**4. Use of design tools for element level performance estimation**

The building is designed using ETABS software which gives the structure and element level performance of building. The performance of building elements can be evaluated using prevalent concrete models of confined concrete and high strength concrete. RC Analysis-Columns [17], web-portal is developed by Virtual Laboratory for Earthquake Engineering (VLEE, UTPL). Also, the SEMAp software developed by Ozmen (2007) gives the element capacity based on four concrete models [18]. The element level performance is suggested by Euro-code and Turkish-code for design of buildings for earthquakes [8, 9]. Hence, evaluating the performance of columns (i.e. failed element at the end of POA) using ETABS, EC-8, RC-Analysis (RCA) and SEMAp is interesting segment for assessing the performance.

forming two hinges (refer **Figure 7a**). The curvature can be found using strain rates and member (*M* � *φ*) curve is used for managing performance at element level. The number of lateral load resisting beams and columns that can be accepted to undergo damage is the decision of either the regulatory bodies or the stakeholders which will influence the target performance to be achieved by design engineer. A sample performance level prescribed by TEC-2007 for Life Safety (LS) gives the basis for defining and making a building with mitigated risk (refer **Figure 8**). However, such limits are not prescribed by IS-1893 and makes it more critical for engineers to select and debate performance levels with their clients or stakeholders. Similarly, ASCE-41 suggests the rotation limits for Life Safety (LS) performance level which is 75% use of post-elastic rotation of the member (refer

The ultimate rotation limit is suggested by EC-8 for Near Collapse (NC) performance i.e. 100% use of post-yield deformation and Life Safety (LS) is 75%

*Ultimate chord rotation capacity for Near Collapse (NC) performance level:*

*Lpl* <sup>1</sup> � <sup>0</sup>*:*5*Lpl*

*LV*

*Lpl* ¼ 0*:*025*LV* þ 0*:*125*h* þ 0*:*02*db f <sup>y</sup>* (5)

*θ<sup>y</sup>* ¼ *φy:LV=*3 (4)

(3)

*θum* ¼ *θ<sup>y</sup>* þ *φ<sup>u</sup>* � *φ<sup>y</sup>*

*Definition of criteria for life safety (LS) performance limit (TEC 2007).*

*Definition of criteria for life safety (LS) performance limit (ASCE-41).*

of ultimate rotation limit (refer Eqs. (4)–(7)).

*Natural Hazards - Impacts, Adjustments and Resilience DOI: http://dx.doi.org/10.5772/intechopen.94303*

*Chord rotation at yield:*

*Length of plastic hinge:*

**Figure 9**).

**Figure 8.**

**Figure 9.**

**219**

## **4.1 Understanding the element deformations**

The change in geometry of elements is picturized in form of curvature (*φ*), rotation (*θ*) and displacement (*δ*). The ductility in these elements will give them ability to absorb seismic forces and display higher performance before failure. The curvature ductility (*φu=φy*) is more meaningful than rotational ductility (*θu=θy*) as the calculation of yield rotation is not singular value [19].

The testing of beams and columns under transverse loading will be the basis for element level performance (refer **Figure 7c**). The building elements follow double curvature and under lateral loading both ends undergo plastic deformations

**Figure 7.** *Element level analysis framework under transverse loading. (a) Double curvature in beams/columns. (b) Plastic analysis of column. (c) Testing of elements under transverse loading.*

*Natural Hazards - Impacts, Adjustments and Resilience DOI: http://dx.doi.org/10.5772/intechopen.94303*

**4. Use of design tools for element level performance estimation**

RC-Analysis (RCA) and SEMAp is interesting segment for assessing the

The change in geometry of elements is picturized in form of curvature (*φ*), rotation (*θ*) and displacement (*δ*). The ductility in these elements will give them ability to absorb seismic forces and display higher performance before failure. The curvature ductility (*φu=φy*) is more meaningful than rotational ductility (*θu=θy*) as

The testing of beams and columns under transverse loading will be the basis for element level performance (refer **Figure 7c**). The building elements follow double curvature and under lateral loading both ends undergo plastic deformations

*Element level analysis framework under transverse loading. (a) Double curvature in beams/columns.*

*(b) Plastic analysis of column. (c) Testing of elements under transverse loading.*

**4.1 Understanding the element deformations**

*Natural Hazards - Impacts, Adjustments and Resilience*

the calculation of yield rotation is not singular value [19].

performance.

**Figure 7.**

**218**

The building is designed using ETABS software which gives the structure and element level performance of building. The performance of building elements can be evaluated using prevalent concrete models of confined concrete and high strength concrete. RC Analysis-Columns [17], web-portal is developed by Virtual Laboratory for Earthquake Engineering (VLEE, UTPL). Also, the SEMAp software developed by Ozmen (2007) gives the element capacity based on four concrete models [18]. The element level performance is suggested by Euro-code and Turkish-code for design of buildings for earthquakes [8, 9]. Hence, evaluating the performance of columns (i.e. failed element at the end of POA) using ETABS, EC-8, forming two hinges (refer **Figure 7a**). The curvature can be found using strain rates and member (*M* � *φ*) curve is used for managing performance at element level. The number of lateral load resisting beams and columns that can be accepted to undergo damage is the decision of either the regulatory bodies or the stakeholders which will influence the target performance to be achieved by design engineer. A sample performance level prescribed by TEC-2007 for Life Safety (LS) gives the basis for defining and making a building with mitigated risk (refer **Figure 8**).

However, such limits are not prescribed by IS-1893 and makes it more critical for engineers to select and debate performance levels with their clients or stakeholders. Similarly, ASCE-41 suggests the rotation limits for Life Safety (LS) performance level which is 75% use of post-elastic rotation of the member (refer **Figure 9**).

The ultimate rotation limit is suggested by EC-8 for Near Collapse (NC) performance i.e. 100% use of post-yield deformation and Life Safety (LS) is 75% of ultimate rotation limit (refer Eqs. (4)–(7)).

*Ultimate chord rotation capacity for Near Collapse (NC) performance level:*

$$\theta\_{um} = \theta\_{\mathcal{Y}} + \left(\rho\_u - \rho\_{\mathcal{Y}}\right) L\_{pl} \left(\mathbf{1} - \frac{\mathbf{0}.5 L\_{pl}}{L\_{V}}\right) \tag{3}$$

*Chord rotation at yield:*

$$
\theta\_\mathcal{Y} = \varphi\_\mathcal{Y} L\_\mathcal{V} / \mathfrak{Z} \tag{4}
$$

*Length of plastic hinge:*

$$L\_{pl} = 0.025L\_V + 0.125h + 0.02d\_b f\_y \tag{5}$$

**Figure 8.** *Definition of criteria for life safety (LS) performance limit (TEC 2007).*

**Figure 9.** *Definition of criteria for life safety (LS) performance limit (ASCE-41).*

*Ultimate compression strain in concrete (EC8):*

$$
\varepsilon\_{\varepsilon u} = 0.004 + 1.4 \rho\_s f\_{yh} \varepsilon\_m / f\_{\infty}^\circ \tag{6}
$$

**Figure 11.**

**Figure 12.**

**221**

*EC8 design code.*

*ACI-318 code.*

*Section analysis results for RC column designed as per ACI-318 code. (a) M* � *φ curve as per RC analysis tool for column designed as per ACI-318 code. (b) M* � *φ curve as per SEMAp tool for column designed as per*

*Natural Hazards - Impacts, Adjustments and Resilience DOI: http://dx.doi.org/10.5772/intechopen.94303*

*Section analysis results for RC column designed as per EC8 design code. (a) M* � *φ curve as per RC analysis tool for column designed as per EC8 design code. (b) M* � *φ curve as per SEMAp tool for column designed as per*

*f* , *cc* = confined compressive strength of concrete *fl* = confining pressure *Ash* = area of confinement reinforcement

#### **4.2 Tools for section analysis of building elements**

The section analysis of confined concrete is dependent on the type of detailing done for beams and columns which undergo in-elastic deformations. ETABS software uses *Mander*-model for confined concrete to estimate increased strength due to lateral reinforcements. However, without complete detailing of the column reinforcement it is not suitable to directly assume the performance. Hence, it is suitable to use a separate tool to generate (*M* � *φ*) and (*σ* � *ε*) plots and the results of which can be uploaded in ETABS software to give more accuracy in terms of overall performance of building. The two such tools are RCA and SEMAp, which are used to compare the performance limits (refer **Figures 10**–**12**).

#### **4.3 Mapping of section analysis using design tools and design codes**

The mapping of threshold limits using design tools and codes gives an envelope for comparison. The ultimate rotation (*θu*) is sum of yield rotation (*θy*) and plastic rotation (*θp*). The length of plastic hinge is taken as 0.5D and absolute concrete strain (*εcu*) is calculated [20, 21]. It is observed that for IS designed building, the

#### **Figure 10.**

*Section analysis results for RC column designed as per IS code. (a) M* � *φ curve as per RC analysis tool for column designed as per IS code. (b) M* � *φ curve as per SEMAp tool for column designed as per IS code.*
