West with a bridge weighed 1300 tonnes post launch and had an In-situ deck on 'Omnia' permanent formwork [25]. Minimum clearance of 650 mm to overhead lines. It was found that the bridge had moved longitudinally 38 mm out of position post launch. This necessitated corrective plan jacking that had not been envisaged during pre-planning. At approximately 19:15 hours on 28th May 2008, an hour after work had stopped, the site security guard heard three loud bangs. The Bridge deck had dropped by approx. 200 mm resulting in damage to scaffolding and bearings. Five planks fell onto the live rail below the bridge, ponded water onto the overhead lines and track and the track had to be closed. There were no injuries to any members of the public or employees. PTFE material had been placed on a slope,

*(a) Barton bridge scaffold collapse (1959) and (b) lifting failure of a modern bridge (2016) (figures* 

*DOI: http://dx.doi.org/10.5772/intechopen.92364*

**7.2 GE 19 bridge on East London Line**

*Temporary Works in Construction of Bridges Near Third Party Assets DOI: http://dx.doi.org/10.5772/intechopen.92364*

### **7.2 GE 19 bridge on East London Line**

GE19 is an 84 m long, single span Warren truss girder bridge on a 3.3% gradient from East to West with a bridge weighed 1300 tonnes post launch and had an In-situ deck on 'Omnia' permanent formwork [25]. Minimum clearance of 650 mm to overhead lines. It was found that the bridge had moved longitudinally 38 mm out of position post launch. This necessitated corrective plan jacking that had not been envisaged during pre-planning. At approximately 19:15 hours on 28th May 2008, an hour after work had stopped, the site security guard heard three loud bangs. The Bridge deck had dropped by approx. 200 mm resulting in damage to scaffolding and bearings. Five planks fell onto the live rail below the bridge, ponded water onto the overhead lines and track and the track had to be closed. There were no injuries to any members of the public or employees. PTFE material had been placed on a slope,

**Figure 4.**

*Structural Integrity and Failure*

• Assess the risks.

Safe systems of work shall comprise:

• Check that the plans are accurate.

• Carry out the work in a safe manner.

• At all stages THINK and REVIEW.

a serious illness or injury, but effects on well-being are also taken into account. A hazard is a potential cause of harm to a person, for example a faulty staircase. A hazardous situation exists when a person is exposed to a hazard, for example by using a faulty staircase. The risk associated with a hazard is a function of (a) the likelihood of the hazard causing harm and (b) the severity of the harms or their consequences.

• Plan the work - obtain all information relating to the work carried out.

The assessment of risk should be considered at all stages of the work, from planning through to final reinstatement. This may be accomplished by the use of formal risk assessments coupled, where necessary, with a work permit system. Risk assessment should include all related work activities and identify training and competency needs as well as the level of supervision required for the risks involved [10].

Sometimes, it is necessary to carry out trials on site before the bridge structure construction begins. This may take include some mock structures to be built on site to validate all the assumptions in the design. The purpose is to ensure that the sequence of construction can be carried out safely. Examples include test loading on the trestles or surcharge loading, and monitoring of displacements etc. and mock assembly in case of structural steel joints. Eurocodes can be implemented to

In the following section, we give more recent literature survey of failures in the temporary works that involved public and third party asset owners and give additional examples of how we have managed the risks (as explained in Sections 3 and 4) during the construction for the projects in which Sir Robert McAlpine and their joint partners were involved. Our recent project also demonstrate how we have used trials on site for back analysis and how monitoring was carried out to improve the

In the UK the First Barton bridge collapsed in 1959 whilst erecting 4 No, 200 ton steel girders, 80 ft. above the ground [3, 14]. The supporting scaffolding collapsed bringing down the girders and killing 4 men. Sixty men, that would normally have been on the girders, were lining up for their pay at the time. Ironically after 57 years, at the same location in 2016, temporary lifting system failed collapsing a major chunk of the new bridge span across the river as shown in

**6. Need for construction: pre trials, tests and other monitoring**

optimise the temporary works design if suitable testing is carried out.

confidence in predictions and stakeholder assurances.

**7. Survey of lessons learnt from recent failures**

**7.1 Barton Bridge, Eccles, Feb 1959 & 2016**

**98**

**Figure 4a** and **b**.

*(a) Barton bridge scaffold collapse (1959) and (b) lifting failure of a modern bridge (2016) (figures reproduced from Refs. [3, 14]).*

**Figure 5.** *Temporary bearing.*

### *Structural Integrity and Failure*

the vertical load of the bridge generated a horizontal force component. The presence of a second slip plane allowed the wedge of packing between the PTFE surface and bearing surface to be ejected as in **Figure 5**. A similar incident did not occur at the West abutment because the permanent bearings were of a fixed type and hence did not fail (see **Figure 6**).

### **7.3 Motorway bridge temporary works collapse Colombian Bridge**

In March 2019 the temporary works of a motorway bridge near Ancona, Italy, shown in **Figure 7** [26] failed with the immediate collapse of the bridge deck onto cars passing below sadly killing two members of the public [14, 26]. The motorway was subsequently closed. An example of both the human and financial consequences of errors in construction. A design error was blamed for the collapse of the bridge.

### **7.4 Grayston Drive collapse (Johannesburg)**

Two people were killed and 19 injured when the formwork supporting the under-construction bridge collapsed unexpectedly in 2016 shown in **Figure 8** [27]. The initial inquiry showed that some of the site inspection registers for the period just before the collapse were not available [27].

**Figure 6.** *Bridge launch over railway (reproduced from Ref. [25]).*

**101**

**Figure 9.**

*Temporary Works in Construction of Bridges Near Third Party Assets*

A Hydrogen embrittlement crack has been identified as causing the failure of one of the cable anchor bolts of the Norway Halogaland Bridge shortly after installation shown in **Figure 9** [28]. The initial enquiry showed that that the root cause of the cracking is the hydrogen exposure of the bolts. It is not known if the bolts were

Incorrect positioning of temporary bearings during incremental launching was identified as the primary cause of the fatal 1998 Injaka Bridge collapse in South

Inexperienced design and construction staff, poor construction quality control and a failure to react to a 'clear warning that all was not well' with the structure, led to the disaster. At 300 m long, 14 m wide and up to 37 m above the river bed, Injaka Bridge was a major structure and the consultant and contractor had extensive experience with such incrementally launched post-tensioned structures. The collapse occurred after the contractor had slid out five of the 20, 15 m long sections of the 3 m deep box section deck. The sixth segment was being jacked as the structure collapsed. At that point the concrete deck extended 24.4 m beyond pier 2 with the leading edge of the 27 m long launching nose projecting 7.1 m

exposed to Hydrogen during manufacturing, transportation or at the site.

*DOI: http://dx.doi.org/10.5772/intechopen.92364*

**7.5 Norway Bridge Collapse 2018**

**7.6 Injaka Bridge, South Africa 1998**

Africa [29].

beyond pier 3.

**Figure 8.**

*Collapse of temporary supports 2018 (figure reproduced from Ref. [27]).*

*Hydrogen cracking in bolts (figure reproduced from Ref. [28]).*

**Figure 7.** *Colombian bridge failure (reproduced from Ref. [26]).*

### **7.5 Norway Bridge Collapse 2018**

*Structural Integrity and Failure*

did not fail (see **Figure 6**).

**7.4 Grayston Drive collapse (Johannesburg)**

just before the collapse were not available [27].

the vertical load of the bridge generated a horizontal force component. The presence of a second slip plane allowed the wedge of packing between the PTFE surface and bearing surface to be ejected as in **Figure 5**. A similar incident did not occur at the West abutment because the permanent bearings were of a fixed type and hence

In March 2019 the temporary works of a motorway bridge near Ancona, Italy, shown in **Figure 7** [26] failed with the immediate collapse of the bridge deck onto cars passing below sadly killing two members of the public [14, 26]. The motorway was subsequently closed. An example of both the human and financial consequences of errors in construction. A design error was blamed for the collapse of the bridge.

Two people were killed and 19 injured when the formwork supporting the under-construction bridge collapsed unexpectedly in 2016 shown in **Figure 8** [27]. The initial inquiry showed that some of the site inspection registers for the period

**7.3 Motorway bridge temporary works collapse Colombian Bridge**

**100**

**Figure 7.**

**Figure 6.**

*Colombian bridge failure (reproduced from Ref. [26]).*

*Bridge launch over railway (reproduced from Ref. [25]).*

A Hydrogen embrittlement crack has been identified as causing the failure of one of the cable anchor bolts of the Norway Halogaland Bridge shortly after installation shown in **Figure 9** [28]. The initial enquiry showed that that the root cause of the cracking is the hydrogen exposure of the bolts. It is not known if the bolts were exposed to Hydrogen during manufacturing, transportation or at the site.

### **7.6 Injaka Bridge, South Africa 1998**

Incorrect positioning of temporary bearings during incremental launching was identified as the primary cause of the fatal 1998 Injaka Bridge collapse in South Africa [29].

Inexperienced design and construction staff, poor construction quality control and a failure to react to a 'clear warning that all was not well' with the structure, led to the disaster. At 300 m long, 14 m wide and up to 37 m above the river bed, Injaka Bridge was a major structure and the consultant and contractor had extensive experience with such incrementally launched post-tensioned structures. The collapse occurred after the contractor had slid out five of the 20, 15 m long sections of the 3 m deep box section deck. The sixth segment was being jacked as the structure collapsed. At that point the concrete deck extended 24.4 m beyond pier 2 with the leading edge of the 27 m long launching nose projecting 7.1 m beyond pier 3.

**Figure 8.** *Collapse of temporary supports 2018 (figure reproduced from Ref. [27]).*

**Figure 9.** *Hydrogen cracking in bolts (figure reproduced from Ref. [28]).*

The primary cause of the collapse was found to have been the positioning of temporary bearings on which the deck structure slid out during construction as shown in **Figure 10**.

### **Figure 10.**

*Failure of a multi span bridge (figure reproduced from Ref. [29]).*

### **Figure 11.**

*Florida Bridge collapse, 2019 (reproduced from Ref. [25]).*

**103**

**Figure 13.** *Bridge launch.*

*Temporary Works in Construction of Bridges Near Third Party Assets*

tance of design, checking, and monitoring and back analysis.

plant on the sensitive underground railway tunnels (**Figure 13**).

**8.1 Case Study 1: Arsenal bridges, London, UK**

**8.2 Case Study 2: Gogarburn Bridge, Scotland**

shown in **Figure 16**.

The initial investigation showed that where the tow truss members meet, at joint 11, there was overestimation of the capacity and under estimation of the loads as

Examples of case studies from our recent project experience published by the author in various reports (internal and external) are outlined below. These case studies show how the temporary works design should address the stake holder's expectations in managing risks. Five case histories discussed here show the impor-

An example of assets affected by the bridge launch—temporary trestle foundations next to network rail assets, and piling plant and movement of construction

Assessments were carried out to ensure that the settlements, and movements and surcharge loadings were managed. Monitoring was carried out to gain confidence in the predictions and to ensure that mitigation measures can be placed (**Figure 14**).

The road bridge is on the new spur off the A8 into the new headquarters for the Royal Bank of Scotland. The bridge deck was being erected on temporary trestles, located on either side of the road and in the central reservation. The box girders will be lifted into place in half span sections, each weighing approximately 73 T. Secondary beams span between the box girders to support the deck. The deck was cast on 'omnia plank' permanent formwork. The sequence is depicted in **Figure 15** and the temporary trestles that required design for impact loads are

*DOI: http://dx.doi.org/10.5772/intechopen.92364*

shown in **Figures 11** and **12** [25, 30, 31].

**7.7 Florida Bridge collapse 2019**

**8. Case studies of mitigation**

**Figure 12.** *Node 11 failure (reproduced from Ref. [30]).*

### **7.7 Florida Bridge collapse 2019**

*Structural Integrity and Failure*

shown in **Figure 10**.

The primary cause of the collapse was found to have been the positioning of temporary bearings on which the deck structure slid out during construction as

**102**

**Figure 12.**

*Node 11 failure (reproduced from Ref. [30]).*

**Figure 11.**

**Figure 10.**

*Florida Bridge collapse, 2019 (reproduced from Ref. [25]).*

*Failure of a multi span bridge (figure reproduced from Ref. [29]).*

The initial investigation showed that where the tow truss members meet, at joint 11, there was overestimation of the capacity and under estimation of the loads as shown in **Figures 11** and **12** [25, 30, 31].

### **8. Case studies of mitigation**

Examples of case studies from our recent project experience published by the author in various reports (internal and external) are outlined below. These case studies show how the temporary works design should address the stake holder's expectations in managing risks. Five case histories discussed here show the importance of design, checking, and monitoring and back analysis.

### **8.1 Case Study 1: Arsenal bridges, London, UK**

An example of assets affected by the bridge launch—temporary trestle foundations next to network rail assets, and piling plant and movement of construction plant on the sensitive underground railway tunnels (**Figure 13**).

Assessments were carried out to ensure that the settlements, and movements and surcharge loadings were managed. Monitoring was carried out to gain confidence in the predictions and to ensure that mitigation measures can be placed (**Figure 14**).

### **8.2 Case Study 2: Gogarburn Bridge, Scotland**

The road bridge is on the new spur off the A8 into the new headquarters for the Royal Bank of Scotland. The bridge deck was being erected on temporary trestles, located on either side of the road and in the central reservation. The box girders will be lifted into place in half span sections, each weighing approximately 73 T. Secondary beams span between the box girders to support the deck. The deck was cast on 'omnia plank' permanent formwork. The sequence is depicted in **Figure 15** and the temporary trestles that required design for impact loads are shown in **Figure 16**.

**Figure 13.** *Bridge launch.*

**Figure 14.**

*General arrangement plan and section showing trestles, UG services, tunnels, and network rail.*

**Figure 15.** *Erection sequence of the bridge, trestle.*

The arch was being erected in three sections. Each of the two outer pieces was supported by the bearing plate at one end and a trestle on top of the deck at the other.

Finally the centre section was dropped in to complete the arch. The arch was welded together, 25 m above the road. Ten tension rods support the bridge in the centre.

**105**

**Figure 17.**

*Ref. [31]).*

**trestles**

*Temporary trestles near live highway.*

**Figure 16.**

ground line.

*Temporary Works in Construction of Bridges Near Third Party Assets*

**8.3 Case Study 3: Motorway M74, UK, Bridge Launch from the temporary** 

As a part of the M74 completion project in Glasgow, Sir Robert McAlpine Design group, working closely with the site based Joint Venture, has been responsible for many elements of design and checking for the West section of the work [31]. Included in the West section is a 1350 m length of an elevated structure formed of trapezoidal steel girders with in-situ concrete deck and parapets. This section passes over three sections of the overground line which are a part of Network Rails assets; the Paisley Line, the Cook Street Link, and the West Coast Mainline. Parts are also close to a section of the Strathclyde Passenger Transport (SPT) under-

With the exception of the West Coast Mainline section, the steel sections were lifted in place using mobile cranes. These sections were supported on temporary trestles whilst they were welded. The section of superstructure spanning over a 65 m wide cutting containing the West Coast mainline was installed by launching the bridge as shown in **Figure 17a**. A 235 m long, 4200 tonne section was formed to the West of the cutting, complete with a section of in situ deck and parapet, and then launched a total of 166 m during a series of short night-time possessions. The

*(a) Launch of the bridge over the live highway and railway, (b) aerial photo of the launch (extract from* 

*DOI: http://dx.doi.org/10.5772/intechopen.92364*

*Temporary Works in Construction of Bridges Near Third Party Assets DOI: http://dx.doi.org/10.5772/intechopen.92364*

**Figure 16.** *Temporary trestles near live highway.*

*Structural Integrity and Failure*

**104**

**Figure 15.**

**Figure 14.**

the other.

the centre.

*Erection sequence of the bridge, trestle.*

The arch was being erected in three sections. Each of the two outer pieces was supported by the bearing plate at one end and a trestle on top of the deck at

*General arrangement plan and section showing trestles, UG services, tunnels, and network rail.*

Finally the centre section was dropped in to complete the arch. The arch was welded together, 25 m above the road. Ten tension rods support the bridge in

### **8.3 Case Study 3: Motorway M74, UK, Bridge Launch from the temporary trestles**

As a part of the M74 completion project in Glasgow, Sir Robert McAlpine Design group, working closely with the site based Joint Venture, has been responsible for many elements of design and checking for the West section of the work [31]. Included in the West section is a 1350 m length of an elevated structure formed of trapezoidal steel girders with in-situ concrete deck and parapets. This section passes over three sections of the overground line which are a part of Network Rails assets; the Paisley Line, the Cook Street Link, and the West Coast Mainline. Parts are also close to a section of the Strathclyde Passenger Transport (SPT) underground line.

With the exception of the West Coast Mainline section, the steel sections were lifted in place using mobile cranes. These sections were supported on temporary trestles whilst they were welded. The section of superstructure spanning over a 65 m wide cutting containing the West Coast mainline was installed by launching the bridge as shown in **Figure 17a**. A 235 m long, 4200 tonne section was formed to the West of the cutting, complete with a section of in situ deck and parapet, and then launched a total of 166 m during a series of short night-time possessions. The

**Figure 17.** *(a) Launch of the bridge over the live highway and railway, (b) aerial photo of the launch (extract from Ref. [31]).*

### *Structural Integrity and Failure*

cantilever distance to the first temporary trestle support beyond the cutting is 89 m. In order to ensure safety to both Public and the existing network rail assets, the temporary works design included the following and was developed collaboratively with the supply chain partners in the joint venture project.


Retaining and within a main road. The design had to take account of the need to avoid unacceptable movements to the nearby masonry retaining wall.


Working collaboratively with our supply chain partners, loads on each of the trestles for the launching operations were derived and were used in the analysis of temporary trestles. Trestles foundations included piles where space was restricted and pad foundation where space was not restricted. The analysis for various combinations of normal loads and accidental loads were carried out in ANSYS and typical results from the analysis were summarised in **Table 3**. These were used for monitoring the loads and the movements of the foundations using targets on trestles and foundations.

### **8.4 Case Study 4: construction of a segmental arch bridge over a railway, Dobwalls Bypass, UK**

This case study, published in detail in Ref. 32 by the author, shows how the temporary works were managed by the project team in order to ensure that there was no repeat of 'Gerrards cross failure'. The failure at Gerrards Cross, reported in 2005, demonstrated the importance of controlling the backfill and carefully controlling and monitoring the deflections of the arch bridges during construction. The 87 m long arch unit spanning 15.5 m with a rise of 5.6 m was built on the monolithic principle, which means it acts as one single structure. The radius of the curved track underneath is 500 m, which proved a challenging aspect of the project.

**107**

the fill;

tion as described below.

presented in this paper.

install piles and pile caps; Phase 3: Construct arch;

embankment;

The construction phases are summarised below.

to 75% of the overall height of the arch segments;

between sides of 600 mm, with compaction load of 11.5 kN/m2

*Temporary Works in Construction of Bridges Near Third Party Assets*

The structure was in the form of a short tunnel, a proprietary system by Asset International, comprising pre-cast concrete arch segments springing from an RC slab and upstand, supported on piled foundations. The arch was formed from pre-cast concrete elements using a proprietary arch system with an elliptical crosssection. The two ends of the tunnel consisted of portal sections which are bevelled to follow the slope of the new embankment for the realigned section of road. Since the bridge structure is made up of arch-shaped pre-cast elements, the elements at the ends of the tunnel are cut-off, and no longer form a full arch. These truncated elements, therefore, are connected to each other by means of cast-in-situ reinforced concrete collars to form a monolithic reinforced concrete shell. This monolithic shell includes the two outermost full arch rings which allow all loads acting on one side of the bevel to be transferred to the other side and to the foundations. Working collaboratively with the project team, we have developed a safe system of construc-

Total maximum vertical load on support +5000 kN 34,500 kN 20,000 kN Total minimum vertical load on support −4350 kN — —

**Item Trestle 1 Trestle 2 Trestle 3** Vertical settlement 8 mm 8 mm 0 mm (under

In order to predict the behaviour of the tunnels during construction and to advise the construction teams on the methodology, it was necessary to model each stage both in 2D and 3D models. The construction sequence was represented in the analysis by a total of 15 stages as shown in **Figure 18**. Full details of the FE model, assumptions, approach, and the sequence including sensitivity analyses were published in a separate paper Ref. [32] by the author(s). Only extracts from Ref. [32] are

Phase 1: Establish initial conditions for existing ground and railway

Phase 2: Place new fill up to the level of the existing railway embankment, and

Phase 4: Place fill for the new road embankment away from the arch structure up

on the surface of

lifting strut). 6 mm elsewhere.

10 mm 10 mm 9 mm

— — 21 mm

— — 14 mm

— — 3 to 5 mm

Phases 5–13: Place backfill against the arch with a maximum differential

*DOI: http://dx.doi.org/10.5772/intechopen.92364*

Anticipated lateral movement (at pile cap).

Maximum lateral movement (worst case soils)

Maximum lateral movement (worst case) at pile cap. Perpendicular to NR retaining wall

Worst case lateral movement at network rail wall for worst case soils and bridge being pulled

*Amber trigger levels for movements and loads on trestles.*

Parallel to launch

back (westwards)

**Table 3.**

at pile cap. Parallel to launch


*Temporary Works in Construction of Bridges Near Third Party Assets DOI: http://dx.doi.org/10.5772/intechopen.92364*

**Table 3.**

*Structural Integrity and Failure*

(SPT) infrastructure.

ing wall.

foundations.

**Dobwalls Bypass, UK**

cantilever distance to the first temporary trestle support beyond the cutting is 89 m. In order to ensure safety to both Public and the existing network rail assets, the temporary works design included the following and was developed collaboratively

i.Assessment of the ground was necessary for designing working platforms for all the plant and craneage required for the steel lifts. Outrigger loads from the cranes were up to 4200 kN, with 6000 kN of superlift loadings.

ii.Assessing the effect of the applied loads on the Scotland Public Transport

iii.Design of frames and anchored rock netting to protect Network Rail assets during piling and pier construction operations adjacent to the railway cutting.

iv.Design of temporary support trestles and their support piles to take the vertical and horizontal loads applied during the bridge launch operations. The calculated vertical loads were up to 18,000 kN on a single temporary leg under the worst case loading. The design of the trestles evolved as work proceeded as exploratory works were carried out in advance of the piling and

One pair of temporary trestle bases was cast adjacent to a Network Rail Retaining and within a main road. The design had to take account of the need to avoid unacceptable movements to the nearby masonry retain-

v.The six 1200 mm piles to each base had to be installed in locations which avoided impacting on three gas mains, electric cables and a brick sewer.

vi.Design of additional support walls to take the bridge launch loads on the pile

Working collaboratively with our supply chain partners, loads on each of the trestles for the launching operations were derived and were used in the analysis of temporary trestles. Trestles foundations included piles where space was restricted and pad foundation where space was not restricted. The analysis for various combinations of normal loads and accidental loads were carried out in ANSYS and typical results from the analysis were summarised in **Table 3**. These were used for monitoring the loads and the movements of the foundations using targets on trestles and

**8.4 Case Study 4: construction of a segmental arch bridge over a railway,** 

underneath is 500 m, which proved a challenging aspect of the project.

This case study, published in detail in Ref. 32 by the author, shows how the temporary works were managed by the project team in order to ensure that there was no repeat of 'Gerrards cross failure'. The failure at Gerrards Cross, reported in 2005, demonstrated the importance of controlling the backfill and carefully controlling and monitoring the deflections of the arch bridges during construction. The 87 m long arch unit spanning 15.5 m with a rise of 5.6 m was built on the monolithic principle, which means it acts as one single structure. The radius of the curved track

with the supply chain partners in the joint venture project.

services or obstructions were encountered:

caps under the temporary loading conditions.

**106**

*Amber trigger levels for movements and loads on trestles.*

The structure was in the form of a short tunnel, a proprietary system by Asset International, comprising pre-cast concrete arch segments springing from an RC slab and upstand, supported on piled foundations. The arch was formed from pre-cast concrete elements using a proprietary arch system with an elliptical crosssection. The two ends of the tunnel consisted of portal sections which are bevelled to follow the slope of the new embankment for the realigned section of road. Since the bridge structure is made up of arch-shaped pre-cast elements, the elements at the ends of the tunnel are cut-off, and no longer form a full arch. These truncated elements, therefore, are connected to each other by means of cast-in-situ reinforced concrete collars to form a monolithic reinforced concrete shell. This monolithic shell includes the two outermost full arch rings which allow all loads acting on one side of the bevel to be transferred to the other side and to the foundations. Working collaboratively with the project team, we have developed a safe system of construction as described below.

In order to predict the behaviour of the tunnels during construction and to advise the construction teams on the methodology, it was necessary to model each stage both in 2D and 3D models. The construction sequence was represented in the analysis by a total of 15 stages as shown in **Figure 18**. Full details of the FE model, assumptions, approach, and the sequence including sensitivity analyses were published in a separate paper Ref. [32] by the author(s). Only extracts from Ref. [32] are presented in this paper.

The construction phases are summarised below.

Phase 1: Establish initial conditions for existing ground and railway embankment;

Phase 2: Place new fill up to the level of the existing railway embankment, and install piles and pile caps;

Phase 3: Construct arch;

Phase 4: Place fill for the new road embankment away from the arch structure up to 75% of the overall height of the arch segments;

Phases 5–13: Place backfill against the arch with a maximum differential between sides of 600 mm, with compaction load of 11.5 kN/m2 on the surface of the fill;

### *Structural Integrity and Failure*

### **Figure 18.**

*Construction sequence model analysed in the finite difference software (FLAC).*

Phase 14: Place final layer of fill over the arch, with compaction load of 11.5 kN/m<sup>2</sup> over the full width of the model on the top surface;

Phase 15: Remove compaction load of 11.5 kN/m2 on top surface of the model. It was important to carry out sensitivity studies with respect to soil stiffness, backfill characteristics, interface stiffness, and initial conditions of the arch to establish lower and upper bounds of movements. These sensitivity studies helped us to develop a safe and robust scheme of backfilling sequence and helped us to set new trigger limits for safe construction. Closed-form solutions predict the movements for a fully backfilled scenario however they will not predict the movements for unsymmetrical backfilling on either side of the arches and therefore numerical models in 2D and 3D will give insight to real behaviour. The models developed here in 2D and 3D, therefore, gave insight into the development of the movement throughout the construction process. The power of the modelling is demonstrated by comparing the analytical results with observations on site. The site observations matched well with the numerical predictions from 2D and 3D models as shown in **Figure 19**.

**109**

*Temporary Works in Construction of Bridges Near Third Party Assets*

**8.5 Case Study 5: construction of a hanging building from the truss over railway,** 

*Movement of the crown of the arch while backfilling sequence is progressed to build the highway bridge over the* 

The Bull Ring Redevelopment in Birmingham consisted of demolishing the existing 1960s concrete shopping centre and replacing it with a new one. The northern part of this new complex lies directly above the New Street South railway tunnels, which carry the main lines to London and the West Country through them. During the redevelopment work there was the potential to affect the railway tunnels

To maximise the available retail space at the northern end of the development, 2 No. hanging structures were to be constructed to extend the development over the Northern Arm road, with the pedestrian footbridge described above providing the 'sandwich' between the hanging structures. To support these hanging structures a structural steelwork bowstring truss is positioned at either end of each structure, spanning across the Northern Arm to carry all other intermediate steelwork,

The western hanging structure is supported by trusses T1 and T2, which are supported at their northern end by double columns supported off a reinforced concrete pile cap founded on a cluster of mini piles constructed within the basement of the Rotunda. At its southern end these trusses are again supported by a twin steel column section founded behind the contiguous piled wall and thus forming part of the main development structural frame. The brick arch railway tunnels are not continuous for the full length of the Northern Arm. At its western end the brick arch tunnels give way to a reinforced concrete road bridge, built 1961–1962. This road bridge continues in a westerly direction towards the New Street station junction, noting that immediately northwest of truss T1 the road bridge deck slab is discontinuous with an open section of railway exposed and only protected by a 1.8 m high concrete parapet wall constructed around the opening. Working collaboratively with our supply chain

partners, we have developed a safe erection methodology as described below.

Once the fabrication location was established, crane sizes and locations were firmed up, thus allowing a detailed crane analysis to be carried out to produce theoretical outrigger loads, including any redistribution of loads resulting from any crane slewing, jibbing in/out, etc. during the lifts. The Railtrack structures were then assessed under these loads, with feedback to the site team accordingly if the

*DOI: http://dx.doi.org/10.5772/intechopen.92364*

**Bull Ring, Birmingham, UK**

**Figure 19.**

*railway.*

at various stages of construction.

reinforced concrete floor slabs, roof, cladding, etc.

### **Figure 19.**

*Structural Integrity and Failure*

**108**

**Figure 19**.

11.5 kN/m<sup>2</sup>

**Figure 18.**

Phase 14: Place final layer of fill over the arch, with compaction load of

It was important to carry out sensitivity studies with respect to soil stiffness, backfill characteristics, interface stiffness, and initial conditions of the arch to establish lower and upper bounds of movements. These sensitivity studies helped us to develop a safe and robust scheme of backfilling sequence and helped us to set new trigger limits for safe construction. Closed-form solutions predict the movements for a fully backfilled scenario however they will not predict the movements for unsymmetrical backfilling on either side of the arches and therefore numerical models in 2D and 3D will give insight to real behaviour. The models developed here in 2D and 3D, therefore, gave insight into the development of the movement throughout the construction process. The power of the modelling is demonstrated by comparing the analytical results with observations on site. The site observations matched well with the numerical predictions from 2D and 3D models as shown in

on top surface of the model.

over the full width of the model on the top surface;

Phase 15: Remove compaction load of 11.5 kN/m2

*Construction sequence model analysed in the finite difference software (FLAC).*

*Movement of the crown of the arch while backfilling sequence is progressed to build the highway bridge over the railway.*

### **8.5 Case Study 5: construction of a hanging building from the truss over railway, Bull Ring, Birmingham, UK**

The Bull Ring Redevelopment in Birmingham consisted of demolishing the existing 1960s concrete shopping centre and replacing it with a new one. The northern part of this new complex lies directly above the New Street South railway tunnels, which carry the main lines to London and the West Country through them. During the redevelopment work there was the potential to affect the railway tunnels at various stages of construction.

To maximise the available retail space at the northern end of the development, 2 No. hanging structures were to be constructed to extend the development over the Northern Arm road, with the pedestrian footbridge described above providing the 'sandwich' between the hanging structures. To support these hanging structures a structural steelwork bowstring truss is positioned at either end of each structure, spanning across the Northern Arm to carry all other intermediate steelwork, reinforced concrete floor slabs, roof, cladding, etc.

The western hanging structure is supported by trusses T1 and T2, which are supported at their northern end by double columns supported off a reinforced concrete pile cap founded on a cluster of mini piles constructed within the basement of the Rotunda. At its southern end these trusses are again supported by a twin steel column section founded behind the contiguous piled wall and thus forming part of the main development structural frame. The brick arch railway tunnels are not continuous for the full length of the Northern Arm. At its western end the brick arch tunnels give way to a reinforced concrete road bridge, built 1961–1962. This road bridge continues in a westerly direction towards the New Street station junction, noting that immediately northwest of truss T1 the road bridge deck slab is discontinuous with an open section of railway exposed and only protected by a 1.8 m high concrete parapet wall constructed around the opening. Working collaboratively with our supply chain partners, we have developed a safe erection methodology as described below.

Once the fabrication location was established, crane sizes and locations were firmed up, thus allowing a detailed crane analysis to be carried out to produce theoretical outrigger loads, including any redistribution of loads resulting from any crane slewing, jibbing in/out, etc. during the lifts. The Railtrack structures were then assessed under these loads, with feedback to the site team accordingly if the

**Figure 20.** *Erection of 140 T truss over the railway with a soil cover of 3 m.*

structures were likely to be overstressed, with recommendations to relocate cranes, increase outrigger mats, distribute outrigger loads onto twin mats, etc.

Once craneage locations were finalised, craneage layouts were firmed up, structural checks were completed, scaffold layouts finalised and method statements produced. Craneage used for the fabrication of the trusses and associated erection of the temporary works support scaffold varied from truss to truss, but for each truss one of the cranes used for the tandem lift of that truss was utilised as the service crane for the above works. Therefore, for trusses T1 and T2 a 400 T crane was used with an 800 T crane used for trusses T3 and T4. As part of the checks undertaken during the initial piling works to establish constraints for the piling plant, its location, and associated excavations, a considerable amount of design checks using finite element analysis had been undertaken on the brick arch tunnels. To satisfy railtrack/network rail requirements the following monitoring equipment had been installed into the tunnels before works started and included, electro level beam surveys, vibration sensors, tilt meters, and tape extensometers.

Temporary works design checks undertaken were based on theoretical outrigger loads prepared by the crane manufacturers following assessment of the different lifts by the different cranes. On the basis that these outrigger loads did not cause distress to the structures below, it was essential that outrigger loads were checked to ensure that the theoretical maximum loads were not exceeded. Hence use was made of the crane digital outrigger load readout indicator to monitor these loads. The details of the finite element analysis and the assumptions are presented in a full paper in Ref. [33] and only extracts from Ref. 33 are presented in this paper.

During each lift and at various times during the fabrication of the trusses, the tunnel monitoring system PC was attended full time by one of our site engineers to observe any changes, notably deformation movements. A site engineer would also monitor the full time the crane outrigger load indicator during major lifts.

During the crane lifts and during the fabrication of the trusses no discernible deformation to the tunnel was recorded—noting that, when the tunnel monitoring system PC was not being observed full time, the system did activate a telephone alarm once a deformation of 7 mm occurred.

**111**

**Table 4.**

*Measured and observed movements of the arch for 70 T rig on the tunnels.*

**Figure 21.**

*live railway.*

*Temporary Works in Construction of Bridges Near Third Party Assets*

outrigger load of 92 T against a predicted value of 98 T.

**Figure 20** shows the truss T1 over the tunnels.

The crane outrigger loads, as observed on the outrigger load indicator, were generally well inside the theoretical figures. On truss T1 lift the 800 T crane on the bridge beams had a maximum outrigger load of 74 T against a predicted value of 106 T. On truss T2 lift the 800 T crane on the tunnel central wall had a maximum

One the same lift the 400 T crane on the transfer beams spanning across the beams had a maximum outrigger load of 99 T against a predicted value of 120 T.

*Non-linear finite element analysis of soil structure interaction for the loads from erection of the truss over the* 

Immediately following each lift on the first available track possession/isolation a visual inspection of the tunnel was undertaken and no visible signs of distress and

*DOI: http://dx.doi.org/10.5772/intechopen.92364*

*Temporary Works in Construction of Bridges Near Third Party Assets DOI: http://dx.doi.org/10.5772/intechopen.92364*

The crane outrigger loads, as observed on the outrigger load indicator, were generally well inside the theoretical figures. On truss T1 lift the 800 T crane on the bridge beams had a maximum outrigger load of 74 T against a predicted value of 106 T. On truss T2 lift the 800 T crane on the tunnel central wall had a maximum outrigger load of 92 T against a predicted value of 98 T.

One the same lift the 400 T crane on the transfer beams spanning across the beams had a maximum outrigger load of 99 T against a predicted value of 120 T. **Figure 20** shows the truss T1 over the tunnels.

Immediately following each lift on the first available track possession/isolation a visual inspection of the tunnel was undertaken and no visible signs of distress and

### **Figure 21.**

*Structural Integrity and Failure*

**Figure 20.**

structures were likely to be overstressed, with recommendations to relocate cranes,

Once craneage locations were finalised, craneage layouts were firmed up, structural checks were completed, scaffold layouts finalised and method statements produced. Craneage used for the fabrication of the trusses and associated erection of the temporary works support scaffold varied from truss to truss, but for each truss one of the cranes used for the tandem lift of that truss was utilised as the service crane for the above works. Therefore, for trusses T1 and T2 a 400 T crane was used with an 800 T crane used for trusses T3 and T4. As part of the checks undertaken during the initial piling works to establish constraints for the piling plant, its location, and associated excavations, a considerable amount of design checks using finite element analysis had been undertaken on the brick arch tunnels. To satisfy railtrack/network rail requirements the following monitoring equipment had been installed into the tunnels before works started and included, electro level

increase outrigger mats, distribute outrigger loads onto twin mats, etc.

*Erection of 140 T truss over the railway with a soil cover of 3 m.*

beam surveys, vibration sensors, tilt meters, and tape extensometers.

paper in Ref. [33] and only extracts from Ref. 33 are presented in this paper.

monitor the full time the crane outrigger load indicator during major lifts.

alarm once a deformation of 7 mm occurred.

During each lift and at various times during the fabrication of the trusses, the tunnel monitoring system PC was attended full time by one of our site engineers to observe any changes, notably deformation movements. A site engineer would also

During the crane lifts and during the fabrication of the trusses no discernible deformation to the tunnel was recorded—noting that, when the tunnel monitoring system PC was not being observed full time, the system did activate a telephone

Temporary works design checks undertaken were based on theoretical outrigger loads prepared by the crane manufacturers following assessment of the different lifts by the different cranes. On the basis that these outrigger loads did not cause distress to the structures below, it was essential that outrigger loads were checked to ensure that the theoretical maximum loads were not exceeded. Hence use was made of the crane digital outrigger load readout indicator to monitor these loads. The details of the finite element analysis and the assumptions are presented in a full

**110**

*Non-linear finite element analysis of soil structure interaction for the loads from erection of the truss over the live railway.*



### **Table 4.**

*Measured and observed movements of the arch for 70 T rig on the tunnels.*

### *Structural Integrity and Failure*

movement were ever observed. Tape extensometer checks were also undertaken and again no significant movement attributable to the crane lifts was ever recorded.

Finite element models were developed in ANSYS (commercially available software) in view of the above. In particular, two-dimensional linear and nonlinear global analysis and a three-dimensional non-linear local analysis were carried out. **Figure 21** shows the finite element model. Planar elements were used for two-dimensional analysis whereas solid elements with no tension were used in the three-dimensional analysis.

ANSYS results were calibrated against site observations by making test trails on-site by surcharging pile plant loading on the tunnels and results are shown in **Table 4**.

Analysis method, assumptions, and further details of the finite elements are presented in the detailed paper by the authors in CIRIA report on tunnelling [33]. Only extracts are presented in this paper.

### **9. Summary**

Temporary works are an integral part of the safe construction of bridges and should be designed by competent bodies. Independent checks, and balances are to be in place to ensure that the public and asset owners are protected by the construction method, construction sequence of bridges. This paper summarises more recent failures and draws the conclusion that some of the best practice guidelines as developed in the UK can be adopted outside the UK. Early engagement by the contractor and communication to all the parties involved play a significant role in the safe delivery of the works at the site. Every aspect of the temporary work should be looked into in detail with reasonable margins of safety. Regular monitoring during the construction to ensure that the early warnings are not exceeded and are vital to verify the performance is as predicted and that no unsafe condition is being approached.

### **Acknowledgements**

The author is thankful to Parsons Brickenhoff for supply of the data and Asset International for sharing site measurements and photos. The author is thankful to our JV team of M74 and Paul Doughty of Sir Robert McAlpine Design Group for sharing data and photographs.

**113**

**Author details**

Ganga Kasi V. Prakhya

Sir Robert McAlpine Ltd, Eaton Court, United Kingdom

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\*Address all correspondence to: g.prakhya@srm.com

provided the original work is properly cited.

*Temporary Works in Construction of Bridges Near Third Party Assets*

*DOI: http://dx.doi.org/10.5772/intechopen.92364*

### **Conflict of interest**

The authors declare no conflict of interest.

*Temporary Works in Construction of Bridges Near Third Party Assets DOI: http://dx.doi.org/10.5772/intechopen.92364*

*Structural Integrity and Failure*

three-dimensional analysis.

Only extracts are presented in this paper.

**Table 4**.

**9. Summary**

approached.

**Acknowledgements**

**Conflict of interest**

sharing data and photographs.

The authors declare no conflict of interest.

movement were ever observed. Tape extensometer checks were also undertaken and again no significant movement attributable to the crane lifts was ever recorded. Finite element models were developed in ANSYS (commercially available software) in view of the above. In particular, two-dimensional linear and nonlinear global analysis and a three-dimensional non-linear local analysis were carried out. **Figure 21** shows the finite element model. Planar elements were used for two-dimensional analysis whereas solid elements with no tension were used in the

ANSYS results were calibrated against site observations by making test trails on-site by surcharging pile plant loading on the tunnels and results are shown in

Analysis method, assumptions, and further details of the finite elements are presented in the detailed paper by the authors in CIRIA report on tunnelling [33].

Temporary works are an integral part of the safe construction of bridges and should be designed by competent bodies. Independent checks, and balances are to be in place to ensure that the public and asset owners are protected by the construction method, construction sequence of bridges. This paper summarises more recent failures and draws the conclusion that some of the best practice guidelines as developed in the UK can be adopted outside the UK. Early engagement by the contractor and communication to all the parties involved play a significant role in the safe delivery of the works at the site. Every aspect of the temporary work should be looked into in detail with reasonable margins of safety. Regular monitoring during the construction to ensure that the early warnings are not exceeded and are vital to verify the performance is as predicted and that no unsafe condition is being

The author is thankful to Parsons Brickenhoff for supply of the data and Asset International for sharing site measurements and photos. The author is thankful to our JV team of M74 and Paul Doughty of Sir Robert McAlpine Design Group for

**112**

### **Author details**

Ganga Kasi V. Prakhya Sir Robert McAlpine Ltd, Eaton Court, United Kingdom

\*Address all correspondence to: g.prakhya@srm.com

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

### **References**

[1] Grant M, Pallet P. Temporary Works: Principles of Design and Construction. London, UK: ICE Publishing; 2012

[2] Bridle R, Sims F. The effect of bridge failures on UK technical policy and practice. Proceedings of the Institution of Civil Engineers: Engineering History and Heritage. 2009;**162**(1):39-49

[3] Smith D. Bridge failures. Proceedings of the Institution of Civil Engineers: Part. 1976;**1**(60):367-382

[4] HSE (Health and Safety Executive). Final Report of the Advisory Committee on Falsework. The Bragg Report. London, UK: HMSO; 1976

[5] BSI. BS 5975: 2008+A1:2011. Code of Practice for Falsework. London, UK: BSI Publication; 1982

[6] BS EN 12811-1. Temporary Works Equipment. Scaffolds. Performance Requirements and General Design; 2003

[7] BSI. BS EN 12812: 2008. Falsework. Performance Requirements and General Design. London, UK: BSI; 2008

[8] Temporary works forum. Toolkits for Design. Available from: https:// www.twforum.org.uk/home [Accessed: January 2020]

[9] Hewlett W, Jones A, Marchand S, Bell B. Re-visiting Bragg to keep UK's temporary works safe under EuroNorms. Proceedings of the ICE: Forensic Engineering. 2014;**167**(2):58-68

[10] Structural Safety Reports on Temp Works. Available from: https://www. structural-safety.org/ [Accessed: January 2020]

[11] Soane A. Temporary works toolkit. Part 5: Temporary works failures—What are the common causes? The Structural Engineer. 2017;**95**(1):24-26

[12] Bennion C. Temporary works associated with precast concrete bridge beam construction. In: Proceedings of the Institution of Structural Engineers, London, May 20. 1987. pp. 37-41

[13] André J, Beale R, Baptista AM. A Survey of Failures of Bridge Falsework Systems Since 1970. ICE—Forensic Engineering, Institute of Civil Engineers; 2012. 4/12

[14] Wilkipedia—Bridge Failures. Available from: https://en.wikipedia. org/wiki/List\_of\_bridge\_failures [Accessed: January 2020]

[15] Broughton K, Gill J. Bridge Installation Techniques. London: ICE Publication; 2015

[16] Khan MA. Accelerated Bridge Construction, Best Practices and Techniques. Elsevier Publication; 2015. ISBN: 97820-12-407224-4

[17] BSI. BS EN 1990: 2002 + A1: 2005. Eurocode—Basis of Structural Design (Incorporating Corrigendum December 2008 and April 2010). London: BSI; 2005

[18] BSI. BS EN 1991-1-6: 2005. Eurocode 1. Actions on Structures. General Actions. Actions during Execution. London, UK: BSI; 2005

[19] HSE Publication. Construction (Design and Management) Regulations (CDM). London: HSE Publication; 2015. Available from: https://www.hse.gov. uk/construction/cdm/2015/index.htm [Accessed: January 2020]

[20] Thames Water Publication. Guidance on Piling, Heavy Loads, Excavation, Tunneling and Dewatering. Available from: https://developers. thameswater.co.uk/Developing-a-largesite/Planning-your-development/

**115**

*Temporary Works in Construction of Bridges Near Third Party Assets*

2019;**172**(3):226-240. DOI: 10.1680/

[33] McKibbins L, Elmer R, Roberts K. Tunnels: Inspection, assessment and maintenance. In: CIRIA Technical Report C671. London: CIRIA Publication; January 2010

jbren.18.00027

*DOI: http://dx.doi.org/10.5772/intechopen.92364*

Working-near-or-diverting-our-pipes

[Accessed: January 2020]

[21] Cross rail Information for developers. March 2019. Available from: http://www.crossrail.co.uk/ route/safeguarding/?folder=/l0/856/ asset/6043 [Accessed: January 2020]

[22] Gaba A, Hardy S, Doughty L, Powrie W, Selemetas D. Guidance on embedded retaining wall design. In: CIRIA Technical Report C

760D. London: CIRIA Publications; 2017

[23] Gilbertson A, Kappia L, Bosher L, Gibb A. Guidance on catastrophic events in construction. In: CIRIA Publication C

[24] Preventing catastrophic events in construction. In: Health & Safety Executive Research Report, HSE RR 834. London: HSE Publication; 2011

[25] Bridge Design & Engineering.

[26] Bridge Design & Engineering.

[27] Bridge Design & Engineering.

[28] Bridge Design & Engineering.

[29] New Civil Engineer. UK: Publication of Inst of Civil Engineers; August 2002

[30] New Civil Engineer. UK: Publication of Inst of Civil Engineers; January

[31] New Civil Engineer. Supplement on M74. UK: Publication of Inst of Civil

[32] Prakhya G, Hopkin I, Hansford B. Construction of a concrete segmental

699. London, UK; 2011

2019;**95**(2nd Q ):6

2018;**91**:6

2018;**92**:6-7

2019;**97**:7

2020:38-39

Engineers; June 2011

arch bridge over a railway. Proceedings of the Institution of Civil Engineers—Bridge Engineering. *Temporary Works in Construction of Bridges Near Third Party Assets DOI: http://dx.doi.org/10.5772/intechopen.92364*

Working-near-or-diverting-our-pipes [Accessed: January 2020]

[21] Cross rail Information for developers. March 2019. Available from: http://www.crossrail.co.uk/ route/safeguarding/?folder=/l0/856/ asset/6043 [Accessed: January 2020]

[22] Gaba A, Hardy S, Doughty L, Powrie W, Selemetas D. Guidance on embedded retaining wall design. In: CIRIA Technical Report C 760D. London: CIRIA Publications; 2017

[23] Gilbertson A, Kappia L, Bosher L, Gibb A. Guidance on catastrophic events in construction. In: CIRIA Publication C 699. London, UK; 2011

[24] Preventing catastrophic events in construction. In: Health & Safety Executive Research Report, HSE RR 834. London: HSE Publication; 2011

[25] Bridge Design & Engineering. 2019;**95**(2nd Q ):6

[26] Bridge Design & Engineering. 2018;**91**:6

[27] Bridge Design & Engineering. 2018;**92**:6-7

[28] Bridge Design & Engineering. 2019;**97**:7

[29] New Civil Engineer. UK: Publication of Inst of Civil Engineers; August 2002

[30] New Civil Engineer. UK: Publication of Inst of Civil Engineers; January 2020:38-39

[31] New Civil Engineer. Supplement on M74. UK: Publication of Inst of Civil Engineers; June 2011

[32] Prakhya G, Hopkin I, Hansford B. Construction of a concrete segmental arch bridge over a railway. Proceedings of the Institution of Civil Engineers—Bridge Engineering. 2019;**172**(3):226-240. DOI: 10.1680/ jbren.18.00027

[33] McKibbins L, Elmer R, Roberts K. Tunnels: Inspection, assessment and maintenance. In: CIRIA Technical Report C671. London: CIRIA Publication; January 2010

**114**

*Structural Integrity and Failure*

**References**

[1] Grant M, Pallet P. Temporary Works: Principles of Design and Construction. London, UK: ICE Publishing; 2012

[12] Bennion C. Temporary works associated with precast concrete bridge beam construction. In: Proceedings of the Institution of Structural Engineers, London, May 20. 1987. pp. 37-41

[13] André J, Beale R, Baptista AM. A Survey of Failures of Bridge Falsework Systems Since 1970. ICE—Forensic Engineering, Institute of Civil

[14] Wilkipedia—Bridge Failures. Available from: https://en.wikipedia. org/wiki/List\_of\_bridge\_failures

Engineers; 2012. 4/12

[Accessed: January 2020]

ISBN: 97820-12-407224-4

Publication; 2015

2005

[15] Broughton K, Gill J. Bridge Installation Techniques. London: ICE

[16] Khan MA. Accelerated Bridge Construction, Best Practices and Techniques. Elsevier Publication; 2015.

[17] BSI. BS EN 1990: 2002 + A1: 2005. Eurocode—Basis of Structural Design (Incorporating Corrigendum December 2008 and April 2010). London: BSI;

[18] BSI. BS EN 1991-1-6: 2005. Eurocode 1. Actions on Structures. General Actions. Actions during Execution. London, UK: BSI; 2005

[19] HSE Publication. Construction (Design and Management) Regulations (CDM). London: HSE Publication; 2015. Available from: https://www.hse.gov. uk/construction/cdm/2015/index.htm

[Accessed: January 2020]

[20] Thames Water Publication. Guidance on Piling, Heavy Loads, Excavation, Tunneling and Dewatering. Available from: https://developers. thameswater.co.uk/Developing-a-largesite/Planning-your-development/

[2] Bridle R, Sims F. The effect of bridge failures on UK technical policy and practice. Proceedings of the Institution of Civil Engineers: Engineering History and Heritage. 2009;**162**(1):39-49

[3] Smith D. Bridge failures. Proceedings of the Institution of Civil Engineers:

[4] HSE (Health and Safety Executive). Final Report of the Advisory Committee

[5] BSI. BS 5975: 2008+A1:2011. Code of Practice for Falsework. London, UK: BSI

[6] BS EN 12811-1. Temporary Works Equipment. Scaffolds. Performance Requirements and General Design; 2003

[7] BSI. BS EN 12812: 2008. Falsework. Performance Requirements and General

[8] Temporary works forum. Toolkits for Design. Available from: https:// www.twforum.org.uk/home [Accessed:

[9] Hewlett W, Jones A, Marchand S, Bell B. Re-visiting Bragg to keep UK's temporary works safe under EuroNorms. Proceedings of the ICE: Forensic Engineering. 2014;**167**(2):58-68

[10] Structural Safety Reports on Temp Works. Available from: https://www. structural-safety.org/ [Accessed:

[11] Soane A. Temporary works toolkit. Part 5: Temporary works failures—What are the common causes? The Structural

Engineer. 2017;**95**(1):24-26

Design. London, UK: BSI; 2008

on Falsework. The Bragg Report. London, UK: HMSO; 1976

Part. 1976;**1**(60):367-382

Publication; 1982

January 2020]

January 2020]

**Chapter 7**

**Abstract**

health monitoring

**1. Introduction**

**117**

Monitoring

Geometric Accuracy of Digital

We present an exploratory analysis of the geometric accuracy of digital twins generated for existing infrastructure using point clouds. The Level of Geometric Accuracy is a vital specification to measure the twinning quality of the resulting twins. However, there is a lack of a clear definition of the Level of Geometric Accuracy for twins generated in the operation and maintenance stage, especially for structural health monitoring purposes. We critically review existing industry applications and twinning methods. To highlight the technical challenges with creating high-fidelity digital replicas, we present a case study of twinning a bridge using real-world point clouds. We do not provide conclusive methods or results but envisage potential twinning strategies to achieve the desired geometry accuracy. This chapter aims to inform the future development of a geometric accuracy-based evaluation system for use in twinning and updating processes. Since a major barrier for a fully automated twinning workflow is the lack of rigorous interpretation of 'geometric accuracy' outside design environments, it is imperative to develop comprehensive standards to guide practitioners and researchers in order to achieve model certainty. As such, this chapter also aims to educate all stakeholders in order to minimise risk when drafting contracts and exchanging digital deliverables.

**Keywords:** digital twin, geometric accuracy, point clouds, bridge, structural

In the wake of the Notre Dame Cathedral fire, digital scans collected by Dr. Andrew Tallon [1] offer the hope for future restoration. One question raised is, what Level of Geometric Accuracy (LOGA) can the reconstructed digital replica achieve with respect to the physical asset? In the Architecture, Engineering and Construction (AEC) sector, operation and maintenance (O&M) costs can range between 60 and 80% of total life cycle costs, which is three times greater than the

cost of design and construction [2]. This demonstrates the significance of implementing intelligent asset documentation and structural health monitoring (SHM) approaches for existing built assets. Laser scanning has been widely used to

Twins for Structural Health

*Ruodan Lu, Chris Rausch, Marzia Bolpagni,*

*Ioannis Brilakis and Carl T. Haas*

### **Chapter 7**

## Geometric Accuracy of Digital Twins for Structural Health Monitoring

*Ruodan Lu, Chris Rausch, Marzia Bolpagni, Ioannis Brilakis and Carl T. Haas*

### **Abstract**

We present an exploratory analysis of the geometric accuracy of digital twins generated for existing infrastructure using point clouds. The Level of Geometric Accuracy is a vital specification to measure the twinning quality of the resulting twins. However, there is a lack of a clear definition of the Level of Geometric Accuracy for twins generated in the operation and maintenance stage, especially for structural health monitoring purposes. We critically review existing industry applications and twinning methods. To highlight the technical challenges with creating high-fidelity digital replicas, we present a case study of twinning a bridge using real-world point clouds. We do not provide conclusive methods or results but envisage potential twinning strategies to achieve the desired geometry accuracy. This chapter aims to inform the future development of a geometric accuracy-based evaluation system for use in twinning and updating processes. Since a major barrier for a fully automated twinning workflow is the lack of rigorous interpretation of 'geometric accuracy' outside design environments, it is imperative to develop comprehensive standards to guide practitioners and researchers in order to achieve model certainty. As such, this chapter also aims to educate all stakeholders in order to minimise risk when drafting contracts and exchanging digital deliverables.

**Keywords:** digital twin, geometric accuracy, point clouds, bridge, structural health monitoring

### **1. Introduction**

In the wake of the Notre Dame Cathedral fire, digital scans collected by Dr. Andrew Tallon [1] offer the hope for future restoration. One question raised is, what Level of Geometric Accuracy (LOGA) can the reconstructed digital replica achieve with respect to the physical asset? In the Architecture, Engineering and Construction (AEC) sector, operation and maintenance (O&M) costs can range between 60 and 80% of total life cycle costs, which is three times greater than the cost of design and construction [2]. This demonstrates the significance of implementing intelligent asset documentation and structural health monitoring (SHM) approaches for existing built assets. Laser scanning has been widely used to document and monitor existing conditions of real-world assets in the form of point clouds [3, 4]. A point cloud is an unstructured low-level digital representation, which by itself does not contain any meaningful information of the documented asset. A 'twinning' process is utilised to convert the low-level data into a high-level digital representation in a structured format, namely, a geometric Digital Twin (gDT) [5]. The gDT can be further enriched with other information, such as semantic meanings, texture, materials, damage, energy use, maintenance data and so forth from its physical twin using IoT technologies [6], to form an information enriched model over time, namely, a 'digital twin' (DT). 'Geometric accuracy' is a vital indicator that guides and describes the degree of spatial accuracy of the resulting twin. It is conventionally deemed as the Represented Accuracy [7] that denotes the standard deviation range to be achieved once the point cloud is twinned into a geometric model. Twinning a real-world asset is an interpretive process, where geometric accuracy largely depends on a modeller's experience and discretion [5]. While in their unstructured state, point clouds contain more geometric details than a resulting gDT created from the point cloud. Therefore, the resulting 'best-fit' gDTs are highly unlikely to be as accurate as the measured data (e.g., a point cloud) at the end of the twinning process [8]. This is also true for the automated methods since there is a trade-off between the achieved geometric accuracy and the quantity of information used for describing existing constructive objects in arbitrary shapes [9]. This occurs because the process of twinning involves simplifications to create polygon- or mesh-based primitives so that it 'smooths' discontinuities and gaps in point clouds [10]. This means that almost every object is approximated in order to transform point-cloud-based descriptors (in non-parametric formats) into parametric primitives [11]. **Figure 1** illustrates a series of components for a bridge asset where the point cloud is converted into bespoke gDT elements. However, since point clouds often contain defects, such as varying point density [12] and occlusions [13], it is difficult or often not feasible to achieve a desired LOGA for resulting gDTs [5]. When these conditions occur, what are realistic expectations for a modeller or of an automated method with regard to representing the reality and meeting the required accuracies for SHM?

requires '1 cm accuracy' or 'every element to be within a half centimetre'? This chapter explores these questions, aiming (1) to provide a critical review of existing specifications and twinning implementations, (2) to identify technical twinning challenges, and (3) to inform the establishment of a geometric-accuracy-based

*Geometric Accuracy of Digital Twins for Structural Health Monitoring*

The term 'LOD' was initially introduced by Vico Software [15]. Ambiguity of defining LOD stems largely from the fact that the American Institute of Architects (AIA) later adopted this concept and kept the acronym LOD but changed it to mean 'Level of Development' rather than 'Level of Detail' [16]. It was then superseded by the document AIA G202™ [17], which defines five progressively detailed levels of completeness: LOD100–LOD500. Based on the AIA protocols, the BIMForum [18] released another LOD specification, which was identical to those published in the AIA's Digital Practice Documents [19], but with two exceptions. First, a new LOD was designated as LOD350. Second, the LOD500 was removed from the specification. The geometric requirements of gDT elements of LOD300, LOD350, and LOD400 are defined in the same way in terms of accuracy. However, this

BIMForum document does not elaborate on what is implied by 'accurate' or how to measure it. Bolpagni [20–22] summarised the history of the LOX classification system in **Table 1**. Various new classification systems have been developed to accompany and complement the BIMForum's LOD specification. For example, New Zealand proposed a LOD specification that contains five maturity levels [23], each of which is a sum of different aspects that define the geometry and information of gDT elements. Among these, Level of Detail (LOD) and Level of Accuracy (LOA) do not specify any quantitative standards. Royal Institution of Chartered Surveyors [24] proposed a concept of building survey detail accuracy banding, which defines accuracies to be achieved for different surveyed features when an employer requires a customised geometric accuracy and confidence level. This banding, however, is tailored for designing building settings consisting of cuboids defined by length, width, and height. Similarly, Abualdenien and Borrmann [25] introduced a multi-LOD meta scheme, taking into account the geometric uncertainties by assigning quantitative fuzziness in cm. Again, the usefulness of this scheme in describing the twinning quality is unknown. To this end, Banfi [26] and Banfi et al. [27] proposed a new Grades of Generation (GoG) protocol for twinning highly complex historic structures from point clouds. LOGA was defined as the error resulting between the reconstructed objects and the point clouds using metrics such as the mean distance, median distance, and standard deviation. The USIBD specifications [7] were the first to provide the means to report twinning results of existing building conditions (from point clouds) based on standard deviation (stdev). It articulates the 'accuracy' as well as the five different LOAs (**Figure 2**) by which to represent real-world out-of-plumb geometries. Specifically, the Measured Accuracy represents the stdev range that is to be achieved to acquire a point cloud, regardless of the method used. In contrast, the Represented Accuracy represents the stdev range that is to be achieved when a point cloud is twinned. This guideline, however, does not indicate how to achieve and how to measure the Measured Accuracy and Represented Accuracy. As shown, various acronyms are used across countries and organisations. These acronyms are either identical or interchangeable, making them

evaluation system for twinning and updating.

*DOI: http://dx.doi.org/10.5772/intechopen.92775*

very challenging to be understood or adopted.

**119**

**2. Background**

**2.1 Existing LOX**

Numerous specifications termed as LOX (e.g. Level of Development and Level of Detail) have been developed to guide practitioners and researchers when creating digital models [14]. What do the LOX mean? How to measure whether the specifications were met? What is the best practice approach to reflect when the employer

**Figure 1.** *Customising shapes of bridge components and fitting them to point clusters.*

requires '1 cm accuracy' or 'every element to be within a half centimetre'? This chapter explores these questions, aiming (1) to provide a critical review of existing specifications and twinning implementations, (2) to identify technical twinning challenges, and (3) to inform the establishment of a geometric-accuracy-based evaluation system for twinning and updating.

### **2. Background**

document and monitor existing conditions of real-world assets in the form of point clouds [3, 4]. A point cloud is an unstructured low-level digital representation, which by itself does not contain any meaningful information of the documented asset. A 'twinning' process is utilised to convert the low-level data into a high-level digital representation in a structured format, namely, a geometric Digital Twin (gDT) [5]. The gDT can be further enriched with other information, such as semantic meanings, texture, materials, damage, energy use, maintenance data and so forth from its physical twin using IoT technologies [6], to form an information enriched model over time, namely, a 'digital twin' (DT). 'Geometric accuracy' is a vital indicator that guides and describes the degree of spatial accuracy of the resulting twin. It is conventionally deemed as the Represented Accuracy [7] that denotes the standard deviation range to be achieved once the point cloud is twinned into a geometric model. Twinning a real-world asset is an interpretive process, where geometric accuracy largely depends on a modeller's experience and discretion [5]. While in their unstructured state, point clouds contain more geometric details than a resulting gDT created from the point cloud. Therefore, the resulting 'best-fit' gDTs are highly unlikely to be as accurate as the measured data (e.g., a point cloud) at the end of the twinning process [8]. This is also true for the automated methods since there is a trade-off between the achieved geometric accuracy and the quantity of information used for describing existing constructive objects in arbitrary shapes [9]. This occurs because the process of twinning involves simplifications to create polygon- or mesh-based primitives so that it 'smooths' discontinuities and gaps in point clouds [10]. This means that almost every object is approximated in order to transform point-cloud-based descriptors (in non-parametric formats) into parametric primitives [11]. **Figure 1** illustrates a series of components for a bridge asset where the point cloud is converted into bespoke gDT elements. However, since point clouds often contain defects, such as varying point density [12] and occlusions [13], it is difficult or often not feasible to achieve a desired LOGA for resulting gDTs [5]. When these conditions occur, what are realistic expectations for a modeller or of an automated method with regard to representing the reality and meeting the

Numerous specifications termed as LOX (e.g. Level of Development and Level of Detail) have been developed to guide practitioners and researchers when creating digital models [14]. What do the LOX mean? How to measure whether the specifications were met? What is the best practice approach to reflect when the employer

required accuracies for SHM?

*Structural Integrity and Failure*

**Figure 1.**

**118**

*Customising shapes of bridge components and fitting them to point clusters.*

### **2.1 Existing LOX**

The term 'LOD' was initially introduced by Vico Software [15]. Ambiguity of defining LOD stems largely from the fact that the American Institute of Architects (AIA) later adopted this concept and kept the acronym LOD but changed it to mean 'Level of Development' rather than 'Level of Detail' [16]. It was then superseded by the document AIA G202™ [17], which defines five progressively detailed levels of completeness: LOD100–LOD500. Based on the AIA protocols, the BIMForum [18] released another LOD specification, which was identical to those published in the AIA's Digital Practice Documents [19], but with two exceptions. First, a new LOD was designated as LOD350. Second, the LOD500 was removed from the specification. The geometric requirements of gDT elements of LOD300, LOD350, and LOD400 are defined in the same way in terms of accuracy. However, this BIMForum document does not elaborate on what is implied by 'accurate' or how to measure it. Bolpagni [20–22] summarised the history of the LOX classification system in **Table 1**. Various new classification systems have been developed to accompany and complement the BIMForum's LOD specification. For example, New Zealand proposed a LOD specification that contains five maturity levels [23], each of which is a sum of different aspects that define the geometry and information of gDT elements. Among these, Level of Detail (LOD) and Level of Accuracy (LOA) do not specify any quantitative standards. Royal Institution of Chartered Surveyors [24] proposed a concept of building survey detail accuracy banding, which defines accuracies to be achieved for different surveyed features when an employer requires a customised geometric accuracy and confidence level. This banding, however, is tailored for designing building settings consisting of cuboids defined by length, width, and height. Similarly, Abualdenien and Borrmann [25] introduced a multi-LOD meta scheme, taking into account the geometric uncertainties by assigning quantitative fuzziness in cm. Again, the usefulness of this scheme in describing the twinning quality is unknown. To this end, Banfi [26] and Banfi et al. [27] proposed a new Grades of Generation (GoG) protocol for twinning highly complex historic structures from point clouds. LOGA was defined as the error resulting between the reconstructed objects and the point clouds using metrics such as the mean distance, median distance, and standard deviation. The USIBD specifications [7] were the first to provide the means to report twinning results of existing building conditions (from point clouds) based on standard deviation (stdev). It articulates the 'accuracy' as well as the five different LOAs (**Figure 2**) by which to represent real-world out-of-plumb geometries. Specifically, the Measured Accuracy represents the stdev range that is to be achieved to acquire a point cloud, regardless of the method used. In contrast, the Represented Accuracy represents the stdev range that is to be achieved when a point cloud is twinned. This guideline, however, does not indicate how to achieve and how to measure the Measured Accuracy and Represented Accuracy. As shown, various acronyms are used across countries and organisations. These acronyms are either identical or interchangeable, making them very challenging to be understood or adopted.


**2.2 Industry applications**

*Measured and represented accuracy [7].*

**Country/ region**

UK NBS BIM

China SZGWS

**Table 1.**

**Figure 2.**

**121**

(Shenzhen)

Toolkit

**Document Year LOX Whole**

*Geometric Accuracy of Digital Twins for Structural Health Monitoring*

Belgium ABEB-VBA 2015 Level of

*DOI: http://dx.doi.org/10.5772/intechopen.92775*

Germany D&R 2015 Level of

USA BIMForum 2015 Level of

UK AEC (UK) 2015 Level of Definition

*Comparison of the LOX classification system across countries.*

China CBC 2014 Level of Detail √√ √ √

Development

Development

Development

Associated Attribute Information

Level of Information

Level of Information Grade/Level of Detail

**gDT**

Element Geometry √ √

2015 LOD √ √√

2015 Level of Detail √ √

**gDT element**

√ √

**Geometric data/info**

√√ √

√√ √

√ √

√ √

√√ √ √ √

√ √

**Nongeometric data/info**

Leading software vendors provide advanced commercial twinning solutions, which are currently semi-automated processes at best. *ClearEdge3D Edgewise* software can automatically extract geometric features for industrial constructive elements and basic architectural elements using cross-sections in user-cropped regions followed by fitting 3D shapes from a library of preloaded features [28, 29]. This means, the current practice can achieve a high degree of automation of twinning if the resulting geometries are assumed to be generic or pre-defined. However, in the context of SHM, this assumption


### *Geometric Accuracy of Digital Twins for Structural Health Monitoring DOI: http://dx.doi.org/10.5772/intechopen.92775*

### **Table 1.**

**Country/ region**

Hong Kong

USA Department

*Structural Integrity and Failure*

of VA

Penn State University

US Army Corps of Engineers (USACE)

UK CIC BIM

**120**

Protocol

Germany BMVBS 2013 Level of

Canada AEC 2014 Level of

Australia BCPP 2014 Level of

France Le Moniteur 2014 Level of Detail/

**Document Year LOX Whole**

2010 Level of

Australia CRC 2009 Object Data

Australia NATSPEC 2011 Level of

USA NYC DDC 2012 Model Level of

UK PAS 1192–2 2013 Level of Model

Denmark BIPS 2007 Information Level √√ √ √

Levels/Level of Detail

Development

Development

Development/ Level of Development

Development

Development

Definition

Level of Model Detail

Level of Model Information

Development

Development

Level of Development

Development

Level of Information

Level of Coordination

Netherland BIM 2014 Information Level √√ √ √

Singapore BCA 2013 Level of Detail √√ √

USC 2012 Level of Detail √ √

2012 Level of

2012 Level of

USA Vico Software 2011 Level of Detail √√ √ √

HKIBIM 2011 Level of Detail √√ √

**gDT**

**gDT element** **Geometric data/info**

√√ √

√√ √

√√ √

√√ √

√√ √

√√ √

√ √

√√ √

√√ √

√√ √

√ √

—— — —

√ √

√√ √ √

Model Granularity √√ √

2013 Level of Detail √ —— —

√ √

Level of Detail √ √

Level of Accuracy √√ √

**Nongeometric data/info**

*Comparison of the LOX classification system across countries.*

**Figure 2.** *Measured and represented accuracy [7].*

### **2.2 Industry applications**

Leading software vendors provide advanced commercial twinning solutions, which are currently semi-automated processes at best. *ClearEdge3D Edgewise* software can automatically extract geometric features for industrial constructive elements and basic architectural elements using cross-sections in user-cropped regions followed by fitting 3D shapes from a library of preloaded features [28, 29]. This means, the current practice can achieve a high degree of automation of twinning if the resulting geometries are assumed to be generic or pre-defined. However, in the context of SHM, this assumption is unrealistic if a millimetre twinning accuracy is required. Twinning arbitrary geometries using point clouds is quite challenging [30]. Most authoring tools are designed to model orthogonally, or along local coordinate axes. They employ the use of rigid-body parameters to design construction elements by defining cross-sectional shapes, length, width and height parameters, whereas in the real world, as-is components are often warped, off-plumb, or contain deflections [31]. While finite element analysis and multi-physics engines can be used to predict elastic and plastic distortions in materials [32], current digitization workflows that produce parametric objects cannot capture distortion such as bowing in a beam or welding distortion in steel frames. Errors are introduced when the as-is geometries are twinned as being plumb and subjected to rigid-body physics [33]. In this case, geometry deviation analysis is important because unfitted geometries would potentially reduce the reliability of the gDT to be used for structural analysis and defect detection for SHM purposes. Current authoring applications are not capable of carrying out geometry deviation analysis for point clouds. The actual geometry deviation analysis requires third-party middleware software to interpret and investigate. *FARO BuildIT Construction* [34] is the most recent verification software for dimensional quality control (QC) process. Measured data collected from laser scanners can be compared against a gDT to analyse geometric deviations (**Figure 3**). However, it is worth noting that the nature and origin of a deviation is not identified in the analysis directly. Specifically, the analysis itself is often in the form of a 'heat map', where deviations are plotted in colours that correspond to a specific magnitude and direction from a perfect state (i.e. 0 mm deviation). However, point clouds contain voids and sparse measurements, which as directly classified deviations. These false positive measurements make it difficult to interpret the deviation analysis results. Users must manually inspect datasets to observe and detect gross errors or missing components. Currently, there are no available automated solutions for this in existing middleware. In addition, once deviations are identified through deviation analysis and manual interpretation, users must also manually apply changes to update the authoring gDTs. This is currently a large challenge since there is very little research into automated updating of gDT from point clouds [35, 36].

### **2.3 Existing research methods**

Automated methods have been proposed to streamline the twinning process (**Table 2**) [37, 38]. However, user intervention was still required for some crucial

**Point cloud** 

**123**

**real (R) or synthetic (S)**

[39] R

[40] S

[41] S

[42] R

[38] R

[43] R

[44] R

[45] R

[37] R

[46] R

[47] R

[11] R

[27] R

[48] R

[49] R

[50]

[5] R

**Table 2.**

*Twinning methods and evaluation*

 *metrics.*

—

 √

 √ √

—

 √

  √

 √

√

 

   √

 √√

 √

A

——

 —

Cloud-to-cloud

 distance

√

 √

I

√

 √

 √ √

 √

A A

Standard deviation Standard deviation

Thresholding

/√

A/I

 

——

 —

Control points and

point-to-gDT

 √

√

 A/I

I

 √

√

 √

A

Progressive

Cylinder radius and orientation

CloudCompare

densification

A

Mean

point-surface

 distance

√ √

√

 √ √√

 √

A A/I

Plane positioning/sizing

 error

fitting/orientation/dimensional

 error,

*Geometric Accuracy of Digital Twins for Structural Health Monitoring*

Visual assessment

√

√ √

√

 √

I

 

 √ √√

 √

A

——

 —

Hausdorff distance

*DOI: http://dx.doi.org/10.5772/intechopen.92775*

Centroid Euclidean distance, area difference

(width and length), angular difference

√

A

Minimum Euclidian distance and

thresholding

**authenticity**

**Manual**  **(**√**) twining process**

**()/automated**

**Structure**

**LOGA**

**Manual ()/**

**Micro (I)/macro**

**LODGA assessment**

**method/metrics**

**automated**

**LOGA**

**assessment**

**assessment**

 **(**

√**)**

**(A) levels**

**LOGA**

**completeness**

**assessment**

**availability**


### *Geometric Accuracy of Digital Twins for Structural Health Monitoring DOI: http://dx.doi.org/10.5772/intechopen.92775*

is unrealistic if a millimetre twinning accuracy is required. Twinning arbitrary geometries using point clouds is quite challenging [30]. Most authoring tools are designed to model orthogonally, or along local coordinate axes. They employ the use of rigid-body parameters to design construction elements by defining cross-sectional shapes, length, width and height parameters, whereas in the real world, as-is components are often warped, off-plumb, or contain deflections [31]. While finite element analysis and multi-physics engines can be used to predict elastic and plastic distortions in materials [32], current digitization workflows that produce parametric objects cannot capture distortion such as bowing in a beam or welding distortion in steel frames. Errors are introduced when the as-is geometries are twinned as being plumb and subjected to rigid-body physics [33]. In this case, geometry deviation analysis is important because unfitted geometries would potentially reduce the reliability of the gDT to be used for structural analysis and defect detection for SHM purposes. Current authoring applications are not capable of carrying out geometry deviation analysis for point clouds. The actual geometry deviation analysis requires third-party middleware software to interpret and investigate. *FARO BuildIT Construction* [34] is the most recent verification software for dimensional quality control (QC) process. Measured data collected from laser scanners can be compared against a gDT to analyse geometric deviations (**Figure 3**). However, it is worth noting that the nature and origin of a deviation is not identified in the analysis directly. Specifically, the analysis itself is often in the form of a 'heat map', where deviations are plotted in colours that correspond to a specific magnitude and direction from a perfect state (i.e. 0 mm deviation). However, point clouds contain voids and sparse measurements, which as directly classified deviations. These false positive measurements make it difficult to interpret the deviation analysis results. Users must manually inspect datasets to observe and detect gross errors or missing components. Currently, there are no available automated solutions for this in existing middleware. In addition, once deviations are identified through deviation analysis and manual interpretation, users must also manually apply changes to update the authoring gDTs. This is currently a large challenge since there is very little research into auto-

Automated methods have been proposed to streamline the twinning process (**Table 2**) [37, 38]. However, user intervention was still required for some crucial

*Deviation analysis of a pipe assembly (point cloud data courtesy of FARO Technologies, Inc.).*

mated updating of gDT from point clouds [35, 36].

**2.3 Existing research methods**

*Structural Integrity and Failure*

**Figure 3.**

**122**

**Table 2.**

 *metrics.* steps [44]. Zhang et al. [40] and Laefer and Truong-Hong [47] produced gDTs for bridges and industry plants, but without a geometric deviation assessment. Anil et al. [39] were among the pioneers who discussed in depth the problem of geometric deviation. They suggested using *minimum Euclidean distance* and *thresholding* [49] as metrics to evaluate the fitting quality (CAD model against point clouds). The deviation analysis at macro level (for the whole structure) was performed using a commercial software application (i.e. Polyworks v9). Bonduel et al. [46] suggested assessing the twinning results at both macro and micro levels. They used *CloudCompare* to analyse the deviations between a point cloud and a manually generated building floor gDT. They also discussed the achieved represented accuracy using LOAs provided by USIBD. Then, *Hausdorff distance* was proposed to measure the fitting deviation of a mesh-based building gDT reconstructed from a synthetic point cloud [41]. Thomson and Boehm [42] suggested using *Euclidean distance* and *area difference* based on the width and length, and angular difference to measure the fitting quality of walls. Although these measurements can assess elementwise quality, they are tailored for generic building walls in cuboid shapes. Similarly, Valero et al. [43] assessed fitting deviations of individual furniture objects and walls using *orientation*, *dimension*, *positioning*, and *sizing* metrics, assuming these objects consist of planar surfaces. Lu et al. [5] proposed an automated fitting method to twin bridge components. They gauged the fitting accuracy using *Cloud-to-Cloud* (*C2C*) *distance* metrics—a similar metric used by Shirowzhan et al. [51]. However, the geometric deviation evaluation was performed only at the macro level. NURBS-based methods [27, 44, 45, 48] were employed to reconstruct geometric surfaces for building, industry plant, and historic building elements. Note that the generation of compound pipes requires user intervention to group a set of cylindrical segments followed by automatically fitting surfaces [44]. Likewise, highly complex historic structures require manual surface generation, although extremely high twinning accuracy was reported [27]. *Point-to-surface* distance metrics were used to evaluate the fitting quality [44, 48]. In contrast, Barazzetti [45] used the commercial package Geomagic Studio to evaluate the fitting accuracy of the NURBS curves through a *progressive densification* (i.e. multi-resolution) approach. As shown, there is no fully automatic method to produce geometrically highly accurate twins for existing assets. Also, more comprehensive evaluation metrics need to be established for assessing twinning quality.

*ET* ¼ *ERA* þ *EM* þ *ER*, (1)

where *ERA* is the ranging error associated with the laser scanner, *EM* is the measured error introduced during scanning and registration, and *ER* is the represented error resulting from the process of scan-to-gDT. It is important to specify the error associated with each source independent of each other since they are assumed to be mutually exclusive. In this chapter, we only focus on discussing the represented error *ER*, which is independent of the sensor, or parameters of the documented object, or scanning and registration methods. It is related to the manner with which the measured point cloud is being transformed into the outcome, i.e.

As mentioned earlier, existing authoring software packages are by nature orthographic modelling tools. The challenge with using these software packages becomes how to represent a structure's up-to-date conditions. To complicate matters further, the as-weathered, as-damaged, or as-deviated information of existing assets further increases the representation difficulty. Fitting deviations will be generated and propagated if these conditions are represented in an over-simplified fashion. In addition, sparseness, hidden, or concealed conditions are often encountered in point clouds, making it difficult or impossible to twin constructive objects with certainty. Thus, *ER* is the accumulated error from the geometric deviations and the

**Figure 4** demonstrates current efforts on parametric bridge design [54]. The essential feature for bridges is the horizontal and vertical alignments, which control the parametric relationships and dependencies between assembly systems and all components. The deck cross-sections are then driven by the bridge alignment curves. They are profiles that are used in conjunction with the alignment to derive

When SHM and retrofit planning is being performed, accurate as-is condition data is required regardless of the availability of the as-designed parametric information. Point clouds can depict the as-is geometries of an asset using thousands of data points. However, maintaining the dimensional accuracy and geometric fidelity of a given bridge point cloud is challenging because the usefulness of topological and geometric constraints is limited to very simple geometric shapes and spatial relationships. As-is geometries do not exhibit a parametric pattern with respect to the initial primitives used to create the as-designed model. **Figure 5** illustrates the non-orthogonal geometries of a real-world bridge point cloud cannot be fitted using

*Parametric cross section design of a slab-beam bridge with user-defined geometric constraints [54].*

a gDT and describes the extent the gDT matches the acquired points.

*Geometric Accuracy of Digital Twins for Structural Health Monitoring*

*DOI: http://dx.doi.org/10.5772/intechopen.92775*

propagation of data uncertainty.

**Figure 4.**

**125**

the overall 3D shape of the bridge deck.

### **3. Case study**

Previous sections have discussed that twinning existing assets using point clouds is restricted by current software tools which are limited in their ability to represent out-of-plumb conditions and non-rigid formations. It is also restricted by the limits of the data itself. This section discusses this problem in detail through a case study.

Laser scanning can sample an object's surface as it exists with highly accurate spatial measurements in the form of 3D points. If the documented object is not straight or plumb, the scanner can capture its geometric status. Theoretically, a terrestrial laser scanner such as the FARO Focus 3D X330 [52] has a ranging error of 2 mm at 10 m, equating to a systematic measurement error at around of 1σ at 10 m. However, the measured accuracy is affected by many factors, including the standard deviation of the sensor, registration methods, material type being scanned, low temperature, bad weather, and strong sunlight [53]. The overall twinning error *ET* can be expressed as a combination of three primary sources of error:

*Geometric Accuracy of Digital Twins for Structural Health Monitoring DOI: http://dx.doi.org/10.5772/intechopen.92775*

steps [44]. Zhang et al. [40] and Laefer and Truong-Hong [47] produced gDTs for bridges and industry plants, but without a geometric deviation assessment. Anil et al. [39] were among the pioneers who discussed in depth the problem of geometric deviation. They suggested using *minimum Euclidean distance* and *thresholding* [49] as metrics to evaluate the fitting quality (CAD model against point clouds). The deviation analysis at macro level (for the whole structure) was performed using

suggested assessing the twinning results at both macro and micro levels. They used *CloudCompare* to analyse the deviations between a point cloud and a manually generated building floor gDT. They also discussed the achieved represented accuracy using LOAs provided by USIBD. Then, *Hausdorff distance* was proposed to measure the fitting deviation of a mesh-based building gDT reconstructed from a synthetic point cloud [41]. Thomson and Boehm [42] suggested using *Euclidean distance* and *area difference* based on the width and length, and angular difference to measure the fitting quality of walls. Although these measurements can assess elementwise quality, they are tailored for generic building walls in cuboid shapes. Similarly, Valero et al. [43] assessed fitting deviations of individual furniture objects and walls using *orientation*, *dimension*, *positioning*, and *sizing* metrics, assuming these objects consist of planar surfaces. Lu et al. [5] proposed an automated fitting method to twin bridge components. They gauged the fitting accuracy using *Cloud-to-Cloud* (*C2C*) *distance* metrics—a similar metric used by Shirowzhan et al. [51]. However, the geometric deviation evaluation was performed only at the macro level. NURBS-based methods [27, 44, 45, 48] were employed to reconstruct geometric surfaces for building, industry plant, and historic building elements. Note that the generation of compound pipes requires user intervention to group a set of cylindrical segments followed by automatically fitting surfaces [44]. Likewise, highly complex historic structures require manual surface generation, although extremely high twinning accuracy was reported [27]. *Point-to-surface* distance metrics were used to evaluate the fitting quality [44, 48]. In contrast, Barazzetti [45] used the commercial package Geomagic Studio to evaluate the fitting accuracy of the NURBS curves through a *progressive densification* (i.e. multi-resolution) approach. As shown, there is no fully automatic method to produce geometrically highly accurate twins for existing assets. Also, more comprehensive evaluation

a commercial software application (i.e. Polyworks v9). Bonduel et al. [46]

metrics need to be established for assessing twinning quality.

Previous sections have discussed that twinning existing assets using point clouds is restricted by current software tools which are limited in their ability to represent out-of-plumb conditions and non-rigid formations. It is also restricted by the limits of the data itself. This section discusses this problem in detail through a

Laser scanning can sample an object's surface as it exists with highly accurate spatial measurements in the form of 3D points. If the documented object is not straight or plumb, the scanner can capture its geometric status. Theoretically, a terrestrial laser scanner such as the FARO Focus 3D X330 [52] has a ranging error of 2 mm at 10 m, equating to a systematic measurement error at around of 1σ at 10 m. However, the measured accuracy is affected by many factors, including the standard deviation of the sensor, registration methods, material type being scanned, low temperature, bad weather, and strong sunlight [53]. The overall twinning error *ET* can be expressed as a combination of three primary

**3. Case study**

*Structural Integrity and Failure*

case study.

sources of error:

**124**

$$E\_T = E\_{RA} + E\_M + E\_R,\tag{1}$$

where *ERA* is the ranging error associated with the laser scanner, *EM* is the measured error introduced during scanning and registration, and *ER* is the represented error resulting from the process of scan-to-gDT. It is important to specify the error associated with each source independent of each other since they are assumed to be mutually exclusive. In this chapter, we only focus on discussing the represented error *ER*, which is independent of the sensor, or parameters of the documented object, or scanning and registration methods. It is related to the manner with which the measured point cloud is being transformed into the outcome, i.e. a gDT and describes the extent the gDT matches the acquired points.

As mentioned earlier, existing authoring software packages are by nature orthographic modelling tools. The challenge with using these software packages becomes how to represent a structure's up-to-date conditions. To complicate matters further, the as-weathered, as-damaged, or as-deviated information of existing assets further increases the representation difficulty. Fitting deviations will be generated and propagated if these conditions are represented in an over-simplified fashion. In addition, sparseness, hidden, or concealed conditions are often encountered in point clouds, making it difficult or impossible to twin constructive objects with certainty. Thus, *ER* is the accumulated error from the geometric deviations and the propagation of data uncertainty.

**Figure 4** demonstrates current efforts on parametric bridge design [54]. The essential feature for bridges is the horizontal and vertical alignments, which control the parametric relationships and dependencies between assembly systems and all components. The deck cross-sections are then driven by the bridge alignment curves. They are profiles that are used in conjunction with the alignment to derive the overall 3D shape of the bridge deck.

When SHM and retrofit planning is being performed, accurate as-is condition data is required regardless of the availability of the as-designed parametric information. Point clouds can depict the as-is geometries of an asset using thousands of data points. However, maintaining the dimensional accuracy and geometric fidelity of a given bridge point cloud is challenging because the usefulness of topological and geometric constraints is limited to very simple geometric shapes and spatial relationships. As-is geometries do not exhibit a parametric pattern with respect to the initial primitives used to create the as-designed model. **Figure 5** illustrates the non-orthogonal geometries of a real-world bridge point cloud cannot be fitted using

**Figure 4.** *Parametric cross section design of a slab-beam bridge with user-defined geometric constraints [54].*

generic shapes, such as cuboids, in an orthogonal fashion. The modelled slabs do not follow the point cloud and produce fitting deviations when they are joined at sharp angles (**Figure 5a**). These deviations become smaller if the cross-sections are outlined with as-is 2D shapes. However, the bridge gDT does not necessarily close better and become manifold as the fitting quality is improved at the expense of broken or clashing connections (**Figure 5b**). This is especially true when twinning point clouds of pipes with sags, beams and columns with welding distortion or walls that are skewed. Adjacent components do not fit to properly watertight connections unless they are joined at right angles. For example, **Figure 6** illustrates part of a piping system generated using point clouds. The local deviation is reduced from 30 to 1 mm when watertight connections are not used. Given the challenge with the mediation of non-parametric real-world deviations to parametric model primitives, modellers are often forced to leave objects 'slightly off-axis' or perform 'unnatural shape editing' by eliminating or ignoring as many overlapping and joint warnings as possible in order to match the points.

When facing occlusions and damage conditions, the geometric accuracy has a reliance on human perception followed by inferring the hidden information based on assumptions. For example, a bearing plays an important role in a bridge, but its surface is less than 1% of that of the deck slab and has a complex composition. These characteristics make it difficult to be fully captured by a laser sensor (**Figure 7a**). In addition, point clouds need to be down sampled before feeding into in-memorysystem-based authoring tools or automated algorithms that cannot handle huge datasets. The down sampling is often performed using a third-party processing

> software application, which applies generic filters to evenly down sample the points without considering local geometric context. While this is certainly helpful and creates beneficial data compression, the resulting datasets often lose information along the way (i.e. sparse areas or smaller objects will have little to measurements). Thus, only a few points are retained for the bearing surface which does not provide enough information to support the twinning task and result in geometry uncertainties (**Figure 7b**). The interpretation of bearing shapes largely depends on

*Fitting cylinders to piping point clouds (point cloud data courtesy of FARO Technologies, Inc.).*

*Geometric Accuracy of Digital Twins for Structural Health Monitoring*

*DOI: http://dx.doi.org/10.5772/intechopen.92775*

*Bearing gDT generation under uncertainty. (a) Original point cloud; (b) down-sampled point cloud;*

*(c) bearing shapes and connection problem; (d) (e) geometry uncertainty in point clouds.*

**Figure 6.**

**Figure 7.**

**127**

### **Figure 5.**

*Fitting geometric shapes to bridge point clouds. (a) Point clouds fitted by cuboids; (b) point clouds fitted by best-fit shapes.*

*Geometric Accuracy of Digital Twins for Structural Health Monitoring DOI: http://dx.doi.org/10.5772/intechopen.92775*

**Figure 6.**

generic shapes, such as cuboids, in an orthogonal fashion. The modelled slabs do not follow the point cloud and produce fitting deviations when they are joined at sharp angles (**Figure 5a**). These deviations become smaller if the cross-sections are outlined with as-is 2D shapes. However, the bridge gDT does not necessarily close better and become manifold as the fitting quality is improved at the expense of broken or clashing connections (**Figure 5b**). This is especially true when twinning point clouds of pipes with sags, beams and columns with welding distortion or walls that are skewed. Adjacent components do not fit to properly watertight connections unless they are joined at right angles. For example, **Figure 6** illustrates part of a piping system generated using point clouds. The local deviation is reduced from 30 to 1 mm when watertight connections are not used. Given the challenge with the mediation of non-parametric real-world deviations to parametric model primitives, modellers are often forced to leave objects 'slightly off-axis' or perform 'unnatural shape editing' by eliminating or ignoring as many overlapping and joint warnings as

When facing occlusions and damage conditions, the geometric accuracy has a reliance on human perception followed by inferring the hidden information based on assumptions. For example, a bearing plays an important role in a bridge, but its surface is less than 1% of that of the deck slab and has a complex composition. These characteristics make it difficult to be fully captured by a laser sensor (**Figure 7a**). In addition, point clouds need to be down sampled before feeding into in-memorysystem-based authoring tools or automated algorithms that cannot handle huge datasets. The down sampling is often performed using a third-party processing

*Fitting geometric shapes to bridge point clouds. (a) Point clouds fitted by cuboids; (b) point clouds fitted by*

possible in order to match the points.

*Structural Integrity and Failure*

**Figure 5.**

**126**

*best-fit shapes.*

*Fitting cylinders to piping point clouds (point cloud data courtesy of FARO Technologies, Inc.).*

software application, which applies generic filters to evenly down sample the points without considering local geometric context. While this is certainly helpful and creates beneficial data compression, the resulting datasets often lose information along the way (i.e. sparse areas or smaller objects will have little to measurements). Thus, only a few points are retained for the bearing surface which does not provide enough information to support the twinning task and result in geometry uncertainties (**Figure 7b**). The interpretation of bearing shapes largely depends on

### **Figure 7.**

*Bearing gDT generation under uncertainty. (a) Original point cloud; (b) down-sampled point cloud; (c) bearing shapes and connection problem; (d) (e) geometry uncertainty in point clouds.*

modeller's knowledge and discretion, which could introduce connection problems (e.g., clashing/gaps) (**Figure 7c**). Uncertainty increases when working with point clouds containing skewness and noise (**Figure 7d** and **e**). Although methods have been suggested to work under occlusions and sparseness [5, 55], the certainty of the resulting models is rarely investigated.

**Figure 8** shows an example of a bridge where little-to-no measurements were captured in the girder areas due to a limited line of sight [56]. Like many existing works, both the manual and the automated method inferred specific girder profiles and produced gDTs with detailed dimensions using engineering knowledge. Then, *Cloud-to-Cloud* (*C2C*) distance could be used [5] to compute the deviation between the point clouds sampled from the manually generated gDTs (*Manual*) and the automated ones (*Auto*), and the real point clouds (*Real*):

$$\text{C2C} = \max\left(\overline{\text{dist}}\_{\text{Manual or Auto/Real}}, \overline{\text{dist}}\_{\text{Real}/\text{Manual or Auto}}\right), \tag{2}$$

unchanged. Yet still, the improved accuracy only aligns with USIBD's LOA 20 (lower range: 15 mm, and upper range: 5 cm, at 2σ) [7], corresponding to a relatively low accuracy standard. USIBD provides different represented accuracy levels, but it does not specify how to measure it. For example, we can only use a couple of reference points to estimate the accuracy. It is the averaged fraction between pair reference-point distances in the registered scan data and the corresponding pair on-

*Geometric Accuracy of Digital Twins for Structural Health Monitoring*

pair reference � point distance pair on � site or gDT point distance � �

where *M* is the number of investigated pair-wise distance. Then, it is possible to acquire acc that aligns with a higher LOA in USIBD. By contrast, unlike acc, *C2C* is an estimation using thousands of calculated points. Therefore, the resulting *C2C*based accuracy is almost surely not going to achieve an expected 'high accuracy' level (e.g., �10 mm or USIBD's LOA 30 onwards). The *C2C* comparison between the *Auto* and *Real* revealed that points sampled from bottom flanges of girders were well matched with the original points while the mismatched points were mainly from the central part of the deck slab where points were not evenly distributed. This is attributed to the undulating-surfaces of the gDT generated using the proposed *ConcaveHull alpha-shape* algorithm (**Figure 9**). Local indentations or bumps are generated when *alpha* value is too small to smooth out the surface affected by unavoidable noise, raising the fitting deviations. However, optimising the *alpha* value is difficult because an indentation, for instance, could be due to a defect or a hole but could also due to localised sparse and unevenly distributed points. In addition, although the *ConcaveHull alpha-shape* algorithm can describe slab geome-

*i*

, (3)

site or gDT point distances:

acc <sup>¼</sup> <sup>1</sup> *M* X *M*

*DOI: http://dx.doi.org/10.5772/intechopen.92775*

*i*¼1

tries in a 2D space, it oversimplifies a 3D space.

*Geometric deviation with incomplete girder profiles in occluded areas.*

**Figure 9.**

**129**

where dist is the estimated distance between a compared point cloud (i.e. Manual or Auto) and a reference point cloud (i.e. *Real*). Non-trivial fitting deviations occurred and raised the overall macro-level deviation (C2C*Auto*—12.5 cm and C2C*Manual*—5.7 cm) [5]. These significant fitting deviations were due to the occluded areas, as no measurements were available to compare against, resulting in an incorrect gDT from a geometric accuracy standpoint. This solution is straightforward since it does not take the modelling uncertainties into account. It simply takes uncertain areas as errors. **Figure 9** illustrates that the fitting deviation was drastically reduced by approximately 70% (C2C*Auto*—4.2 cm) if we replace the complete girder profiles with unclosed mesh-based gDTs while other parts remain

**Figure 8.** *Geometric deviation with complete girder profiles in occluded areas.*

*Geometric Accuracy of Digital Twins for Structural Health Monitoring DOI: http://dx.doi.org/10.5772/intechopen.92775*

modeller's knowledge and discretion, which could introduce connection problems (e.g., clashing/gaps) (**Figure 7c**). Uncertainty increases when working with point clouds containing skewness and noise (**Figure 7d** and **e**). Although methods have been suggested to work under occlusions and sparseness [5, 55], the certainty of the

**Figure 8** shows an example of a bridge where little-to-no measurements were captured in the girder areas due to a limited line of sight [56]. Like many existing works, both the manual and the automated method inferred specific girder profiles and produced gDTs with detailed dimensions using engineering knowledge. Then, *Cloud-to-Cloud* (*C2C*) distance could be used [5] to compute the deviation between the point clouds sampled from the manually generated gDTs (*Manual*) and the

*C*2*C* ¼ max dist*Manual or Auto=Real*, dist*Real=Manual or Auto*

where dist is the estimated distance between a compared point cloud (i.e. Manual or Auto) and a reference point cloud (i.e. *Real*). Non-trivial fitting deviations occurred and raised the overall macro-level deviation (C2C*Auto*—12.5 cm and C2C*Manual*—5.7 cm) [5]. These significant fitting deviations were due to the

occluded areas, as no measurements were available to compare against, resulting in an incorrect gDT from a geometric accuracy standpoint. This solution is straightforward since it does not take the modelling uncertainties into account. It simply takes uncertain areas as errors. **Figure 9** illustrates that the fitting deviation was drastically reduced by approximately 70% (C2C*Auto*—4.2 cm) if we replace the complete girder profiles with unclosed mesh-based gDTs while other parts remain

, (2)

resulting models is rarely investigated.

*Structural Integrity and Failure*

**Figure 8.**

**128**

*Geometric deviation with complete girder profiles in occluded areas.*

automated ones (*Auto*), and the real point clouds (*Real*):

unchanged. Yet still, the improved accuracy only aligns with USIBD's LOA 20 (lower range: 15 mm, and upper range: 5 cm, at 2σ) [7], corresponding to a relatively low accuracy standard. USIBD provides different represented accuracy levels, but it does not specify how to measure it. For example, we can only use a couple of reference points to estimate the accuracy. It is the averaged fraction between pair reference-point distances in the registered scan data and the corresponding pair onsite or gDT point distances:

$$\overline{\text{acc}} = \frac{1}{M} \sum\_{i=1}^{M} \left( \frac{\text{pair reference} - \text{point distance}}{\text{pair on } - \text{site or gDT point distance}} \right)\_i,\tag{3}$$

where *M* is the number of investigated pair-wise distance. Then, it is possible to acquire acc that aligns with a higher LOA in USIBD. By contrast, unlike acc, *C2C* is an estimation using thousands of calculated points. Therefore, the resulting *C2C*based accuracy is almost surely not going to achieve an expected 'high accuracy' level (e.g., �10 mm or USIBD's LOA 30 onwards). The *C2C* comparison between the *Auto* and *Real* revealed that points sampled from bottom flanges of girders were well matched with the original points while the mismatched points were mainly from the central part of the deck slab where points were not evenly distributed. This is attributed to the undulating-surfaces of the gDT generated using the proposed *ConcaveHull alpha-shape* algorithm (**Figure 9**). Local indentations or bumps are generated when *alpha* value is too small to smooth out the surface affected by unavoidable noise, raising the fitting deviations. However, optimising the *alpha* value is difficult because an indentation, for instance, could be due to a defect or a hole but could also due to localised sparse and unevenly distributed points. In addition, although the *ConcaveHull alpha-shape* algorithm can describe slab geometries in a 2D space, it oversimplifies a 3D space.

**Figure 9.** *Geometric deviation with incomplete girder profiles in occluded areas.*

### **4. Prospective twinning methods and deviation analysis**

The analysis provided in the previous section demonstrates that real-world conditions are seldom orthogonal and perfect, rendering it extremely difficult to perform high-fidelity twinning with a geometric accuracy on the millimetre scale. Commonly used representation models include but are not limited to: implicit representation such as mathematical formula-based methods [57], Boundary Representation such as polygon- and mesh-based methods [41], Constructive Solid Geometry [58], Swept Solid Representation [47], and NURBS representation [45, 48]. Depending on the nature of defects, the as-damaged geometries may be represented in different ways. **Figure 10** illustrates the vision of the concept of an as-damaged bridge gDT implemented for the inspection work. The method proposed by Hüthwohl et al. [59] can be used to integrate superficial defects such as cracks, efflorescence, corrosion, and slight spalling [**Figure 10a**—(3) and (4)] to the affected element using the back-project technology [59] (**Figure 10b**). In contrast, major defects, such as severe spalling, cavity and pothole [**Figure 10a**—(1) and (2)], are significantly different in geometry compared to their surrounding healthy (i.e. good condition) surfaces. The method proposed by Lu et al. [5] can be used to represent healthy elements; however, it cannot describe the unhealthy areas precisely, due to the extrusion-based twinning nature. Finer representation, such as mesh-based and NURBS-based twinning techniques [50], can be employed to handle the geometry complexity of significant defects in a precise manner (**Figure 10b**). The more variable the defect, the greater the geometric twinning needs to rely on non-parametric representation such as mesh format. One promising solution to produce a gDT that takes the as-damage information into account is to first detect unhealthy areas [60], followed by twinning these unhealthy areas using finer twinning techniques based on their type and size. However, the mesh polygon resolution should not degrade the rendered presentation. This requires an intelligent a priori scheme to resample the point clouds based on the geometric complexity of a sampled surface [61, 62].

Construction elements with different scales may require different twinning techniques. For example, extrusions could be efficient for twinning slab segments; however, they cannot be directly applied to bearings. This means a gDT is highly likely to contain more than one data representation type in order to balance its resolution and the LOGA, which very few works have covered in depth. In addition,

### **Figure 10.**

*Vision of the concept of an as-damaged bridge gDT applied for inspection. (a) actual damages or defects; (b) digital representations.*

*C2C*

**131**

**Macro [5]**

**Micro (element wise)**

**(cm)**

Bridge 1 4.3

Deck

Pier

Pier

Pier

Pier 11 Pier 12 Pier 13 Pier 21 Pier 22 Pier 23 Pier 31 Pier 32 Pier 33

———————

slab

6.3

Area

Bridge 4 9.4

88.0% 2.2% 3

Deck

Pier 11 Pier 12 Pier 13 Pier 14 Pier 15 Pier 16 Pier 21 Pier 22 Pier 23 Pier 24 Pier 25 Pier 26

slab

12.0 3.8

> Area

Bridge 6 4.6

89.6% 1%

Deck

Pier 11 Pier 12 Pier 21 Pier 22 Pier 31 Pier 32

slab

6.9

Area

Bridge 7 12.5

92.8% 1.2% 6

Deck

Pier Girder

Girder

Girder

Girder

Girder

Girder

Girder

Girder

Girder

Girder

Girder

Girder

Girder

Girder

Girder

Girder

Girder

Girder

slab

6.6

Area

Bridge 9 5.6

54.2% 6.2% 2.1% 9

Deck

Pier 11 Pier 12 Pier 21 Pier 22 Pier 31 Pier 32

slab

5.2

Area

> **Table 3.**

*Macro- and micro-level*

 *C2C geometric deviation analysis.*

84.4% 2.6% 6

 3.2

 3.0

 3.4

 3.6

 3.9

 4.0

 3.0

 14

 14

 13

 12

 15

 17

 16

 13

 13

 13 2.3% 9 —————————————

—————————————

—————————————

 13

 14

 17

 17

 12

 16

 12

 13

11

12

13

14

15

16

17

18

19

21

22

23

24

25

26

27

28

29

 3.2

 3.1

 3.4

 3.6

 2.9

 3.3

 0.8% 4

 3.6

 3.6

 3.5

 3.7

 3.9 1%

 1%

 0.8% 4

 3.9

 4.3

 3.7

 3.7

 3.9

 3.9 1% —————————————

—————————————

—————————————

———————

*Geometric Accuracy of Digital Twins for Structural Health Monitoring*

———————

 2.8

 2.7

 2.3

 2.2 0.6% 9

 2.1

 1.9

 1.8

 2.1

 2.2

 2.2

 2.2

 1.9

———————

———————

*DOI: http://dx.doi.org/10.5772/intechopen.92775*

———————

cap 1

cap 2

cap 3

**(bridge wise)**


### *Geometric Accuracy of Digital Twins for Structural Health Monitoring DOI: http://dx.doi.org/10.5772/intechopen.92775*

**4. Prospective twinning methods and deviation analysis**

*Structural Integrity and Failure*

complexity of a sampled surface [61, 62].

**Figure 10.**

**130**

*(b) digital representations.*

The analysis provided in the previous section demonstrates that real-world conditions are seldom orthogonal and perfect, rendering it extremely difficult to perform high-fidelity twinning with a geometric accuracy on the millimetre scale. Commonly used representation models include but are not limited to: implicit representation such as mathematical formula-based methods [57], Boundary Representation such as polygon- and mesh-based methods [41], Constructive Solid Geometry [58], Swept Solid Representation [47], and NURBS representation [45, 48]. Depending on the nature of defects, the as-damaged geometries may be represented in different ways. **Figure 10** illustrates the vision of the concept of an as-damaged bridge gDT implemented for the inspection work. The method proposed by Hüthwohl et al. [59] can be used to integrate superficial defects such as cracks, efflorescence, corrosion, and slight spalling [**Figure 10a**—(3) and (4)] to the affected element using the back-project technology [59] (**Figure 10b**). In contrast, major defects, such as severe spalling, cavity and pothole [**Figure 10a**—(1) and (2)], are significantly different in geometry compared to their surrounding healthy (i.e. good condition) surfaces. The method proposed by Lu et al. [5] can be used to represent healthy elements; however, it cannot describe the unhealthy areas precisely, due to the extrusion-based twinning nature. Finer representation, such as mesh-based and NURBS-based twinning techniques [50], can be employed to handle the geometry complexity of significant defects in a precise manner (**Figure 10b**). The more variable the defect, the greater the geometric twinning needs to rely on non-parametric representation such as mesh format. One promising solution to produce a gDT that takes the as-damage information into account is to first detect unhealthy areas [60], followed by twinning these unhealthy areas using finer twinning techniques based on their type and size. However, the mesh polygon resolution should not degrade the rendered presentation. This requires an intelligent a priori scheme to resample the point clouds based on the geometric

Construction elements with different scales may require different twinning techniques. For example, extrusions could be efficient for twinning slab segments; however, they cannot be directly applied to bearings. This means a gDT is highly likely to contain more than one data representation type in order to balance its resolution and the LOGA, which very few works have covered in depth. In addition,

*Vision of the concept of an as-damaged bridge gDT applied for inspection. (a) actual damages or defects;*

**Table 3.** *Macroandmicro-level*

 *C2C geometric deviation analysis.* as previously mentioned, occlusions and sparseness increase the uncertainty of the resulting gDT. These problems require a more intuitive geometric deviation analysis system. The macro-level deviation analysis can provide an overview of the twinning quality whereas it does not reflect a detailed comparison at the component- or feature-level. Therefore, the dimensional QC system of geometric deviation analysis should consist of both macro- and micro-level analysis. The former, can be used to quickly localise uncertain areas, or areas with major deviations (**Figures 8** and **9**) while the latter can provide detailed deviation analysis at the component-level, indicating a more meaningful LOGA of specific elements. **Table 3** shows an example of the *C2C-based* geometric deviation analysis of five bridge gDTs using an automated twinning method. The micro-level numerical indications show that the deck slab takes the bigger part of the overall deviation whereas the other components such as pier caps, piers, and girders take the smaller part. Specifically, for all these bridges except *Bridge 7*, the deviations stemming from deck slabs are 2.9, 3.2, 2.1, and 1.5 times bigger than that of the averaged value for the remaining components, respectively. *Bridge 7* initially appears misleading since the slab deviations are only 48.8% of that of its girders. However, these abnormal deviations are due to significant occlusions in the raw data. The distribution of the deviations is not necessarily proportional to the LOGA. This can be demonstrated through the coverage area of components. The deck slab takes most of the sampled surface compared to that of the pier caps and piers, which are much smaller in size and in covered area. Specifically, pier caps, piers, and girders take 12, 10.4, 7.2, 31.7, and 15.6% of the overall sampled surface of each bridge, respectively. This means although the absolute twinning accuracy of smaller components is higher than larger ones, their relative accuracy is not necessarily better. A deviation analysis system that combines both macro- and micro-level information can better interpret the twinning accuracy.

gDTs generated in the post-construction stage. The case study (Section 3) demonstrates the technical challenges of the twinning process. High-fidelity twinning within millimetre-level geometric accuracy is challenging to achieve because each step introduces errors. This requires in-depth research on the level of the model certainty. LOGA is closely related to the tools, techniques, and process used to represent the specific object being documented. In the end, the twinning method and LOGA depend highly on what the gDT will be used for (Section 4), on the specific needs and goals of the project, and what kind of metadata is required when

Parameterising point cloud data results in a loss of geometric accuracy along with a decrease of model certainty. This requires practitioners and researchers to effectively communicate the LOGA through a universal consensus before developing, evaluating, and using gDTs. Until there is a consensus and a universal system for describing geometric accuracy of gDTs, the following recommendations are provided. In the case where geometric accuracy requirements are very strict, such as in the O&M stage, it may be useful to store and link the initial as-is captured data along with the resulting gDT. The purpose for this is two-fold. First, it allows for an end-user to view the initial dataset that was used to create the gDT, for conducting its own unique accuracy or structural analysis. Storing the initial raw point cloud data will provide a level of confidence to an end-user when they use the geometric information from a gDT. It also alleviates some of the burden placed on individuals who create the gDT to provide a subjective global accuracy figure (which can have legal impacts depending on end-use of such gDTs). Secondly, linking the initial data capture avoids loss of geometric data. Since point cloud data contains much rawer geometric information than a resulting surface-based or solid-based gDT, data fidelity can be preserved. As twinning processes and algorithms continue to develop and improve (both in accuracy but also in computational efficiency) it will be possible to build, update, manage, and exploit gDTs in a progressive manner.

This research work is supported by the National Sciences and Engineering Research Council (NSERC), Mitacs and Edge Architects Ltd. and Cambridge Trimble Fund. We would like to thank them for their support. We also acknowledge Faro Technologies for their in-kind support, provision of sample point cloud data and access to BuildIT Construction software. Any opinions, findings, and conclusions or recommendations expressed in this work are those of the authors and do not necessarily reflect the views of the stakeholders who have supported this research.

providing information about the geometric accuracy.

*Geometric Accuracy of Digital Twins for Structural Health Monitoring*

*DOI: http://dx.doi.org/10.5772/intechopen.92775*

**Acknowledgements**

**133**

### **5. Conclusions**

This chapter presents an exploratory analysis of the LOGA of geometric twinning for existing assets using point clouds. Twinning existing assets for monitoring the structural health is a daunting task since the as-is geometric conditions can differ from the designed status due to geometric anomalies, physical damages, deflections, and the complexity, ambiguities, and defects in the measured point cloud data. Section 2.1 reviews existing LOX systems that lack a clear elaboration on geometry accuracy. They share the same acronym but do not necessarily carry the same meaning. They are tailored for basic assumptions made in the design phase or at the beginning of a generative process, making them useless to interpret the as-is geometries of gDTs delivered for SHM purposes. Section 2.2 reviews on industry applications and reveals that there remains a gap between the accuracy requirements placed on gDTs and the capabilities of underlying twinning processes. Specifically, there are practical limitations of authoring tools with respect to the context of orthogonal (i.e. idealised parametric primitives) and real-world deviations (i.e. non-parametric data formats such as point clouds and meshes). Their ability to twin or capture non-rigid-body deformations is extremely limited. Likewise, limitations are also revealed for the deviation evaluation tools with respect to geometric accuracy interpretations. Despite the growing state of the art (Section 2.3), a fully automated twinning and updating process is still in its infancy. A major bottleneck for complete automation of the workflow is the definition of LOGA of the documented asset that covers all geometric deviations and data uncertainties. This requires a development of comprehensive LOGA-based evaluation metrics for

### *Geometric Accuracy of Digital Twins for Structural Health Monitoring DOI: http://dx.doi.org/10.5772/intechopen.92775*

gDTs generated in the post-construction stage. The case study (Section 3) demonstrates the technical challenges of the twinning process. High-fidelity twinning within millimetre-level geometric accuracy is challenging to achieve because each step introduces errors. This requires in-depth research on the level of the model certainty. LOGA is closely related to the tools, techniques, and process used to represent the specific object being documented. In the end, the twinning method and LOGA depend highly on what the gDT will be used for (Section 4), on the specific needs and goals of the project, and what kind of metadata is required when providing information about the geometric accuracy.

Parameterising point cloud data results in a loss of geometric accuracy along with a decrease of model certainty. This requires practitioners and researchers to effectively communicate the LOGA through a universal consensus before developing, evaluating, and using gDTs. Until there is a consensus and a universal system for describing geometric accuracy of gDTs, the following recommendations are provided. In the case where geometric accuracy requirements are very strict, such as in the O&M stage, it may be useful to store and link the initial as-is captured data along with the resulting gDT. The purpose for this is two-fold. First, it allows for an end-user to view the initial dataset that was used to create the gDT, for conducting its own unique accuracy or structural analysis. Storing the initial raw point cloud data will provide a level of confidence to an end-user when they use the geometric information from a gDT. It also alleviates some of the burden placed on individuals who create the gDT to provide a subjective global accuracy figure (which can have legal impacts depending on end-use of such gDTs). Secondly, linking the initial data capture avoids loss of geometric data. Since point cloud data contains much rawer geometric information than a resulting surface-based or solid-based gDT, data fidelity can be preserved. As twinning processes and algorithms continue to develop and improve (both in accuracy but also in computational efficiency) it will be possible to build, update, manage, and exploit gDTs in a progressive manner.

### **Acknowledgements**

as previously mentioned, occlusions and sparseness increase the uncertainty of the resulting gDT. These problems require a more intuitive geometric deviation analysis system. The macro-level deviation analysis can provide an overview of the twinning quality whereas it does not reflect a detailed comparison at the component- or feature-level. Therefore, the dimensional QC system of geometric deviation analysis should consist of both macro- and micro-level analysis. The former, can be used to quickly localise uncertain areas, or areas with major deviations (**Figures 8** and **9**) while the latter can provide detailed deviation analysis at the component-level, indicating a more meaningful LOGA of specific elements. **Table 3** shows an

example of the *C2C-based* geometric deviation analysis of five bridge gDTs using an automated twinning method. The micro-level numerical indications show that the deck slab takes the bigger part of the overall deviation whereas the other components such as pier caps, piers, and girders take the smaller part. Specifically, for all these bridges except *Bridge 7*, the deviations stemming from deck slabs are 2.9, 3.2, 2.1, and 1.5 times bigger than that of the averaged value for the remaining components, respectively. *Bridge 7* initially appears misleading since the slab deviations are only 48.8% of that of its girders. However, these abnormal deviations are due to significant occlusions in the raw data. The distribution of the deviations is not necessarily proportional to the LOGA. This can be demonstrated through the coverage area of components. The deck slab takes most of the sampled surface compared to that of the pier caps and piers, which are much smaller in size and in covered area. Specifically, pier caps, piers, and girders take 12, 10.4, 7.2, 31.7, and 15.6% of the overall sampled surface of each bridge, respectively. This means although the absolute twinning accuracy of smaller components is higher than larger ones, their relative accuracy is not necessarily better. A deviation analysis system that combines both macro- and micro-level information can better interpret

This chapter presents an exploratory analysis of the LOGA of geometric twinning for existing assets using point clouds. Twinning existing assets for monitoring the structural health is a daunting task since the as-is geometric conditions can differ from the designed status due to geometric anomalies, physical damages, deflections, and the complexity, ambiguities, and defects in the measured point cloud data. Section 2.1 reviews existing LOX systems that lack a clear elaboration on geometry accuracy. They share the same acronym but do not necessarily carry the same meaning. They are tailored for basic assumptions made in the design phase or at the beginning of a generative process, making them useless to interpret the as-is geometries of gDTs delivered for SHM purposes. Section 2.2 reviews on industry applications and reveals that there remains a gap between the accuracy requirements placed on gDTs and the capabilities of underlying twinning processes. Specifically, there are practical limitations of authoring tools with respect to the context of orthogonal (i.e. idealised parametric primitives) and real-world deviations (i.e. non-parametric data formats such as point clouds and meshes). Their ability to twin or capture non-rigid-body deformations is extremely limited. Likewise, limitations are also revealed for the deviation evaluation tools with respect to geometric accuracy interpretations. Despite the growing state of the art (Section 2.3), a fully automated twinning and updating process is still in its infancy. A major bottleneck

for complete automation of the workflow is the definition of LOGA of the documented asset that covers all geometric deviations and data uncertainties. This requires a development of comprehensive LOGA-based evaluation metrics for

the twinning accuracy.

*Structural Integrity and Failure*

**5. Conclusions**

**132**

This research work is supported by the National Sciences and Engineering Research Council (NSERC), Mitacs and Edge Architects Ltd. and Cambridge Trimble Fund. We would like to thank them for their support. We also acknowledge Faro Technologies for their in-kind support, provision of sample point cloud data and access to BuildIT Construction software. Any opinions, findings, and conclusions or recommendations expressed in this work are those of the authors and do not necessarily reflect the views of the stakeholders who have supported this research.

*Structural Integrity and Failure*

### **Author details**

Ruodan Lu1,2\*, Chris Rausch3 , Marzia Bolpagni<sup>4</sup> , Ioannis Brilakis<sup>5</sup> and Carl T. Haas<sup>3</sup> **References**

17 March 2020]

[1] Shea RH. Historian Uses Lasers to Unlock Mysteries of Gothic Cathedrals. National Geographic Magazine. 2019. Available from: https://news.nationalge ographic.com/2015/06/150622-andrewtallon-notre-dame-cathedral-laser-scanart-history-medieval-gothic/ [Accessed:

*DOI: http://dx.doi.org/10.5772/intechopen.92775*

*Geometric Accuracy of Digital Twins for Structural Health Monitoring*

https://usibd.org/product/level-ofaccuracy-loa-specification-version-2-0/

[8] Qu T, Sun W. Usage of 3D point cloud data in BIM (building information modelling): Current applications and challenges. Journal of Civil Engineering and Architecture. 2015;**9**(11):1269-1278

[9] Weisstein EW. Torus. MathWorld— A Wolfram Web Resource. 2018. Available from: http://mathworld.wolf ram.com/Torus.html [Accessed:

[10] Lu R. Automated generation of geometric digital twins of existing reinforced concrete bridges [Dr. thesis]. 2019. DOI: 10.17863/CAM.36680

Grussenmeyer P. From point clouds to building information models: 3D semiautomatic reconstruction of indoors of existing buildings. Applied Sciences.

[12] Truong-Hong L, Laefer DF. Quantitative evaluation strategies for urban 3D model generation from remote sensing data. Computers and Graphics.

[13] Dimitrov A, Golparvar-Fard M. Segmentation of building point cloud models including detailed architectural/ structural features and MEP systems. Automation in Construction. 2015;**51**

[14] Succar B. Level of X (LoX), BIM Dictionary. Available from: https://bimd

ictionary.com/en/level-of-x/1/ [Accessed: 17 March 2020]

[15] Trimble. VICO Software and Trimble to Integrate Workflows and Use Building Information Models to Construct Better Buildings. 2008. Available from: http://investor.trimble.

[11] Macher H, Landes T,

[Accessed: 17 March 2020]

17 March 2020]

2017;**7**(10):1030

2015;**49**:82-91

(C):32-45

[2] Aziz ND, Nawawi AH, Ariff NRM. Building information modelling (BIM) in facilities management: Opportunities to be considered by facility managers. Procedia - Social and Behavioral Sciences. 31 October 2016;**234**:353-362. DOI: 10.1016/j.sbspro.2016.10.252

[3] Wang Q, Kim MK. Applications of 3D point cloud data in the construction industry: A fifteen-year review from 2004 to 2018. Advanced Engineering Informatics. January 2019;**39**:306-319. DOI: 10.1016/j.aei.2019.02.007

[4] Kim MK, Wang Q, Li H. Noncontact sensing based geometric quality assessment of buildings and civil structures: A review. Automation in Construction. April 2019;**100**:163-179. DOI: 10.1016/j.autcon.2019.01.002

[5] Lu R, Brilakis I. Digital twinning of existing reinforced concrete bridges from labelled point clusters. Automation in Construction. September 2019;**105**:

102837. DOI: 10.1016/j. autcon.2019.102837

4637. E-ISSN 1751-7664

**135**

[6] Davila Delgado JM, Butler LJ, Gibbons N, Brilakis I, Elshafie MZEB, Middleton C. Management of structural monitoring data of bridges using BIM. Proceedings of the Institution of Civil Engineers - Bridge Engineering. September 2017;**170**(3):204-218. DOI: 10.1680/jbren.16.00013. ISSN 1478-

[7] USIBD. Level of Accuracy (LOA) Specification Version 2.0. U.S. Inst. Build. Doc. 2016. Available from:

1 School of Architecture, Building and Civil Engineering, Loughborough University, United Kingdom

2 Darwin College, University of Cambridge, United Kingdom

3 Department of Civil and Environmental Engineering, University of Waterloo, Canada

4 Mace Group, United Kingdom

5 Department of Engineering, University of Cambridge, United Kingdom

\*Address all correspondence to: r.lu@lboro.ac.uk; rl508@cam.ac.uk

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Geometric Accuracy of Digital Twins for Structural Health Monitoring DOI: http://dx.doi.org/10.5772/intechopen.92775*

### **References**

[1] Shea RH. Historian Uses Lasers to Unlock Mysteries of Gothic Cathedrals. National Geographic Magazine. 2019. Available from: https://news.nationalge ographic.com/2015/06/150622-andrewtallon-notre-dame-cathedral-laser-scanart-history-medieval-gothic/ [Accessed: 17 March 2020]

[2] Aziz ND, Nawawi AH, Ariff NRM. Building information modelling (BIM) in facilities management: Opportunities to be considered by facility managers. Procedia - Social and Behavioral Sciences. 31 October 2016;**234**:353-362. DOI: 10.1016/j.sbspro.2016.10.252

[3] Wang Q, Kim MK. Applications of 3D point cloud data in the construction industry: A fifteen-year review from 2004 to 2018. Advanced Engineering Informatics. January 2019;**39**:306-319. DOI: 10.1016/j.aei.2019.02.007

[4] Kim MK, Wang Q, Li H. Noncontact sensing based geometric quality assessment of buildings and civil structures: A review. Automation in Construction. April 2019;**100**:163-179. DOI: 10.1016/j.autcon.2019.01.002

[5] Lu R, Brilakis I. Digital twinning of existing reinforced concrete bridges from labelled point clusters. Automation in Construction. September 2019;**105**: 102837. DOI: 10.1016/j. autcon.2019.102837

[6] Davila Delgado JM, Butler LJ, Gibbons N, Brilakis I, Elshafie MZEB, Middleton C. Management of structural monitoring data of bridges using BIM. Proceedings of the Institution of Civil Engineers - Bridge Engineering. September 2017;**170**(3):204-218. DOI: 10.1680/jbren.16.00013. ISSN 1478- 4637. E-ISSN 1751-7664

[7] USIBD. Level of Accuracy (LOA) Specification Version 2.0. U.S. Inst. Build. Doc. 2016. Available from:

https://usibd.org/product/level-ofaccuracy-loa-specification-version-2-0/ [Accessed: 17 March 2020]

[8] Qu T, Sun W. Usage of 3D point cloud data in BIM (building information modelling): Current applications and challenges. Journal of Civil Engineering and Architecture. 2015;**9**(11):1269-1278

[9] Weisstein EW. Torus. MathWorld— A Wolfram Web Resource. 2018. Available from: http://mathworld.wolf ram.com/Torus.html [Accessed: 17 March 2020]

[10] Lu R. Automated generation of geometric digital twins of existing reinforced concrete bridges [Dr. thesis]. 2019. DOI: 10.17863/CAM.36680

[11] Macher H, Landes T, Grussenmeyer P. From point clouds to building information models: 3D semiautomatic reconstruction of indoors of existing buildings. Applied Sciences. 2017;**7**(10):1030

[12] Truong-Hong L, Laefer DF. Quantitative evaluation strategies for urban 3D model generation from remote sensing data. Computers and Graphics. 2015;**49**:82-91

[13] Dimitrov A, Golparvar-Fard M. Segmentation of building point cloud models including detailed architectural/ structural features and MEP systems. Automation in Construction. 2015;**51** (C):32-45

[14] Succar B. Level of X (LoX), BIM Dictionary. Available from: https://bimd ictionary.com/en/level-of-x/1/ [Accessed: 17 March 2020]

[15] Trimble. VICO Software and Trimble to Integrate Workflows and Use Building Information Models to Construct Better Buildings. 2008. Available from: http://investor.trimble.

**Author details**

United Kingdom

Canada

**134**

Ruodan Lu1,2\*, Chris Rausch3

*Structural Integrity and Failure*

4 Mace Group, United Kingdom

provided the original work is properly cited.

, Marzia Bolpagni<sup>4</sup>

2 Darwin College, University of Cambridge, United Kingdom

1 School of Architecture, Building and Civil Engineering, Loughborough University,

3 Department of Civil and Environmental Engineering, University of Waterloo,

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

5 Department of Engineering, University of Cambridge, United Kingdom

\*Address all correspondence to: r.lu@lboro.ac.uk; rl508@cam.ac.uk

, Ioannis Brilakis<sup>5</sup> and Carl T. Haas<sup>3</sup>

com/news-releases/news-releasedetails/vico-software-and-trimbleintegrate-workflows-and-use-building

[16] AIA. Building Information Modeling Protocol Exhibit. AIA Doc. E202TM; 2008. Available from: https://www. smacna.org/docs/default-source/ building-information-modeling/aiae202-building-information-modelingprotocol-exhibit-pdf.pdf?sfvrsn= 333afea5\_0 [Accessed: 03 June 2020]

[17] AIA. AIA Document E203—2013 Building Information Modeling and Digital Data Exhibit; 2013. Available from: http://content.aia.org/sites/ default/files/2016-09/AIA-E203-2013- Free-Sample-Preview.pdf [Accessed: 03 June 2020]

[18] Reinhardt J et al. Level of Development Specification for Building Information Models. 2013. Available from: https://bimforum.org/resources/ Documents/BIMForum\_LOD\_2013\_ reprint.pdf [Accessed: 03 June 2020]

[19] AIA. Digital Practice Documents— Guide, Instructions and Commentary to the 2013 AIA Digital Practice Documents. AIA Document E202TM; 2013. Available from: https://help. aiacontracts.org/public/wp-content/ uploads/2020/03/Digital-Practice\_ Guide.pdf [Accessed: 03 June 2020]

[20] Bolpagni M, Ciribini ALC. The information modeling and the progression of data-driven projects. In: Proceedings of the CIB World Building Congress 2016. Vol. 3. Building up Business Operations and Their Logic. Shaping Materials and Technologies; 2016

[21] Bolpagni M. The Implementation of BIM within the Public Procurement: A Model-Based Approach for the Construction Industry. 2013. Available from: https://www.vttresearch.com/ sites/default/files/pdf/technology/2013/ T130.pdf [Accessed: 03 June 2020]

[22] Bolpagni M. Digitalisation of tendering and awarding processes: A Building Information Modelling (BIM) based approach to public procurement routes [Doctoral dissertation]. Politecnico di Milano; 2018. Available from: http://hdl.handle.net/10589/ 142140

Spatial Information Sciences. 2017;**IV-2/ W2**:9-16. DOI: 10.5194/isprs-annals-IV-

*DOI: http://dx.doi.org/10.5772/intechopen.92775*

*Geometric Accuracy of Digital Twins for Structural Health Monitoring*

management system for owners during project closeout: A case study. Advanced Engineering Informatics. April 2018;**36**: 178-193. DOI: 10.1016/j.aei.2018.04.001

[36] Hamledari H, Rezazadeh Azar E, McCabe B. IFC-based development of

[37] Patil AK, Holi P, Lee SK, Chai YH. An adaptive approach for the reconstruction and modeling of as-built 3D pipelines from point clouds. Automation in Construction. 2017;**75**:65-78

[38] Ochmann S, Vock R, Wessel R, Klein R. Automatic reconstruction of parametric building models from indoor point clouds. Computers and Graphics.

[39] Anil EB, Tang P, Akinci B, Huber D. Deviation analysis method for the assessment of the quality of the as-is building information models generated from point cloud data. Automation in

Construction. 2013;**35**:507-516

2014. 2014. pp. 406-413

2014;**90**:68-82

[40] Zhang G, Vela PA, Brilakis I. Automatic generation of as-built geometric civil infrastructure models from point cloud data. In: Computing in Civil and Building Engineering. Vol.

[41] Oesau S, Lafarge F, Alliez P. Indoor scene reconstruction using feature sensitive primitive extraction and graph-cut. ISPRS Journal of

Photogrammetry and Remote Sensing.

[42] Thomson C, Boehm J. Automatic geometry generation from point clouds for BIM. Remote Sensing. 2015:**7**(9): 11753-11775. DOI: 10.3390/rs70911753

as-built and as-is BIMs using construction and facility inspection data: Site-to-BIM data transfer automation. Journal of Computing in Civil Engineering. March 2018;**32**(2). DOI: 10.1061/(ASCE)CP.1943-

5487.0000727

2016;**54**:94-103

[28] ClearEdge3D. Structure Modelling Tools. 2019. Available from: https:// www.clearedge3d.com/ [Accessed:

[29] ClearEdge3D. EdgeWise. 2019. Available from: https://www.clearedge 3d.com/products/edgewise/ [Accessed:

[30] Wang C, Cho YK, Kim C.

for sustainability applications.

com/wp-content/uploads/

[Accessed: 17 March 2020]

DOI: 10.3390/s150818360

5487.0000605

17 March 2020]

**137**

Automatic BIM component extraction from point clouds of existing buildings

Automation in Construction. 2015;**56**:

[31] Russo JM. What is meant by 'level of accuracy?'. LIDAR Magazine. 2014;**4** (3). Available from: http://lidarmag.

PDF/LiDARNewsMagazine\_Russo-WhatIsLevelOfAccuracy\_Vol4No3.pdf

[32] Castellazzi G, D'Altri AM, Bitelli G, Selvaggi I, Lambertini A. From laser scanning to finite element analysis of complex buildings by using a semiautomatic procedure. Sensors

(Switzerland). 2015;**15**(8):18360-18380.

[33] Rausch C, Nahangi M, Perreault M, Haas CT, West J. Optimum assembly planning for modular construction components. Journal of Computing in Civil Engineering. January 2017;**31**(1). DOI: 10.1061/(ASCE)CP.1943-

[34] Faro BuildIT Construction. 2019. Available from: https://www.faro.com/ products/construction-bim-cim/farobuildit-construction/ [Accessed:

[35] Lin YC, Lin CP, Hu HT, Su YC. Developing final as-built BIM model

2-W2-9-2017

17 March 2020]

17 March 2020]

1-13

[23] Reding A, Williams J. Appendix C— Levels of Development Definitions. New Zealand BIM Handbook. 2014. Available from: https://www.building. govt.nz/assets/Uploads/projects-andconsents/building-informationmodelling/nz-bim-handbookappendix-c-levels-of-developmentdefinitions.pdf

[24] RICS. Measured Surveys of Land, Buildings and Utilities. 3rd ed. RICS Prof. Guid. Glob. Royal Institution of Chartered Surveyors (RICS); 2014. Available from: https://www.rics.org/g lobalassets/rics-website/media/uphold ing-professional-standards/sector-sta ndards/land/measured-surveys-of-la nd-buildings-and-utilities-3rd-editionrics.pdf

[25] Abualdenien J, Borrmann A. Multi-LOD model for describing uncertainty and checking requirements in different design stages. In: eWork and eBusiness in Architecture, Engineering and Construction. 2019. DOI: 10.1201/ 9780429506215-24

[26] Banfi F. BIM orientation: Grades of generation and information for different type of analysis and management process. International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences—ISPRS Archives. 2017;**XLII-2/W5**:57-64. DOI: 10.5194/isprs-archives-XLII-2-W5-57- 2017

[27] Banfi F, Fai S, Brumana R. BIM automation: Advanced modeling generative process for complex structures. In: ISPRS Annals of the Photogrammetry, Remote Sensing and *Geometric Accuracy of Digital Twins for Structural Health Monitoring DOI: http://dx.doi.org/10.5772/intechopen.92775*

Spatial Information Sciences. 2017;**IV-2/ W2**:9-16. DOI: 10.5194/isprs-annals-IV-2-W2-9-2017

com/news-releases/news-releasedetails/vico-software-and-trimbleintegrate-workflows-and-use-building

*Structural Integrity and Failure*

[16] AIA. Building Information Modeling Protocol Exhibit. AIA Doc. E202TM; 2008. Available from: https://www. smacna.org/docs/default-source/ building-information-modeling/aiae202-building-information-modelingprotocol-exhibit-pdf.pdf?sfvrsn= 333afea5\_0 [Accessed: 03 June 2020]

[22] Bolpagni M. Digitalisation of tendering and awarding processes: A Building Information Modelling (BIM) based approach to public procurement

routes [Doctoral dissertation].

142140

definitions.pdf

rics.pdf

2017

9780429506215-24

Politecnico di Milano; 2018. Available from: http://hdl.handle.net/10589/

[23] Reding A, Williams J. Appendix C— Levels of Development Definitions. New Zealand BIM Handbook. 2014. Available from: https://www.building. govt.nz/assets/Uploads/projects-andconsents/building-informationmodelling/nz-bim-handbookappendix-c-levels-of-development-

[24] RICS. Measured Surveys of Land, Buildings and Utilities. 3rd ed. RICS Prof. Guid. Glob. Royal Institution of Chartered Surveyors (RICS); 2014. Available from: https://www.rics.org/g lobalassets/rics-website/media/uphold ing-professional-standards/sector-sta ndards/land/measured-surveys-of-la nd-buildings-and-utilities-3rd-edition-

[25] Abualdenien J, Borrmann A. Multi-LOD model for describing uncertainty and checking requirements in different design stages. In: eWork and eBusiness in Architecture, Engineering and Construction. 2019. DOI: 10.1201/

[26] Banfi F. BIM orientation: Grades of generation and information for different type of analysis and management process. International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences—ISPRS Archives. 2017;**XLII-2/W5**:57-64. DOI: 10.5194/isprs-archives-XLII-2-W5-57-

[27] Banfi F, Fai S, Brumana R. BIM automation: Advanced modeling generative process for complex structures. In: ISPRS Annals of the Photogrammetry, Remote Sensing and

[17] AIA. AIA Document E203—2013 Building Information Modeling and Digital Data Exhibit; 2013. Available from: http://content.aia.org/sites/ default/files/2016-09/AIA-E203-2013- Free-Sample-Preview.pdf [Accessed: 03

[18] Reinhardt J et al. Level of

the 2013 AIA Digital Practice

Development Specification for Building Information Models. 2013. Available from: https://bimforum.org/resources/ Documents/BIMForum\_LOD\_2013\_ reprint.pdf [Accessed: 03 June 2020]

[19] AIA. Digital Practice Documents— Guide, Instructions and Commentary to

Documents. AIA Document E202TM; 2013. Available from: https://help. aiacontracts.org/public/wp-content/ uploads/2020/03/Digital-Practice\_ Guide.pdf [Accessed: 03 June 2020]

[20] Bolpagni M, Ciribini ALC. The information modeling and the

progression of data-driven projects. In: Proceedings of the CIB World Building Congress 2016. Vol. 3. Building up Business Operations and Their Logic. Shaping Materials and Technologies;

[21] Bolpagni M. The Implementation of BIM within the Public Procurement: A

Construction Industry. 2013. Available from: https://www.vttresearch.com/ sites/default/files/pdf/technology/2013/ T130.pdf [Accessed: 03 June 2020]

Model-Based Approach for the

June 2020]

2016

**136**

[28] ClearEdge3D. Structure Modelling Tools. 2019. Available from: https:// www.clearedge3d.com/ [Accessed: 17 March 2020]

[29] ClearEdge3D. EdgeWise. 2019. Available from: https://www.clearedge 3d.com/products/edgewise/ [Accessed: 17 March 2020]

[30] Wang C, Cho YK, Kim C. Automatic BIM component extraction from point clouds of existing buildings for sustainability applications. Automation in Construction. 2015;**56**: 1-13

[31] Russo JM. What is meant by 'level of accuracy?'. LIDAR Magazine. 2014;**4** (3). Available from: http://lidarmag. com/wp-content/uploads/ PDF/LiDARNewsMagazine\_Russo-WhatIsLevelOfAccuracy\_Vol4No3.pdf [Accessed: 17 March 2020]

[32] Castellazzi G, D'Altri AM, Bitelli G, Selvaggi I, Lambertini A. From laser scanning to finite element analysis of complex buildings by using a semiautomatic procedure. Sensors (Switzerland). 2015;**15**(8):18360-18380. DOI: 10.3390/s150818360

[33] Rausch C, Nahangi M, Perreault M, Haas CT, West J. Optimum assembly planning for modular construction components. Journal of Computing in Civil Engineering. January 2017;**31**(1). DOI: 10.1061/(ASCE)CP.1943- 5487.0000605

[34] Faro BuildIT Construction. 2019. Available from: https://www.faro.com/ products/construction-bim-cim/farobuildit-construction/ [Accessed: 17 March 2020]

[35] Lin YC, Lin CP, Hu HT, Su YC. Developing final as-built BIM model management system for owners during project closeout: A case study. Advanced Engineering Informatics. April 2018;**36**: 178-193. DOI: 10.1016/j.aei.2018.04.001

[36] Hamledari H, Rezazadeh Azar E, McCabe B. IFC-based development of as-built and as-is BIMs using construction and facility inspection data: Site-to-BIM data transfer automation. Journal of Computing in Civil Engineering. March 2018;**32**(2). DOI: 10.1061/(ASCE)CP.1943- 5487.0000727

[37] Patil AK, Holi P, Lee SK, Chai YH. An adaptive approach for the reconstruction and modeling of as-built 3D pipelines from point clouds. Automation in Construction. 2017;**75**:65-78

[38] Ochmann S, Vock R, Wessel R, Klein R. Automatic reconstruction of parametric building models from indoor point clouds. Computers and Graphics. 2016;**54**:94-103

[39] Anil EB, Tang P, Akinci B, Huber D. Deviation analysis method for the assessment of the quality of the as-is building information models generated from point cloud data. Automation in Construction. 2013;**35**:507-516

[40] Zhang G, Vela PA, Brilakis I. Automatic generation of as-built geometric civil infrastructure models from point cloud data. In: Computing in Civil and Building Engineering. Vol. 2014. 2014. pp. 406-413

[41] Oesau S, Lafarge F, Alliez P. Indoor scene reconstruction using feature sensitive primitive extraction and graph-cut. ISPRS Journal of Photogrammetry and Remote Sensing. 2014;**90**:68-82

[42] Thomson C, Boehm J. Automatic geometry generation from point clouds for BIM. Remote Sensing. 2015:**7**(9): 11753-11775. DOI: 10.3390/rs70911753

[43] Valero E, Adán A, Bosché F. Semantic 3D reconstruction of furnished interiors using laser scanning and RFID technology. Journal of Computing in Civil Engineering. 2016;**30**(4):04015053

[44] Dimitrov A, Gu R, Golparvar-Fard M. Non-uniform B-spline surface fitting from unordered 3D point clouds for asbuilt modeling. Computer-Aided Civil and Infrastructure Engineering. 2016; **31**(7):483-498

[45] Barazzetti L. Parametric as-built model generation of complex shapes from point clouds. Advanced Engineering Informatics. August 2016; **30**(3):298-311. DOI: 10.1016/j. aei.2016.03.005

[46] Bonduel M, Bassier M, Vergauwen M, Pauwels P, Klein R. Scan-to-BIM output validation: Towards a standardized geometric quality assessment of building information models based on point clouds. In: International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences—ISPRS Archives. 2017

[47] Laefer DF, Truong-Hong L. Toward automatic generation of 3D steel structures for building information modelling. Automation in Construction. 2017;**74**:66-77

[48] Brumana R et al. Generative HBIM modelling to embody complexity (LOD, LOG, LOA, LOI): Surveying, preservation, site intervention—The Basilica di Collemaggio (L'Aquila). Applied Geomatics. 2018;**10**:545-567. DOI: 10.1007/s12518-018-0233-3

[49] Stojanovic V, Richter R, Döllner J, Trapp M. Comparative visualization of BIM geometry and corresponding point clouds. International Journal of Sustainable Development and Planning. 2018;**13**(1):12-23. DOI: 10.2495/SDP-V13-N1-12-23

[50] Ma L, Sacks R, Kattel U, Bloch T. 3D object classification using geometric features and pairwise relationships. Computer-Aided Civil and Infrastructure Engineering. 2018;**33**(2):152-164

[57] Weisstein EW. Ellipsoid. MathWorld—A Wolfram Web

[Accessed: 17 March 2020]

1-21

**32**(3):04018013

Resource. 2018. Available from: http:// mathworld.wolfram.com/Ellipsoid.html

*DOI: http://dx.doi.org/10.5772/intechopen.92775*

*Geometric Accuracy of Digital Twins for Structural Health Monitoring*

[58] Deng Y, Cheng JCP, Anumba C. Mapping between BIM and 3D GIS in different levels of detail using schema mediation and instance comparison. Automation in Construction. 2016;**67**:

[59] Hüthwohl P, Brilakis I, Borrmann A, Sacks R. Integrating RC bridge defect information into BIM models. Journal of Computing in Civil Engineering. 2018;

[60] Xu Z, Li S, Li H, Li Q. Modeling and problem solving of building defects using point clouds and enhanced casebased reasoning. Automation in

Construction. December 2018;**96**:40-54. DOI: 10.1016/j.autcon.2018.09.003

[61] Chen J, Zhang C, Tang P. Geometry-

[62] Zhang C, Tang P. Visual complexity

analysis of sparse imageries for automatic laser scan planning in dynamic environments. In: Computing in Civil Engineering. 2015. pp. 271-279

**139**

based optimized point cloud compression methodology for construction and infrastructure management. In: Computing in Civil Engineering 2017: Smart Safety, Sustainability and Resilience - Selected Papers from the ASCE International Workshop on Computing in Civil Engineering. American Society of Civil Engineers (ASCE). 2017. pp. 377-385

[51] Shirowzhan S, Sepasgozar SME, Li H, Trinder J, Tang P. Comparative analysis of machine learning and pointbased algorithms for detecting 3D changes in buildings over time using bi-temporal lidar data. Automation in Construction. September 2019;**105**: 102841. DOI: 10.1016/j.autcon. 2019.102841

[52] FARO. FARO® Laser Scanner Focus3D X 330 Manual. 2015. Available from: https://faro.app.box.com/s/4f 908b59hcjjj8mezdr58z6n4qy5neli [Accessed: 17 March 2020]

[53] Lichti DD, Harvey BR. The effects of reflecting surface material properties on time-of-flight laser scanner measurements. In: Geospatial Theory, Processing and Applications. 2002. Available from: http://citeseerx.ist.psu. edu/viewdoc/download?doi= 10.1.1.123.5103&rep=rep1&type=pdf. Corpus ID: 9926219 [Accessed: 03 June 2020]

[54] Ji Y, Borrmann A, Beetz J, Obergrießer M. Exchange of parametric bridge models using a neutral data format. Journal of Computing in Civil Engineering. 2013;**27**(6):593-606

[55] Adan A, Huber D. 3D reconstruction of interior wall surfaces under occlusion and clutter. In: Proceedings of the 2011 International Conference on 3D Imaging, Modeling, Processing, Visualization and Transmission (3DIMPVT). 2011. pp. 275-281

[56] Lu R, Brilakis I, Middleton CR. Detection of structural components in point clouds of existing RC bridges. Computer-Aided Civil and Infrastructure Engineering. March 2019; **34**(3):191-212. DOI: 10.1111/mice.12407

*Geometric Accuracy of Digital Twins for Structural Health Monitoring DOI: http://dx.doi.org/10.5772/intechopen.92775*

[57] Weisstein EW. Ellipsoid. MathWorld—A Wolfram Web Resource. 2018. Available from: http:// mathworld.wolfram.com/Ellipsoid.html [Accessed: 17 March 2020]

[43] Valero E, Adán A, Bosché F. Semantic 3D reconstruction of furnished interiors

[50] Ma L, Sacks R, Kattel U, Bloch T. 3D object classification using geometric features and pairwise relationships. Computer-Aided Civil and Infrastructure

Engineering. 2018;**33**(2):152-164

2019.102841

2020]

[51] Shirowzhan S, Sepasgozar SME, Li H, Trinder J, Tang P. Comparative analysis of machine learning and pointbased algorithms for detecting 3D changes in buildings over time using bi-temporal lidar data. Automation in Construction. September 2019;**105**: 102841. DOI: 10.1016/j.autcon.

[52] FARO. FARO® Laser Scanner Focus3D X 330 Manual. 2015. Available from: https://faro.app.box.com/s/4f 908b59hcjjj8mezdr58z6n4qy5neli [Accessed: 17 March 2020]

[53] Lichti DD, Harvey BR. The effects of reflecting surface material properties on

measurements. In: Geospatial Theory, Processing and Applications. 2002. Available from: http://citeseerx.ist.psu.

10.1.1.123.5103&rep=rep1&type=pdf. Corpus ID: 9926219 [Accessed: 03 June

Obergrießer M. Exchange of parametric bridge models using a neutral data format. Journal of Computing in Civil Engineering. 2013;**27**(6):593-606

[55] Adan A, Huber D. 3D reconstruction of interior wall surfaces under occlusion and clutter. In: Proceedings of the 2011 International Conference on 3D Imaging, Modeling, Processing, Visualization and Transmission (3DIMPVT). 2011. pp. 275-281

[56] Lu R, Brilakis I, Middleton CR. Detection of structural components in point clouds of existing RC bridges.

Infrastructure Engineering. March 2019; **34**(3):191-212. DOI: 10.1111/mice.12407

Computer-Aided Civil and

time-of-flight laser scanner

edu/viewdoc/download?doi=

[54] Ji Y, Borrmann A, Beetz J,

technology. Journal of Computing in Civil Engineering. 2016;**30**(4):04015053

[44] Dimitrov A, Gu R, Golparvar-Fard M. Non-uniform B-spline surface fitting from unordered 3D point clouds for asbuilt modeling. Computer-Aided Civil and Infrastructure Engineering. 2016;

[45] Barazzetti L. Parametric as-built model generation of complex shapes from point clouds. Advanced

Engineering Informatics. August 2016;

**30**(3):298-311. DOI: 10.1016/j.

[46] Bonduel M, Bassier M,

Vergauwen M, Pauwels P, Klein R. Scan-to-BIM output validation: Towards

a standardized geometric quality assessment of building information models based on point clouds. In: International Archives of the

Photogrammetry, Remote Sensing and Spatial Information Sciences—ISPRS

[47] Laefer DF, Truong-Hong L. Toward

[48] Brumana R et al. Generative HBIM modelling to embody complexity (LOD,

[49] Stojanovic V, Richter R, Döllner J, Trapp M. Comparative visualization of BIM geometry and corresponding point

Sustainable Development and Planning. 2018;**13**(1):12-23. DOI: 10.2495/SDP-

clouds. International Journal of

automatic generation of 3D steel structures for building information modelling. Automation in Construction.

LOG, LOA, LOI): Surveying, preservation, site intervention—The Basilica di Collemaggio (L'Aquila). Applied Geomatics. 2018;**10**:545-567. DOI: 10.1007/s12518-018-0233-3

using laser scanning and RFID

*Structural Integrity and Failure*

**31**(7):483-498

aei.2016.03.005

Archives. 2017

2017;**74**:66-77

V13-N1-12-23

**138**

[58] Deng Y, Cheng JCP, Anumba C. Mapping between BIM and 3D GIS in different levels of detail using schema mediation and instance comparison. Automation in Construction. 2016;**67**: 1-21

[59] Hüthwohl P, Brilakis I, Borrmann A, Sacks R. Integrating RC bridge defect information into BIM models. Journal of Computing in Civil Engineering. 2018; **32**(3):04018013

[60] Xu Z, Li S, Li H, Li Q. Modeling and problem solving of building defects using point clouds and enhanced casebased reasoning. Automation in Construction. December 2018;**96**:40-54. DOI: 10.1016/j.autcon.2018.09.003

[61] Chen J, Zhang C, Tang P. Geometrybased optimized point cloud compression methodology for construction and infrastructure management. In: Computing in Civil Engineering 2017: Smart Safety, Sustainability and Resilience - Selected Papers from the ASCE International Workshop on Computing in Civil Engineering. American Society of Civil Engineers (ASCE). 2017. pp. 377-385

[62] Zhang C, Tang P. Visual complexity analysis of sparse imageries for automatic laser scan planning in dynamic environments. In: Computing in Civil Engineering. 2015. pp. 271-279

**Chapter 8**

**Abstract**

Safety Evaluation of Stay Cables

of Cable-Stayed and Extradosed

Cable-stayed and extradosed bridges are thought to be identical structures because both bridges use stay cables for reinforcement. However, the safety factors of their stay cables are stipulated differently in many international standards, i.e., Japanese specifications suggest the safety factors of 2.5 and 1.67 for the design of cable-stayed and extradosed bridges, respectively. In this chapter, a parametric study is carried out for the evaluation of safety factors of stay cables by employing the deterministic and nondeterministic methods at limit states. As a result, it is found that the safety factors in the range of 2.3–2.5 and 1.67 are indispensable for the safe design of cable-stayed and extradosed bridges, respectively, to satisfy the

**Keywords:** cable-stayed bridge, extradosed bridge, stay cable, safety factor,

The extradosed bridge is thought to be a special form of cable-stayed bridge because both bridges use inclined stay cables for supporting the girder load elastically at points along its length in order to increase the span of girder without intermediate piers [1]. The dead and live loads on girders are transferred to towers by axial action of stay cables. Thus, the safety of these kinds of flexible structures is mainly dependent on the safety of stay cables, which is usually assured by introducing a safety factor to provide a margin between theoretical strengths (R) and load effects (S). For instance, the allowable stress (*σall*) at serviceability limit state (SLS) as per the Japan Prestressed Concrete Engineering Association's Specifications, may be determined as 0.4 *σUTS* and 0.6 *σUTS* (where *σUTS* is ultimate tensile strength) for the design of cable-stayed and extradosed bridges, respectively [2]. In that context, Ali et al. [3] estimated an optimum value of safety factor for stay cables of a cable-stayed bridge under ultimate and fatigue limit states by considering the effects of various unexpected events. However, the problem of how much *σall* should be used for the stay cables of extradosed bridges is still controversial because these cables are considered as external cables arranged outside the box girder. Moreover, the safety factors of these cables have not been verified against

Bridges via Deterministic and

Non-deterministic Methods

*Khawaja Ali and Aleena Saleem*

conditions of limit states and target reliability index.

reliability, fatigue, limit state

**1. Introduction**

**141**

### **Chapter 8**

## Safety Evaluation of Stay Cables of Cable-Stayed and Extradosed Bridges via Deterministic and Non-deterministic Methods

*Khawaja Ali and Aleena Saleem*

### **Abstract**

Cable-stayed and extradosed bridges are thought to be identical structures because both bridges use stay cables for reinforcement. However, the safety factors of their stay cables are stipulated differently in many international standards, i.e., Japanese specifications suggest the safety factors of 2.5 and 1.67 for the design of cable-stayed and extradosed bridges, respectively. In this chapter, a parametric study is carried out for the evaluation of safety factors of stay cables by employing the deterministic and nondeterministic methods at limit states. As a result, it is found that the safety factors in the range of 2.3–2.5 and 1.67 are indispensable for the safe design of cable-stayed and extradosed bridges, respectively, to satisfy the conditions of limit states and target reliability index.

**Keywords:** cable-stayed bridge, extradosed bridge, stay cable, safety factor, reliability, fatigue, limit state

### **1. Introduction**

The extradosed bridge is thought to be a special form of cable-stayed bridge because both bridges use inclined stay cables for supporting the girder load elastically at points along its length in order to increase the span of girder without intermediate piers [1]. The dead and live loads on girders are transferred to towers by axial action of stay cables. Thus, the safety of these kinds of flexible structures is mainly dependent on the safety of stay cables, which is usually assured by introducing a safety factor to provide a margin between theoretical strengths (R) and load effects (S). For instance, the allowable stress (*σall*) at serviceability limit state (SLS) as per the Japan Prestressed Concrete Engineering Association's Specifications, may be determined as 0.4 *σUTS* and 0.6 *σUTS* (where *σUTS* is ultimate tensile strength) for the design of cable-stayed and extradosed bridges, respectively [2]. In that context, Ali et al. [3] estimated an optimum value of safety factor for stay cables of a cable-stayed bridge under ultimate and fatigue limit states by considering the effects of various unexpected events. However, the problem of how much *σall* should be used for the stay cables of extradosed bridges is still controversial because these cables are considered as external cables arranged outside the box girder. Moreover, the safety factors of these cables have not been verified against

extreme loading and unexpected damage conditions. Besides this, the stress range in a stay cable due to live load is one of the most important considerations for the design of stay cables against fatigue failure [4]. Owing to the variations in live loads, it is difficult to precisely examine the safety of these kinds of flexible structures through an evaluation method comprising safety factors based on experience. Therefore, it seems to be reasonable to conduct safety and reliability assessment using a nondeterministic reliability method which takes into account the effects of all kinds of uncertainties [5–7].

In this paper, a parametric study is carried out to evaluate the safety factors of stay cables of cable-stayed and extradosed bridges by employing the deterministic and nondeterministic methods at limit states. The effects of various parameters, i.e., cable loss and deterioration of cables due to corrosion, on demand to capacity ratio (DCR) of stay cables are also considered in this study. Finally, it is found that the safety factors in the range of 2.3–2.5 and 1.67 are essential for the safe design of cable-stayed and extradosed bridges, respectively to satisfy the conditions of limit states and target reliability index.

**2.2 FE model of extradosed bridge (EDB)**

*DOI: http://dx.doi.org/10.5772/intechopen.92215*

**Figure 2.**

**Figure 3.**

**143**

*Configuration of traffic lanes.*

girder should be fixed at the piers.

*Configuration of extradosed bridge model.*

Similar to cable-stayed bridge, a 3D FE model of extradosed bridge, with a main span length of 208 m and two side spans of each 100 m, is developed. The structural configuration of bridge model is shown in **Figure 3**. The total width and depth of concrete bridge girder are 21.75 m and 4.5 m, respectively with four lanes as already shown in **Figure 2**. The depth of girder is kept same at the pylon locations as well as at mid-span. The total height of the concrete tower is 40 m and pylon height (20 m) is taken as 1/10th of the main span length. The bridge girder is supported by the piers and a system of 88 stay cables (EDCs) arranged in a modified-fan style. The anchorage points of stay cables (EDCs) at the bridge deck are located at the intervals of 5 m and 6 m on side and main spans, respectively. The connection between tower and girder is assumed to be fixed and monolithic because stress range due to live load in the cables is affected by the girder stiffness and fixity of support on the piers. When the girder is stiff, the stress range in cables due to live load will be small in comparison with permanent loads. To reduce the magnitude of this stress range,

*Safety Evaluation of Stay Cables of Cable-Stayed and Extradosed Bridges via Deterministic…*

**2.3 Design considerations for cable-stayed and extradosed bridges**

Bridge design loads are referred to Japanese specifications for highway bridges [4] as shown in **Table 1**. Dead loads are applied uniformly on entire spans whereas

### **2. Finite element modeling**

### **2.1 FE model of cable-stayed bridge (CSB)**

A 3D FE model of a cable-stayed bridge, with a main span length of 460 m, is developed using a FEM software (Midas Civil). The structural configuration of the bridge model is shown in **Figure 1**. The bridge model is cambered linearly by 2%. The steel box girder is used for this model. The total width and depth of girder are 21.75 m and 3.5 m, respectively with four design lanes of each 3.5 m wide as shown in **Figure 2**. The configuration of tower is an H-shape composed of steel legs. The total height of tower is 140 m and pylon height (110 m) is taken as 1/4th of the main span length. Moreover, cable-stayed bridge model consists of 144 stay cables (Cs), arranged in a modified-fan style. The anchorage points of stay cables at the bridge deck are located at an interval of 12 m. Tower and girder are modeled as elastic beam elements (168 beams) whereas stay cables are modeled as truss elements (only tension). Fishbone modeling technique is adopted to connect the stay cables with deck spine through rigid links. Moreover, the model is supported by roller supports provided on each end of bridge and piers are assumed to be fixed into firm foundation. All bearings of main girder are movable in longitudinal direction of bridge, i.e., there is no connection between tower and girder at their intersection. The attachments of the cables to tower are pinned. Elastomeric rubber bearings are installed to connect the girder with lower transverse beam through elastic links.

**Figure 1.** *Configuration of cable-stayed bridge model.*

*Safety Evaluation of Stay Cables of Cable-Stayed and Extradosed Bridges via Deterministic… DOI: http://dx.doi.org/10.5772/intechopen.92215*

**Figure 2.** *Configuration of traffic lanes.*

extreme loading and unexpected damage conditions. Besides this, the stress range in a stay cable due to live load is one of the most important considerations for the design of stay cables against fatigue failure [4]. Owing to the variations in live loads, it is difficult to precisely examine the safety of these kinds of flexible structures through an evaluation method comprising safety factors based on experience. Therefore, it seems to be reasonable to conduct safety and reliability assessment using a nondeterministic reliability method which takes into account the effects of

In this paper, a parametric study is carried out to evaluate the safety factors of stay cables of cable-stayed and extradosed bridges by employing the deterministic and nondeterministic methods at limit states. The effects of various parameters, i.e., cable loss and deterioration of cables due to corrosion, on demand to capacity ratio (DCR) of stay cables are also considered in this study. Finally, it is found that the safety factors in the range of 2.3–2.5 and 1.67 are essential for the safe design of cable-stayed and extradosed bridges, respectively to satisfy the conditions of limit

A 3D FE model of a cable-stayed bridge, with a main span length of 460 m, is developed using a FEM software (Midas Civil). The structural configuration of the bridge model is shown in **Figure 1**. The bridge model is cambered linearly by 2%. The steel box girder is used for this model. The total width and depth of girder are 21.75 m and 3.5 m, respectively with four design lanes of each 3.5 m wide as shown in **Figure 2**. The configuration of tower is an H-shape composed of steel legs. The total height of tower is 140 m and pylon height (110 m) is taken as 1/4th of the main span length. Moreover, cable-stayed bridge model consists of 144 stay cables (Cs), arranged in a modified-fan style. The anchorage points of stay cables at the bridge deck are located at an interval of 12 m. Tower and girder are modeled as elastic beam elements (168 beams) whereas stay cables are modeled as truss elements (only tension). Fishbone modeling technique is adopted to connect the stay cables with deck spine through rigid links. Moreover, the model is supported by roller supports provided on each end of bridge and piers are assumed to be fixed into firm foundation. All bearings of main girder are movable in longitudinal direction of bridge, i.e., there is no connection between tower and girder at their intersection. The attachments of the cables to tower are pinned. Elastomeric rubber bearings are installed to connect the girder with lower transverse beam through elastic links.

all kinds of uncertainties [5–7].

*Structural Integrity and Failure*

states and target reliability index.

**2. Finite element modeling**

**Figure 1.**

**142**

*Configuration of cable-stayed bridge model.*

**2.1 FE model of cable-stayed bridge (CSB)**

### **2.2 FE model of extradosed bridge (EDB)**

Similar to cable-stayed bridge, a 3D FE model of extradosed bridge, with a main span length of 208 m and two side spans of each 100 m, is developed. The structural configuration of bridge model is shown in **Figure 3**. The total width and depth of concrete bridge girder are 21.75 m and 4.5 m, respectively with four lanes as already shown in **Figure 2**. The depth of girder is kept same at the pylon locations as well as at mid-span. The total height of the concrete tower is 40 m and pylon height (20 m) is taken as 1/10th of the main span length. The bridge girder is supported by the piers and a system of 88 stay cables (EDCs) arranged in a modified-fan style. The anchorage points of stay cables (EDCs) at the bridge deck are located at the intervals of 5 m and 6 m on side and main spans, respectively. The connection between tower and girder is assumed to be fixed and monolithic because stress range due to live load in the cables is affected by the girder stiffness and fixity of support on the piers. When the girder is stiff, the stress range in cables due to live load will be small in comparison with permanent loads. To reduce the magnitude of this stress range, girder should be fixed at the piers.

### **2.3 Design considerations for cable-stayed and extradosed bridges**

Bridge design loads are referred to Japanese specifications for highway bridges [4] as shown in **Table 1**. Dead loads are applied uniformly on entire spans whereas

**Figure 3.** *Configuration of extradosed bridge model.*


(ASD) method. An optimization technique of finding unknown load factors is applied to find the initial pretension forces (PS) through an iterative process in order to achieve the balanced state of bridge under its own weight. Subsequently, the cross-sectional areas of stay cables are calculated and shown in **Figure 4**. In addition to that, stay cables are designed in such a way that axial stresses in stay cables are about 50–60% of *σall* under dead loads and less than 95% of *σall* under

*Safety Evaluation of Stay Cables of Cable-Stayed and Extradosed Bridges via Deterministic…*

Similar to cable-stayed bridge, the preliminary design of stay cables of extradosed bridge (EDCs) is also carried out by using a safety factor of 1.67. For the calculation of initial pretension forces (PS) of stay cables, the continuous beam method is applied. Hit and trial method is used to find the ideal and balanced state of extradosed bridge under dead loads. Many iterations are performed to optimize the bending moment and cable forces, and cross-sectional areas of stay cables are calculated accordingly as shown in **Figure 5**. In extradosed bridge, the prestress force (Pi) is also applied to the concrete girder. Full pre-stressing of the girder is not feasible. Since only concentric pre-stressing can be used locally in the girder (eccentric pre-stressing causes a secondary bending moment as large as the primary bending moment), a prestress force (Pi) of 200,000 kN is required at main span and some portion of side span to keep the girder un-cracked. Pi is required to

dead plus live loads.

**Figure 4.**

**Figure 5.**

**145**

**2.5 Stay cables of extradosed bridge (EDCs)**

*DOI: http://dx.doi.org/10.5772/intechopen.92215*

*Cross-sectional areas of stay cables of cable-stayed bridge.*

*Cross-sectional areas of stay cables of extradosed bridge.*

**Table 1.**

*Design loads.*

B-live loads (concentrated live load: P1 and uniformly distributed load: P2) are applied only on main spans of both bridges. The material and sectional properties of bridge components are also shown in **Tables 2** and 3, respectively.

### **2.4 Stay cables of cable-stayed bridge (Cs)**

Preliminary design of stay cables of cable-stayed bridge (Cs) is carried out by assuming a safety factor of 2.5 against *σUTS* following the allowable stress design


### **Table 2.**

*Material properties of stay cables.*


### **Table 3.**

*Sectional properties of bridge components.*

*Safety Evaluation of Stay Cables of Cable-Stayed and Extradosed Bridges via Deterministic… DOI: http://dx.doi.org/10.5772/intechopen.92215*

(ASD) method. An optimization technique of finding unknown load factors is applied to find the initial pretension forces (PS) through an iterative process in order to achieve the balanced state of bridge under its own weight. Subsequently, the cross-sectional areas of stay cables are calculated and shown in **Figure 4**. In addition to that, stay cables are designed in such a way that axial stresses in stay cables are about 50–60% of *σall* under dead loads and less than 95% of *σall* under dead plus live loads.

### **2.5 Stay cables of extradosed bridge (EDCs)**

Similar to cable-stayed bridge, the preliminary design of stay cables of extradosed bridge (EDCs) is also carried out by using a safety factor of 1.67. For the calculation of initial pretension forces (PS) of stay cables, the continuous beam method is applied. Hit and trial method is used to find the ideal and balanced state of extradosed bridge under dead loads. Many iterations are performed to optimize the bending moment and cable forces, and cross-sectional areas of stay cables are calculated accordingly as shown in **Figure 5**. In extradosed bridge, the prestress force (Pi) is also applied to the concrete girder. Full pre-stressing of the girder is not feasible. Since only concentric pre-stressing can be used locally in the girder (eccentric pre-stressing causes a secondary bending moment as large as the primary bending moment), a prestress force (Pi) of 200,000 kN is required at main span and some portion of side span to keep the girder un-cracked. Pi is required to

**Figure 4.** *Cross-sectional areas of stay cables of cable-stayed bridge.*

**Figure 5.** *Cross-sectional areas of stay cables of extradosed bridge.*

B-live loads (concentrated live load: P1 and uniformly distributed load: P2) are applied only on main spans of both bridges. The material and sectional properties of

Dead load, DLCSB (kN/m) Self-weight of deck *wDC*<sup>1</sup> 48.5

Dead load, DLEDB (kN/m) Girder self-weight *wDC*<sup>1</sup> 335

Live load, LL (kN/m) Concentrated load P1 97.5

Pavement loads *wDW* 34.2 Additional loads *wDC*<sup>2</sup> 4.85

Pavement loads *wDW* 34.2 Additional loads *wDC*<sup>2</sup> 4.85

Uniformly dist. Load P2 29.3 Pedestrian load PL 10

Preliminary design of stay cables of cable-stayed bridge (Cs) is carried out by assuming a safety factor of 2.5 against *σUTS* following the allowable stress design

**Properties Stay cables of CSB Stay cables of EDB** *σUTS* (MPa) 1860 2000 *σ<sup>y</sup>* (MPa) 1302 1400 *σall* (MPa) 744 1200 *E* (GPa) 195 195 *ν* 0.3 0.3

) 77 77

**Members Deck Pylon Pier Transverse beam**

) 0.59 1.11 1.11 0.55

) 14.73 7.96 7.96 2.61

) 5.13 6.24 6.24 2.14

) 29.03 4.72 4.72 1.52

) 13.54 6 12 6

) 168.62 4.7 19.44 4.7

) 54.22 4.5 16 4.5

) 683.84 2 9 2

bridge components are also shown in **Tables 2** and 3, respectively.

**2.4 Stay cables of cable-stayed bridge (Cs)**

**Table 1.** *Design loads.*

*Structural Integrity and Failure*

*γ* (kN/m3

*Material properties of stay cables.*

CSB A (m<sup>2</sup>

EDB A (m<sup>2</sup>

Ixx (m4

Iyy (m4

Izz (m<sup>4</sup>

Ixx (m4

Iyy (m4

Izz (m<sup>4</sup>

*Sectional properties of bridge components.*

**Table 2.**

**Table 3.**

**144**

minimize the deflection and to resist the bending moments due to long-term effects and live loads.

### **2.6 Effects of nonlinearity**

Nonlinearity effects including cable sag effect due to self-weight of stay cables and P-Delta effects due to interaction of deck and tower are also considered in the analysis of both bridge types. Reduced or equivalent modulus of elasticity of stay cables is determined by:

$$\mathbf{E\_{eq}} = \frac{\mathbf{E}}{\mathbf{1} + \frac{(\mathbf{w}\mathbf{L})^2 \mathbf{A} \mathbf{E}}{\mathbf{1} \mathbf{2} \mathbf{T}^3}} \tag{1}$$

*γ* Δ*σ<sup>d</sup>* Δ*σ<sup>R</sup>*

allowable stress range which can be found by using Eq. (3):

*DOI: http://dx.doi.org/10.5772/intechopen.92215*

correction factor for mean stress which can be calculated as:

maximum stress (*σ*max) in stay cables.

**Figure 7.**

**147**

*Effect of fatigue load on DCR of stay cables of cable-stayed bridge.*

*CR* <sup>¼</sup> <sup>1</sup>*:*<sup>3</sup> <sup>1</sup> � *<sup>R</sup>*

*CR* <sup>¼</sup> <sup>1</sup> � *<sup>R</sup>*

where *γ* is safety factor equal to 1.2 based on redundancy and importance of structure, Δσ<sup>d</sup> is design stress range also known as maximum stress range and Δσ*<sup>R</sup>* is

*Safety Evaluation of Stay Cables of Cable-Stayed and Extradosed Bridges via Deterministic…*

where ΔσCE is the basic allowable stress range or cut off limit for constant amplitude stress which is taken as 270 MPa and 200 MPa for parallel wire strand type stay cables of cable-stayed and extradosed bridges, respectively at 2 million load cycles based on the standard SN or Wohler's curves of cables and CR is

1*:*6 � *R*

which *R* is the stress ratio defined as the ratio of minimum stress (*σ*min) to

**Figures 7** and **8** compare the fatigue stress demand to capacity ratios (DCRs) of stay cables of cable-stayed and extradosed bridges, respectively. In case of cablestayed bridge, stay cable C15 shows maximum DCR under fatigue design load and there is a hefty variation in DCR of stay cables depending on their locations with respect to tower-deck intersection. From **Figure 7**, it can be concluded that a minimum safety factor of 2.2 is necessary to satisfy the fatigue limit state.

In case of extradosed bridge, all stay cables (EDCs) exhibit almost same DCR irrespective of their locations with respect to tower-deck intersection. **Figure 8** also

<sup>≤</sup>1*:*<sup>0</sup> (2)

Δ*σ<sup>R</sup>* ¼ Δ*σCE* � *CR* (3)

for *<sup>R</sup>* <sup>≤</sup> � <sup>1</sup> (4)

<sup>1</sup> � <sup>0</sup>*:*9*<sup>R</sup>* for *<sup>R</sup>*<sup>&</sup>gt; � <sup>1</sup> (5)

Eq. (1) is known as Ernst' formula in which Eeq is equivalent modulus of elasticity, E is effective material modulus of elasticity, A is cross-sectional area of stay cable, w is cable weight per unit length, L is horizontal projected length and T is tensile force in stay cable.

### **3. Safety evaluation of stay cables by deterministic method**

### **3.1 Fatigue limit state**

For the evaluation of safety factor of stay cables at fatigue limit state, moving load analysis is performed by applying fatigue design load (T-load: 200 kN) to the cable-stayed and extradosed bridge models. Then, influence line diagrams (ILDs) of axial forces in stay cables are drawn by using Breslau Muller Principle and maximum and minimum design variables are calculated. **Figure 6** shows the ILDs of axial forces of stay cables (C1 and EDC1) of cable-stayed and extradosed bridges, respectively. It is observed that the area under ILD of C1 is larger than that of EDC1 under the same fatigue load which indicates that extradosed bridge is less influenced by fatigue load as compared to cable-stayed bridge. Subsequently, cable reversal stresses and design stress range ð Þ Δ*σ<sup>d</sup>* values are determined by considering the cyclic loads of constant amplitude and fully reversed nature as per the guidelines of fatigue design recommendations for steel structures [8]. To assess the safety factor at fatigue limit state based on equivalent stress range theory, following equation should be satisfied [9]:

**Figure 6.** *ILDs of axial forces of stay cables C1 and EDC1.*

*Safety Evaluation of Stay Cables of Cable-Stayed and Extradosed Bridges via Deterministic… DOI: http://dx.doi.org/10.5772/intechopen.92215*

$$\chi\left(\frac{\Delta\sigma\_d}{\Delta\sigma\_{\mathbb{R}}}\right) \le \mathbf{1.0} \tag{2}$$

where *γ* is safety factor equal to 1.2 based on redundancy and importance of structure, Δσ<sup>d</sup> is design stress range also known as maximum stress range and Δσ*<sup>R</sup>* is allowable stress range which can be found by using Eq. (3):

$$
\Delta \sigma\_R = \Delta \sigma\_{\rm CE} \times \mathbf{C}\_R \tag{3}
$$

where ΔσCE is the basic allowable stress range or cut off limit for constant amplitude stress which is taken as 270 MPa and 200 MPa for parallel wire strand type stay cables of cable-stayed and extradosed bridges, respectively at 2 million load cycles based on the standard SN or Wohler's curves of cables and CR is correction factor for mean stress which can be calculated as:

$$C\_R = 1.3 \left( \frac{1 - R}{1.6 - R} \right) \text{ for } R \le -1 \tag{4}$$

$$C\_R = \frac{1 - R}{1 - 0.9R} \text{ for } R > -1\tag{5}$$

which *R* is the stress ratio defined as the ratio of minimum stress (*σ*min) to maximum stress (*σ*max) in stay cables.

**Figures 7** and **8** compare the fatigue stress demand to capacity ratios (DCRs) of stay cables of cable-stayed and extradosed bridges, respectively. In case of cablestayed bridge, stay cable C15 shows maximum DCR under fatigue design load and there is a hefty variation in DCR of stay cables depending on their locations with respect to tower-deck intersection. From **Figure 7**, it can be concluded that a minimum safety factor of 2.2 is necessary to satisfy the fatigue limit state.

In case of extradosed bridge, all stay cables (EDCs) exhibit almost same DCR irrespective of their locations with respect to tower-deck intersection. **Figure 8** also

**Figure 7.** *Effect of fatigue load on DCR of stay cables of cable-stayed bridge.*

minimize the deflection and to resist the bending moments due to long-term effects

Nonlinearity effects including cable sag effect due to self-weight of stay cables and P-Delta effects due to interaction of deck and tower are also considered in the analysis of both bridge types. Reduced or equivalent modulus of elasticity of stay

<sup>1</sup> <sup>þ</sup> ð Þ wL <sup>2</sup>

Eq. (1) is known as Ernst' formula in which Eeq is equivalent modulus of elasticity, E is effective material modulus of elasticity, A is cross-sectional area of stay cable, w is cable weight per unit length, L is horizontal projected length and T is

For the evaluation of safety factor of stay cables at fatigue limit state, moving load analysis is performed by applying fatigue design load (T-load: 200 kN) to the cable-stayed and extradosed bridge models. Then, influence line diagrams (ILDs) of axial forces in stay cables are drawn by using Breslau Muller Principle and maximum and minimum design variables are calculated. **Figure 6** shows the ILDs of axial forces of stay cables (C1 and EDC1) of cable-stayed and extradosed bridges, respectively. It is observed that the area under ILD of C1 is larger than that of EDC1

influenced by fatigue load as compared to cable-stayed bridge. Subsequently, cable reversal stresses and design stress range ð Þ Δ*σ<sup>d</sup>* values are determined by considering the cyclic loads of constant amplitude and fully reversed nature as per the guidelines of fatigue design recommendations for steel structures [8]. To assess the safety factor at fatigue limit state based on equivalent stress range theory, following

AE 12T3

(1)

Eeq <sup>¼</sup> <sup>E</sup>

**3. Safety evaluation of stay cables by deterministic method**

under the same fatigue load which indicates that extradosed bridge is less

and live loads.

**2.6 Effects of nonlinearity**

*Structural Integrity and Failure*

cables is determined by:

tensile force in stay cable.

**3.1 Fatigue limit state**

equation should be satisfied [9]:

*ILDs of axial forces of stay cables C1 and EDC1.*

**Figure 6.**

**146**

**Figure 8.** *Effect of fatigue load on DCR of stay cables of extradosed bridge.*

shows that the safety factor of 1.67 satisfies the fatigue limit state. From probabilistic point of view, the safety of stay cables under the fatigue limit state is verified by satisfying the Palmgren-Miner hypothesis which states that fatigue failure of stay cables occurs when the accumulated damage exceeds one, *D t*ð Þ≥ 1. Thus, if the fatigue failure time is denoted by *<sup>T</sup> <sup>f</sup>* , then *P T <sup>f</sup>* <sup>≤</sup> *<sup>t</sup>* <sup>¼</sup> *PDt* ð Þ ð Þ≥<sup>1</sup> . But this study is only limited to the deterministic fatigue analysis.

### **3.2 Ultimate limit state**

After evaluation of safety factor of stay cables at fatigue limit state, the safety factor is further evaluated and verified at ultimate limit state. For that, following equation should be verified [9]:

$$\chi\_i \left( \frac{N\_u}{N\_{rd}} \right) \le \mathbf{1.0} \tag{6}$$

not factored with the same coefficient of dead load. This approach is more reason-

*Safety Evaluation of Stay Cables of Cable-Stayed and Extradosed Bridges via Deterministic…*

is why, first method is selected in this paper for the sake of simplification.

The dynamic cable force is applied as an equivalent static force in the correct orientation on both anchorage points of cable by considering CLDF of 2.0 in the load combination. Following the aforementioned approach, the effects of cable loss on DCR of stay cables of cable-stayed and extradosed bridges are investigated thoroughly. **Figure 9** compares the DCR of stay cables of the cable-stayed bridge with and without sudden loss of single and multiple stay cables at different safety

*Effect of cable loss on DCR of stay cables of cable-stayed bridge. (a) Safety factor of 2.5, (b) safety factor of 2.3,*

In design viewpoint of long-span cable-supported bridges, PTI [12] suggests two methods. The first method consists of a simplified quasi-static analysis of cablesupported bridge with a missing cable under factored dead and live loads. These loads are combined with the static cable loss dynamic impact force (CLDF) resulting from the sudden breakage of a cable with the additional load factor of 1.1 on CLDF. In second method, PTI allows the usage of a dynamic analysis to compute the structural response more accurately due to an abrupt cable failure. However, little guidance is provided by PTI on how to conduct such a dynamic analysis. That

able for bridges with a rigid deck according to Mermigas [11].

*DOI: http://dx.doi.org/10.5772/intechopen.92215*

**Figure 9.**

**149**

*and (c) safety factor of 2.2.*

where *γ<sup>i</sup>* is structural importance factor equal to 1.0, *Nrd* is equivalent design resistance of stay cables and *Nu* is ultimate axial load which is estimated by applying load and resistance factor design (LRFD) approach which considers the probabilities associated with simultaneous occurrence of different types of loads. Equations (7) and (8) yield ultimate axial loads for stay cables of cable-stayed and extradosed bridges, respectively [10]:

$$N\_{\rm u,CSB} = \mathbf{1.25(DC+PS)} + \mathbf{1.5DW} + \mathbf{1.75(LL+IM)}\tag{7}$$

$$N\_{u,EDB} = \mathbf{1.25DC} + \mathbf{1.5DW} + \mathbf{PS} + \mathbf{Pi} + \mathbf{1.75}(LL + IM) \tag{8}$$

where the subscripts CSB and EDB are cable-stayed and extradosed bridges, respectively, DC is dead load (components and attachment), DW is dead load (wearing surface and utility), PS is pretension force, Pi is prestress force, LL is live load and IM is dynamic load allowance. In case of extradosed bridge, PS and Pi are

### *Safety Evaluation of Stay Cables of Cable-Stayed and Extradosed Bridges via Deterministic… DOI: http://dx.doi.org/10.5772/intechopen.92215*

not factored with the same coefficient of dead load. This approach is more reasonable for bridges with a rigid deck according to Mermigas [11].

In design viewpoint of long-span cable-supported bridges, PTI [12] suggests two methods. The first method consists of a simplified quasi-static analysis of cablesupported bridge with a missing cable under factored dead and live loads. These loads are combined with the static cable loss dynamic impact force (CLDF) resulting from the sudden breakage of a cable with the additional load factor of 1.1 on CLDF. In second method, PTI allows the usage of a dynamic analysis to compute the structural response more accurately due to an abrupt cable failure. However, little guidance is provided by PTI on how to conduct such a dynamic analysis. That is why, first method is selected in this paper for the sake of simplification.

The dynamic cable force is applied as an equivalent static force in the correct orientation on both anchorage points of cable by considering CLDF of 2.0 in the load combination. Following the aforementioned approach, the effects of cable loss on DCR of stay cables of cable-stayed and extradosed bridges are investigated thoroughly. **Figure 9** compares the DCR of stay cables of the cable-stayed bridge with and without sudden loss of single and multiple stay cables at different safety

### **Figure 9.**

shows that the safety factor of 1.67 satisfies the fatigue limit state. From probabilistic point of view, the safety of stay cables under the fatigue limit state is verified by satisfying the Palmgren-Miner hypothesis which states that fatigue failure of stay cables occurs when the accumulated damage exceeds one, *D t*ð Þ≥ 1. Thus, if the fatigue failure time is denoted by *<sup>T</sup> <sup>f</sup>* , then *P T <sup>f</sup>* <sup>≤</sup> *<sup>t</sup>* <sup>¼</sup> *PDt* ð Þ ð Þ≥<sup>1</sup> . But this study is

After evaluation of safety factor of stay cables at fatigue limit state, the safety factor is further evaluated and verified at ultimate limit state. For that, following

where *γ<sup>i</sup>* is structural importance factor equal to 1.0, *Nrd* is equivalent design resistance of stay cables and *Nu* is ultimate axial load which is estimated by applying load and resistance factor design (LRFD) approach which considers the probabilities associated with simultaneous occurrence of different types of loads. Equations (7) and (8) yield ultimate axial loads for stay cables of cable-stayed and extradosed

where the subscripts CSB and EDB are cable-stayed and extradosed bridges, respectively, DC is dead load (components and attachment), DW is dead load (wearing surface and utility), PS is pretension force, Pi is prestress force, LL is live load and IM is dynamic load allowance. In case of extradosed bridge, PS and Pi are

*Nu*,*CSB* ¼ 1*:*25ð Þþ *DC* þ *PS* 1*:*5*DW* þ 1*:*75ð Þ *LL* þ *IM* (7) *Nu*,*EDB* ¼ 1*:*25*DC* þ 1*:*5*DW* þ *PS* þ *Pi* þ 1*:*75ð Þ *LL* þ *IM* (8)

≤1*:*0 (6)

*γi Nu Nrd* 

only limited to the deterministic fatigue analysis.

*Effect of fatigue load on DCR of stay cables of extradosed bridge.*

**3.2 Ultimate limit state**

*Structural Integrity and Failure*

**Figure 8.**

equation should be verified [9]:

bridges, respectively [10]:

**148**

*Effect of cable loss on DCR of stay cables of cable-stayed bridge. (a) Safety factor of 2.5, (b) safety factor of 2.3, and (c) safety factor of 2.2.*

factors. It can be observed from **Figure 9** that loss of two cables (C35&36) yields maximum DCR in the adjacent stay cables. This multiple cable loss event can also trigger the progressive collapse of the entire cable-stayed bridge.

greater than 1.0 even at a safety factor of 1.67 which elucidates that a minimum safety factor of 1.75 is essential under extreme loading condition for the safe design

*Safety Evaluation of Stay Cables of Cable-Stayed and Extradosed Bridges via Deterministic…*

With the development of reliability-based methods, it has become evident that the traditional deterministic finite element method is not sufficient to properly design advanced structures or structural components subjected to a variety of complex loading conditions. Therefore, uncertainties in loads, material behavior and geometric configuration must be considered to provide rational reliability anal-

In this paper, the safety factors of stay cables are also assessed by the nondeterministic method. For that, a probabilistic based reliability analysis code is prepared based on the mean value first order second moment (MVFOSM) reliability method. Basic random variables used for this program are material strength, dead loads and live loads. One million samples of normally distributed random variables are generated by using Monte Carlo simulation technique. The coefficient of variations (COV) of random variables are taken from the Ref. [13]. The program calculates the cable force (*S*) and resistance (*R*), and verifies the limit state function, i.e., *Z* ¼ *R* � *S* where *R* and *S* are linear and uncorrelated random variables. Subsequently, reliability index (*β*) and probability of failure (*P <sup>f</sup>* ) are determined from the rela-

*<sup>σ</sup><sup>Z</sup>* and *P <sup>f</sup>* ¼ Φð Þ �*β* , respectively where *μ<sup>z</sup>* is mean value, *σ<sup>z</sup>* is standard

**4. Safety evaluation of stay cables by nondeterministic method**

ysis and to describe the structural behavior with higher level of confidence.

deviation and Φ is cumulative distribution function for normal distribution.

**Safety factor** *β P <sup>f</sup>* 2.5 8.17 1.48 � <sup>10</sup>�<sup>16</sup> 2.4 6.79 5.31 � <sup>10</sup>�<sup>12</sup> 2.3 5.04 2.36 � <sup>10</sup>�<sup>7</sup> 2.2 2.91 1.8 � <sup>10</sup>�<sup>3</sup>

**Safety factor** *β P <sup>f</sup>* 1.60 1.9 2.84 � <sup>10</sup>�<sup>2</sup> 1.67 4.37 6.03 � <sup>10</sup>�<sup>6</sup> 1.75 6.81 4.66 � <sup>10</sup>�<sup>12</sup> 1.85 9.32 5.76 � <sup>10</sup>�<sup>21</sup>

For the acceptable values of probability of safety of structures, United States Army Corps of Engineers (USACE) suggests that the estimated reliability indices should be at least 3.0 (for above average performance) and 4.0 (for good performance) [14]. Based on it, the calculations of reliability index and failure probability for both bridge types are carried out and shown in **Tables 4** and **5**. These tables clarify that reliability index decreases when safety factor decreases from 2.5 to 2.2 in case of cable-stayed bridge. For instance, the safety factors of 2.5, 2.3 and 2.2 yield

of extradosed bridges.

*DOI: http://dx.doi.org/10.5772/intechopen.92215*

tionships *<sup>β</sup>* <sup>¼</sup> *<sup>μ</sup><sup>Z</sup>*

**Table 4.**

**Table 5.**

**151**

*Reliability analysis results of C1 of cable-stayed bridge.*

*Reliability analysis results of EDC1 of extradosed bridge.*

Moreover, **Figure 9** also depicts that with the decrease of safety factor of stay cables, DCR increases accordingly and a minimum safety factor of 2.3 is essential to meet the requirements of ultimate limit state. Similarly, the effects of cable loss on DCR of EDCs are also investigated as shown in **Figure 10**. It is observed that the loss of two cables (EDC1&2) yields maximum DCR of EDCs and a safety factor of 1.67 is compulsory under normal loading condition which should be increased to achieve higher safety under extreme damaging condition.

In addition to that, the effect of corrosion as well as the combined effect of corrosion and cable loss on DCR of C1 and EDC1 are also examined at different safety factors in this study. For that, a simple corrosion model is adopted by introducing the uniform corrosion of 10% throughout the cable length as a change in cable area. The effective modulus of elasticity of corroded cable is determined and static analyses are performed. **Figure 11** shows that DCR of C1 is greater than 1.0 at a safety factor of 2.4 which indicates that the safety factor of 2.5 is the minimum factor required to avoid the rupture of C1. On the other hand, DCR of EDC1 is

### **Figure 10.**

*Effect of cable loss on DCR of stay cables of extradosed bridge. (a) Safety factor of 1.67 and (b) safety factor of 1.75.*

*Safety Evaluation of Stay Cables of Cable-Stayed and Extradosed Bridges via Deterministic… DOI: http://dx.doi.org/10.5772/intechopen.92215*

greater than 1.0 even at a safety factor of 1.67 which elucidates that a minimum safety factor of 1.75 is essential under extreme loading condition for the safe design of extradosed bridges.

### **4. Safety evaluation of stay cables by nondeterministic method**

With the development of reliability-based methods, it has become evident that the traditional deterministic finite element method is not sufficient to properly design advanced structures or structural components subjected to a variety of complex loading conditions. Therefore, uncertainties in loads, material behavior and geometric configuration must be considered to provide rational reliability analysis and to describe the structural behavior with higher level of confidence.

In this paper, the safety factors of stay cables are also assessed by the nondeterministic method. For that, a probabilistic based reliability analysis code is prepared based on the mean value first order second moment (MVFOSM) reliability method. Basic random variables used for this program are material strength, dead loads and live loads. One million samples of normally distributed random variables are generated by using Monte Carlo simulation technique. The coefficient of variations (COV) of random variables are taken from the Ref. [13]. The program calculates the cable force (*S*) and resistance (*R*), and verifies the limit state function, i.e., *Z* ¼ *R* � *S* where *R* and *S* are linear and uncorrelated random variables. Subsequently, reliability index (*β*) and probability of failure (*P <sup>f</sup>* ) are determined from the relationships *<sup>β</sup>* <sup>¼</sup> *<sup>μ</sup><sup>Z</sup> <sup>σ</sup><sup>Z</sup>* and *P <sup>f</sup>* ¼ Φð Þ �*β* , respectively where *μ<sup>z</sup>* is mean value, *σ<sup>z</sup>* is standard deviation and Φ is cumulative distribution function for normal distribution.

For the acceptable values of probability of safety of structures, United States Army Corps of Engineers (USACE) suggests that the estimated reliability indices should be at least 3.0 (for above average performance) and 4.0 (for good performance) [14]. Based on it, the calculations of reliability index and failure probability for both bridge types are carried out and shown in **Tables 4** and **5**. These tables clarify that reliability index decreases when safety factor decreases from 2.5 to 2.2 in case of cable-stayed bridge. For instance, the safety factors of 2.5, 2.3 and 2.2 yield


**Table 4.**

factors. It can be observed from **Figure 9** that loss of two cables (C35&36) yields maximum DCR in the adjacent stay cables. This multiple cable loss event can also

Moreover, **Figure 9** also depicts that with the decrease of safety factor of stay cables, DCR increases accordingly and a minimum safety factor of 2.3 is essential to meet the requirements of ultimate limit state. Similarly, the effects of cable loss on DCR of EDCs are also investigated as shown in **Figure 10**. It is observed that the loss of two cables (EDC1&2) yields maximum DCR of EDCs and a safety factor of 1.67 is compulsory under normal loading condition which should be increased to achieve

In addition to that, the effect of corrosion as well as the combined effect of corrosion and cable loss on DCR of C1 and EDC1 are also examined at different safety factors in this study. For that, a simple corrosion model is adopted by introducing the uniform corrosion of 10% throughout the cable length as a change in cable area. The effective modulus of elasticity of corroded cable is determined and static analyses are performed. **Figure 11** shows that DCR of C1 is greater than 1.0 at a safety factor of 2.4 which indicates that the safety factor of 2.5 is the minimum factor required to avoid the rupture of C1. On the other hand, DCR of EDC1 is

*Effect of cable loss on DCR of stay cables of extradosed bridge. (a) Safety factor of 1.67 and (b) safety factor of*

*Effect of corrosion and, combined effect of cable loss and corrosion on DCR of C1 and EDC1.*

trigger the progressive collapse of the entire cable-stayed bridge.

higher safety under extreme damaging condition.

*Structural Integrity and Failure*

**Figure 10.**

**Figure 11.**

**150**

*1.75.*

*Reliability analysis results of C1 of cable-stayed bridge.*


**Table 5.** *Reliability analysis results of EDC1 of extradosed bridge.*

• Finite element analysis results show that cable-stayed and extradosed bridges are sufficiently redundant at safety factors ranging from 2.3 to 2.5 and 1.67, respectively under normal loading conditions. For cable-stayed bridges, ultimate strengths of stay cables are more critical than their fatigue strengths and a minimum safety factor of 2.3 is essential to satisfy the fatigue and ultimate limit states. However, in case of extradosed bridges, the ultimate strengths of stay cables are even more critical than their fatigue strengths and a minimum safety factor of 1.67 is indispensable to meet the limit state design requirements under normal loading conditions and it should be increased

*Safety Evaluation of Stay Cables of Cable-Stayed and Extradosed Bridges via Deterministic…*

• The reliability analysis results elucidate that a minimum safety factor of 2.25 is necessary for stay cables of cable-stayed bridge to achieve the target reliability index of 4.0. Whereas, in case of extradosed bridge, a safety factor of 1.67 yields the reliability index greater than 4.0 and a minimum safety factor of 1.66 is essential for the safe design of extradosed bridges. Moreover, the safety factor of 1.66 for extradosed bridges yields same reliability index as the safety

• The optimum safety factors evaluated by nondeterministic method are close to those obtained by deterministic finite element method. These outcomes imply that the structural reliability solutions for stay cables are rational and correct.

under extreme damaging conditions.

*DOI: http://dx.doi.org/10.5772/intechopen.92215*

factor of 2.25 for cable-stayed bridges.

**Author details**

**153**

Khawaja Ali\* and Aleena Saleem

provided the original work is properly cited.

Department of Civil Engineering, Yokohama National University, Japan

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\*Address all correspondence to: khawaja-ali-cd@ynu.jp

**Figure 12.** *Graphical evaluation of safety factor of C1 of cable-stayed bridge.*

**Figure 13.** *Graphical evaluation of safety factor of EDC1 of extradosed bridge.*

the reliability indices of 8.17, 5.04 and 2.91 for C1, respectively. Similarly, in case of extradosed bridge, the reliability index increases as safety factor increases from 1.60 to 1.85 for EDC1. The reliability analysis results also show that the safety factors of 2.3 and 1.67 yield the target reliability index greater than 4.0 for good performance of both bridge types. Based on these results, the optimum safety factors of C1 and EDC1 are calculated graphically as shown in **Figures 12** and **13**, respectively. It is observed that the safety factors of 2.25 and 1.66 yield the target reliability index of 4.0 and failure probability of 10<sup>5</sup> for stay cables C1 and EDC1, respectively. This also elucidates that the safety factor of 1.66 for extradosed bridges yields same reliability index as the safety factor of 2.25 for cable-stayed bridges.

### **5. Conclusions**

In this paper, a parametric study on safety factor of stay cables of cable-stayed and extradosed bridges is carried out by using deterministic and nondeterministic methods. Following conclusions can be drawn from this study:

*Safety Evaluation of Stay Cables of Cable-Stayed and Extradosed Bridges via Deterministic… DOI: http://dx.doi.org/10.5772/intechopen.92215*


### **Author details**

the reliability indices of 8.17, 5.04 and 2.91 for C1, respectively. Similarly, in case of extradosed bridge, the reliability index increases as safety factor increases from 1.60 to 1.85 for EDC1. The reliability analysis results also show that the safety factors of 2.3 and 1.67 yield the target reliability index greater than 4.0 for good performance of both bridge types. Based on these results, the optimum safety factors of C1 and EDC1 are calculated graphically as shown in **Figures 12** and **13**, respectively. It is observed that the safety factors of 2.25 and 1.66 yield the target reliability index of 4.0 and failure probability of 10<sup>5</sup> for stay cables C1 and EDC1, respectively. This also elucidates that the safety factor of 1.66 for extradosed bridges yields same

In this paper, a parametric study on safety factor of stay cables of cable-stayed and extradosed bridges is carried out by using deterministic and nondeterministic

reliability index as the safety factor of 2.25 for cable-stayed bridges.

methods. Following conclusions can be drawn from this study:

**5. Conclusions**

**152**

**Figure 12.**

*Structural Integrity and Failure*

**Figure 13.**

*Graphical evaluation of safety factor of C1 of cable-stayed bridge.*

*Graphical evaluation of safety factor of EDC1 of extradosed bridge.*

Khawaja Ali\* and Aleena Saleem Department of Civil Engineering, Yokohama National University, Japan

\*Address all correspondence to: khawaja-ali-cd@ynu.jp

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

### **References**

[1] Collings D, Gonzalez AS. Extradosed and cable-stayed bridges, exploring the boundaries. Proceedings of the Institution of Civil Engineers—Bridge Engineering. 2013;**166**(4):231-239

[2] Prestressed Concrete Technical Institute. Extradosed Bridge Design and Construction Standard. Japan: Gihodo Shuppan; 2009

[3] Ali K, Katsuchi H, Yamada H. Parametric study on cable safety of cable-stayed bridge considering ultimate and fatigue limit states. Journal of Structural Engineering, JSCE. 2018; **64**(A):99-108

[4] Japan Road Association. Japanese Specifications for Highway Bridges. Japan; 2002

[5] Elishakoff I. Safety factors and reliability: Deterministic actual stress & random yield stress. Safety Factors and Reliability, Friends or Foes. 2004:75-96. Available from: https://doi.org/10.1007/ 978-1-4020-2131-2\_4

[6] Xiangyang W, Guanghui Z. Bridge reliability analysis based on the FEM and Monte-Carlo method. In: 2010 International Conference on Intelligent Computation Technology and Automation. 2010

[7] Zhang W, Cai CS. Fatigue reliability assessment for existing bridges considering vehicle speed and road surface conditions. Journal of Bridge Engineering. 2012;**17**(3):443-453

[8] Japanese Society of Steel Construction. Fatigue Design Recommendations for Steel Structures. Japan; 1995

[9] Japan Society of Civil Engineers. Standard Specifications for Steel and Composite Structures. Japan; 2007

[10] American Association of State Highway and Transportation Officials. LRFD Bridge Design Specifications. America; 2012

[11] Mermigas K. Behavior and design of extradosed bridges [thesis]. Toronto: University of Toronto; 2008

[12] Post-tensioning institute. Recommendations for Stay cable design, testing and installation. America; 2007

[13] Nowak AS. Calibration of LRFD Bridge Design Code. NCHRP Report 368. Washington, DC: Transportation Research Board, National Research Council; 1999

[14] Phoon KK, editor. Reliability-Based Design in Geotechnical Engineering: Computations and Applications. London and New York: Taylor & Francis; 2008

**References**

Shuppan; 2009

**64**(A):99-108

Japan; 2002

978-1-4020-2131-2\_4

Automation. 2010

Japan; 1995

**154**

[1] Collings D, Gonzalez AS. Extradosed and cable-stayed bridges, exploring the

[10] American Association of State Highway and Transportation Officials. LRFD Bridge Design Specifications.

University of Toronto; 2008

[12] Post-tensioning institute.

[11] Mermigas K. Behavior and design of extradosed bridges [thesis]. Toronto:

Recommendations for Stay cable design, testing and installation. America; 2007

[13] Nowak AS. Calibration of LRFD Bridge Design Code. NCHRP Report 368. Washington, DC: Transportation Research Board, National Research Council; 1999

[14] Phoon KK, editor. Reliability-Based Design in Geotechnical Engineering: Computations and Applications. London and New York: Taylor & Francis; 2008

America; 2012

boundaries. Proceedings of the Institution of Civil Engineers—Bridge Engineering. 2013;**166**(4):231-239

*Structural Integrity and Failure*

[2] Prestressed Concrete Technical Institute. Extradosed Bridge Design and Construction Standard. Japan: Gihodo

[3] Ali K, Katsuchi H, Yamada H. Parametric study on cable safety of cable-stayed bridge considering

ultimate and fatigue limit states. Journal of Structural Engineering, JSCE. 2018;

[4] Japan Road Association. Japanese Specifications for Highway Bridges.

[5] Elishakoff I. Safety factors and reliability: Deterministic actual stress & random yield stress. Safety Factors and Reliability, Friends or Foes. 2004:75-96. Available from: https://doi.org/10.1007/

[6] Xiangyang W, Guanghui Z. Bridge reliability analysis based on the FEM and Monte-Carlo method. In: 2010 International Conference on Intelligent

[7] Zhang W, Cai CS. Fatigue reliability

Recommendations for Steel Structures.

[9] Japan Society of Civil Engineers. Standard Specifications for Steel and Composite Structures. Japan; 2007

Computation Technology and

assessment for existing bridges considering vehicle speed and road surface conditions. Journal of Bridge Engineering. 2012;**17**(3):443-453

[8] Japanese Society of Steel Construction. Fatigue Design

### *Edited by Resat Oyguc and Faham Tahmasebinia*

Structural integrity and failure assessment have been considered by many fields of engineers as it is a multi-disciplinary concept. The assessment procedure vitally ensures that structural elements will remain functional throughout their service lives. Structural failure refers to the loss of structural integrity by means of loss at the component- or system-level elements. The main concern of integrity assessment is that a structural failure may be avoided at the service level by designing the structure to withstand its designated loads. Hence, for satisfactory structural performance, structural safety, failure, and interaction between them should be considered throughout the design and analysis stages. This book is a collection of chapters that provide the researcher with a comprehensive perspective on structural integrity and its sub-disciplines.

Published in London, UK © 2021 IntechOpen © Tatomm / iStock

Structural Integrity and Failure

Structural Integrity

and Failure

*Edited by Resat Oyguc and Faham Tahmasebinia*