Interview of Natural Hazards and Seismic Catastrophe Insurance Research in China DOI: http://dx.doi.org/10.5772/intechopen.84159

stochastic damage scattered points can be viewed in Figure 12 with different color stripe, which represent limit state has shown in Table 3.

The damage zone of limit state can be represented from left to right respectively: none damage, slight damage, light damage, moderate damage, heavy damage and major damage or collapse. Statistics mean values and median values also be drawn

#### Figure 12.

which are shown in Figure 10. The tendency of the seismic vulnerability changed

The damage analysis based two EDPs parameters in IDA for Friuli Italy-02 (i: ISD%; ii: MFA).

The damage scatter distribution of multi-storey RC buildings is shown in Figure 11. The middle black curve means median values of whole damage data and

Damage, in the context of life-cycle cost assessment, refers not only to structural damage but also to non-structural damage. The latter including the case of architectural damage, mechanical, electrical and plumbing damage and also the damage of furniture, equipment and other contents in factory buildings. The maximum inter-storey drift has been considered as the structural damage response parameter. On the other hand, the peak ground acceleration (PGA) is associated with the loss

Five thousand times stochastic calculation has been made using Monte Carlo sampling method consideration of random materials and structural variables and

of contents, like furniture and equipment which located in ground.

is partly based on the work of Elens and Meskouris [8].

Natural Hazards - Risk, Exposure, Response, and Resilience

blue curves means 15% deviation limit.

4.2 Damage analysis of industrial buildings

The relation between the drift ratio limits with the limit state. Employed in this study is partly based on the work of Ghobarah [7] for ductile RC moment resisting frames, and at the same time vast stochastic sampling based Monte Carlo method based local construction code in Western China also impact the limit state setting in this research. The relation of the limit state with the values of the floor acceleration

more obvious than ever.

Figure 10.

Figure 11.

226

The damage scatter distribution of RC buildings.

Damage scattered distribution based limit states (i: ISD, ii: PGA).


#### Table 3.

Limit state drift ratio, floor acceleration of factory buildings.

Figure 13. The annual seismic column vulnerability in 50 years.

as blue line in scatter diagram. The trend of scatters has clearly radial and diverging pattern like a slant bell mouth and every circle point in figure means single time history wave.

Ca

<sup>i</sup> and Pa

PDI

P DI ð Þ¼ . DIi

service life, which is almost 50 years in China.

where C<sup>θ</sup>

(Figure 14).

Limit state

Table 4.

229

median LCC is 1.89 Yuan/m<sup>2</sup>

Mean damage index %

Limit state parameters for cost estimation.

LS and C<sup>a</sup>

DOI: http://dx.doi.org/10.5772/intechopen.84159

The probabilities P<sup>θ</sup>

LSð Þ¼ t; s

annual monetary discount rate λ is taken constant and equal to 5%.

ν λ 1 � e �λ<sup>t</sup> ∑

Interview of Natural Hazards and Seismic Catastrophe Insurance Research in China

violation calculated based ISDmax and PGA according to Eqs. (4) and (5). The

�1

located in high seismic hazardous region of western China. In this research <sup>2500</sup>Yuan=m<sup>2</sup> is considered as CIN, meantime �10% variance is also included

The statistics median covered area of typical RC building is 3600 m<sup>2</sup>

Expected minor injury rate

N0 0 0 0 <sup>S</sup> 0.5 3.0 � <sup>10</sup>�<sup>5</sup> 4.0 � <sup>10</sup>�<sup>6</sup> 1.0 � <sup>10</sup>�<sup>6</sup> LI <sup>2</sup> 1.3 � <sup>10</sup>�<sup>4</sup> 1.8 � <sup>10</sup>�<sup>5</sup> 0.4 � <sup>10</sup>�<sup>5</sup> LII <sup>5</sup> 3.0 � <sup>10</sup>�<sup>4</sup> 4.0 � <sup>10</sup>�<sup>5</sup> 1.0 � <sup>10</sup>�<sup>5</sup> MI <sup>9</sup> 1.4 � <sup>10</sup>�<sup>3</sup> 1.6 � <sup>10</sup>�<sup>4</sup> 0.4 � <sup>10</sup>�<sup>4</sup> MII <sup>20</sup> 3.0 � <sup>10</sup>�<sup>3</sup> 4.0 � <sup>10</sup>�<sup>4</sup> 1.0 � <sup>10</sup>�<sup>4</sup> <sup>H</sup> <sup>45</sup> 3.0 � <sup>10</sup>�<sup>2</sup> 4.0 � <sup>10</sup>�<sup>3</sup> 1.0 � <sup>10</sup>�<sup>3</sup> Ma <sup>80</sup> 3.0 � <sup>10</sup>�<sup>1</sup> 4.0 � <sup>10</sup>�<sup>2</sup> 1.0 � <sup>10</sup>�<sup>2</sup>

average LCC is 2.06 Yuan/m<sup>2</sup> after calculation using above procedure, and annual

Calculate index based FEMA-227 [12]

companies will establish catastrophe insurance at moment. The final insurance

. There will add up 25% additional fee if insurance

Expected serious injury rate

where DIi, DIiþ1are the lower and upper bounds of the ith limit state for the two damage indices considered, while P DI ð Þ . DIi is the exceedance probability given occurrence of the earthquake for every limit state given by the following expression:

where Ptð Þ DI . DIi is the exceedance probability over a period [0,t]; and t is the

A more detailed description of the different damage rate and cost evaluation for each limit state cost can be found in Tables 4 and 5. The basic cost refers to the first component of the calculation formulas. While they are given in monetary units Yuan. The values of the mean damage index, loss of function, down time, expected minor injury rate, expected serious injury rate and expected death rate used in this study are based on [12]. Death rate denotes the number of persons that may die at a specific limit state and it is defined as the number of occupants � death rate. Table 4 provides the revised limit state parameters of cost evaluation in this work on the base of FEMA-227 limit state dependent damage consequence severities. After study local statistics data of construction engineering in Yinchuan, which

N i¼1 Ci,a LS � <sup>P</sup><sup>a</sup>

LS is respectively the seismic loss cost for the ith limit state

<sup>i</sup> of Eqs. (7) and (8) are calculated as follows:

<sup>i</sup> ¼ P DI ð Þ� . DIi P DI ð Þ . DIiþ<sup>1</sup> (10)

<sup>ν</sup><sup>t</sup> � ln 1 � Ptð Þ DI . DIi ½ � (11)

<sup>i</sup> (9)

. The annual

Expected death rate

The object of life-cycle seismic cost estimation is provide high reliable seismic insurance premium data for spread industrial buildings seismic catastrophe insurance of high seismic hazard region of China in consideration of multiple undetermined factors.

The basic calculation equations are based on the work of Lagaros and Mitropoulou [9] and background reference data come from our post research. So we can calculate statistical annual damage number according 7 limit states. Further the annual seismic column vulnerability according to 7 limit states after considering respective annual seismic exceedance probability at all Hazard levels shown in Figure 13.

#### 5. Life-cycle seismic disaster insurance premium estimation

In the research the hazard levels are defined in accordance to the hazard curve transferred from China seismic code and of the city of Yinchuan, western of China (latitude(N)38.4<sup>o</sup> , longitude(W)106.2<sup>o</sup> ). The life-cycle seismic cost (LCSC) was calculated finally through incremental dynamic analyses based on the post work of Jian Zhu [10, 11]. And then the seismic disaster insurance ratio is determined.

#### 5.1 Seismic insurance ratio of RC buildings

The total cost CTOT of a structure may refer either to the design life period of a new building or to the remaining life period of an existing or retrofitting one. The cost can be expressed as a function of time and the design vector s as follows Eqs. (4)–(11).

$$\mathbf{C}\_{TOT} = \mathbf{C}\_{IN}(\mathbf{s}) + \mathbf{C}\_{LS}(\mathbf{t}, \mathbf{s}) \tag{4}$$

where CIN is the initial cost of new or retrofitted buildings. CLS is the present value of the limit state seismic damage cost, that means seismic loss of the RC buildings through different limit state to consider in the work.

$$\mathbf{C}\_{LS}^{i,\theta} = \mathbf{C}\_{dam}^{i} + \mathbf{C}\_{con}^{i,\theta} + \mathbf{C}\_{ren}^{i} + \mathbf{C}\_{inc}^{i} + \mathbf{C}\_{inj}^{i} + \mathbf{C}\_{fat}^{i} \tag{5}$$

$$\mathbf{C}\_{LS}^{i,a} = \mathbf{C}\_{con}^{i,a} \tag{6}$$

where C<sup>i</sup> dam is the damage repair cost, Ci, <sup>θ</sup> con is the loss contents cost due to the structural damage Ci ren is the loss of rental cost, C<sup>i</sup> inc is the income loss cost, C<sup>i</sup> inj is the cost of injuries and C<sup>i</sup> fat is the cost of human fatality. These cost components are related to the damage of the structural system. Ci,a con is the loss contents cost due to ground acceleration or floor acceleration.

Based on a Poisson process model of the earthquake occurrences and an assumption that damaged buildings are immediately retrofitted to their original intact conditions after every seismic damage due to seismic attack.

$$\mathbf{C}\_{LS} = \mathbf{C}\_{LS}^{\theta} + \mathbf{C}\_{LS}^{t} \tag{7}$$

$$\mathbf{C}\_{LS}^{\theta}(t,s) = \frac{\nu}{\lambda} \left(\mathbf{1} - e^{-\lambda t}\right) \sum\_{i=1}^{N} \mathbf{C}\_{LS}^{i,\theta} \cdot P\_i^{\theta} \tag{8}$$

Interview of Natural Hazards and Seismic Catastrophe Insurance Research in China DOI: http://dx.doi.org/10.5772/intechopen.84159

$$\mathbf{C}\_{LS}^{a}(t,s) = \frac{\nu}{\lambda} \left(\mathbf{1} - e^{-\lambda t}\right) \sum\_{i=1}^{N} \mathbf{C}\_{LS}^{i\_{s}a} \cdot P\_{i}^{a} \tag{9}$$

where C<sup>θ</sup> LS and C<sup>a</sup> LS is respectively the seismic loss cost for the ith limit state violation calculated based ISDmax and PGA according to Eqs. (4) and (5). The annual monetary discount rate λ is taken constant and equal to 5%.

The probabilities P<sup>θ</sup> <sup>i</sup> and Pa <sup>i</sup> of Eqs. (7) and (8) are calculated as follows:

$$P\_i^{DI} = P(DI \ge DI\_i) - P(DI \ge DI\_{i+1}) \tag{10}$$

where DIi, DIiþ1are the lower and upper bounds of the ith limit state for the two damage indices considered, while P DI ð Þ . DIi is the exceedance probability given occurrence of the earthquake for every limit state given by the following expression:

$$P(DI \ge DI\_i) = \frac{-1}{\nu t} \cdot \ln\left[1 - P\_t(DI \ge DI\_i)\right] \tag{11}$$

where Ptð Þ DI . DIi is the exceedance probability over a period [0,t]; and t is the service life, which is almost 50 years in China.

A more detailed description of the different damage rate and cost evaluation for each limit state cost can be found in Tables 4 and 5. The basic cost refers to the first component of the calculation formulas. While they are given in monetary units Yuan. The values of the mean damage index, loss of function, down time, expected minor injury rate, expected serious injury rate and expected death rate used in this study are based on [12]. Death rate denotes the number of persons that may die at a specific limit state and it is defined as the number of occupants � death rate. Table 4 provides the revised limit state parameters of cost evaluation in this work on the base of FEMA-227 limit state dependent damage consequence severities.

After study local statistics data of construction engineering in Yinchuan, which located in high seismic hazardous region of western China. In this research <sup>2500</sup>Yuan=m<sup>2</sup> is considered as CIN, meantime �10% variance is also included (Figure 14).

The statistics median covered area of typical RC building is 3600 m<sup>2</sup> . The annual average LCC is 2.06 Yuan/m<sup>2</sup> after calculation using above procedure, and annual median LCC is 1.89 Yuan/m<sup>2</sup> . There will add up 25% additional fee if insurance companies will establish catastrophe insurance at moment. The final insurance


Table 4. Limit state parameters for cost estimation.

as blue line in scatter diagram. The trend of scatters has clearly radial and diverging pattern like a slant bell mouth and every circle point in figure means single time

The object of life-cycle seismic cost estimation is provide high reliable seismic insurance premium data for spread industrial buildings seismic catastrophe insur-

Mitropoulou [9] and background reference data come from our post research. So we can calculate statistical annual damage number according 7 limit states. Further the annual seismic column vulnerability according to 7 limit states after considering respective annual seismic exceedance probability at all Hazard levels shown in

In the research the hazard levels are defined in accordance to the hazard curve transferred from China seismic code and of the city of Yinchuan, western of China

calculated finally through incremental dynamic analyses based on the post work of Jian Zhu [10, 11]. And then the seismic disaster insurance ratio is determined.

The total cost CTOT of a structure may refer either to the design life period of a new building or to the remaining life period of an existing or retrofitting one. The cost can be expressed as a function of time and the design vector s as follows

where CIN is the initial cost of new or retrofitted buildings. CLS is the present value of the limit state seismic damage cost, that means seismic loss of the RC

ren <sup>þ</sup> <sup>C</sup><sup>i</sup>

con <sup>þ</sup> <sup>C</sup><sup>i</sup>

Based on a Poisson process model of the earthquake occurrences and an assumption that damaged buildings are immediately retrofitted to their original

CLS <sup>¼</sup> <sup>C</sup><sup>θ</sup>

ν λ 1 � e �λ<sup>t</sup> ∑

LS <sup>þ</sup> <sup>C</sup><sup>a</sup>

N i¼1 Ci, <sup>θ</sup> LS � <sup>P</sup><sup>θ</sup>

Ci,a LS <sup>¼</sup> <sup>C</sup>i,a

). The life-cycle seismic cost (LCSC) was

CTOT ¼ CINðÞþs CLSð Þ t; s (4)

inc <sup>þ</sup> <sup>C</sup><sup>i</sup>

fat is the cost of human fatality. These cost components are

inj <sup>þ</sup> <sup>C</sup><sup>i</sup>

con (6)

con is the loss contents cost due to the

inc is the income loss cost, C<sup>i</sup>

con is the loss contents cost due to

LS (7)

<sup>i</sup> (8)

fat (5)

inj is the

ance of high seismic hazard region of China in consideration of multiple

Natural Hazards - Risk, Exposure, Response, and Resilience

5. Life-cycle seismic disaster insurance premium estimation

, longitude(W)106.2<sup>o</sup>

buildings through different limit state to consider in the work.

dam is the damage repair cost, Ci, <sup>θ</sup>

related to the damage of the structural system. Ci,a

Cθ

ground acceleration or floor acceleration.

dam <sup>þ</sup> <sup>C</sup>i,<sup>θ</sup>

ren is the loss of rental cost, C<sup>i</sup>

intact conditions after every seismic damage due to seismic attack.

LSð Þ¼ t; s

5.1 Seismic insurance ratio of RC buildings

Ci,<sup>θ</sup> LS <sup>¼</sup> <sup>C</sup><sup>i</sup>

The basic calculation equations are based on the work of Lagaros and

history wave.

Figure 13.

(latitude(N)38.4<sup>o</sup>

Eqs. (4)–(11).

where C<sup>i</sup>

228

structural damage Ci

cost of injuries and C<sup>i</sup>

undetermined factors.


Table 5.

Limit state costs-calculation formula.

Figure 14. The probability characteristics and constitution of RC buildings' LCC.

payment per people is about 70.9–77.2 Yuan annually in considering of local life endurance in this research on base of average living space per person equal 30 m<sup>2</sup> . The result is complete acceptable level for local people in Yinchuan city of western China as research sample region finally and have applied into local insurance policy successfully.

#### 5.2 Seismic insurance ratio of industrial buildings

Then we can use the Eqs. (4)–(11) based data of Table 6 to calculate life-cycle seismic cost of factory buildings in selected region in consideration of random variables from ground vibration, material character and time cost.

The initial unit construction cost of the building is estimated ¥1200/m2 and 10% deviation is considered in calculation. The cost of machines and nonstructural contents is supposed as ¥3000/m<sup>2</sup> and ¥300/m<sup>2</sup> respectively in research.

The annual median seismic cost of structural damage of industrial buildings is ¥3419 and corresponding annual median value of non-structural damage including machine and facilities in factory buildings is ¥8505 in Figure 15. The average and median values of every cost category are shown in Table 7.

<sup>p</sup> <sup>¼</sup> <sup>L</sup> 1 � r � e

Where p is insurance premium rate, L is expected loss rate, r is discount rate, e is additional charges rate including e<sup>1</sup> special reserve rate for claims, e<sup>2</sup> is commission rate, e<sup>3</sup> is development fund rate and e<sup>4</sup> is other fee rate. In research refer to Taiwan seismic insurance rate, e<sup>1</sup> ¼ 4%, e<sup>2</sup> ¼ 12:5%, e<sup>3</sup> ¼ 0:5%, e<sup>4</sup> ¼ 22%, r ¼ 5%.So the

Single-storey industrial buildings Cost category Calculation formula Basic cost Damage/repair Replacement cost � FA\* � DI\* ¥1200/m<sup>2</sup> Loss of machine & contents Unit cost � FA\* � DI\* ¥3300/m<sup>2</sup> Rental Rental rate � FA\* � LF\* ¥30/mo/m<sup>2</sup> Income Rental rate � FA\* � LF\* ¥2000/ye/m<sup>2</sup> Minor injury MI per cost � FA\* � OR\* � rate ¥2000/per Serious injury SI per cost � FA\* � OR\* � rate ¥2 � <sup>10</sup><sup>5</sup>

Interview of Natural Hazards and Seismic Catastrophe Insurance Research in China

Human fatality HF per cost � FA\* � OR\* � rate ¥5 � <sup>10</sup><sup>5</sup>

The annual median SLCC probability distribution of factory buildings (from left to right: Structural damage,

Damage/repair 3603 5.67 3419 5.65 Rental 599 57.66 497 52.35 Income 742 63.35 603 57.12 Loss of contents 8286 1.24 8505 1.34 Minor & Serous Injury 39 186.2 27 156.7 Human fatality 221 189.8 155 157.7 Total seismic cost annually 13,491 1.11 13,577 1.12

CNY

\*FA = floor area, DI = damage index, LF = loss function, OR = occupancy rate.

Table 6.

Figure 15.

Table 7.

231

Limit state costs-calculation formula.

DOI: http://dx.doi.org/10.5772/intechopen.84159

non-structural damage and total).

LCC statistics results comparison.

Cost category Average value

, e ¼ e<sup>1</sup> þ e<sup>2</sup> þ e<sup>3</sup> þ e<sup>4</sup> (12)

CoV (%) Median value

CNY

/per

/per

CoV (%)

Insurance is a highly legal business. Relevant insurance matters are regulated by the laws of various countries. Generally, the calculation formula of seismic catastrophe insurance premium rate is as follows.

Interview of Natural Hazards and Seismic Catastrophe Insurance Research in China DOI: http://dx.doi.org/10.5772/intechopen.84159


#### Table 6.

Limit state costs-calculation formula.

#### Figure 15.

payment per people is about 70.9–77.2 Yuan annually in considering of local life endurance in this research on base of average living space per person equal 30 m<sup>2</sup>

Cost category Basic cost Damage/repair (Cdam) 1200 Yuan=m<sup>2</sup> Loss of contents (Ccon) 300 Yuan=m<sup>2</sup> rental (Cren) 20 Yuan=month=m<sup>2</sup> Income (Cinc) 400 Yuan=year=m<sup>2</sup> Minor injury (Cinj,m) 2000 Yuan=person Serious injury (Cinj,s) 2 <sup>10</sup><sup>4</sup> Yuan=person Human fatality (Cfat) 8 <sup>10</sup><sup>5</sup> Yuan=person

Natural Hazards - Risk, Exposure, Response, and Resilience

5.2 Seismic insurance ratio of industrial buildings

The probability characteristics and constitution of RC buildings' LCC.

ables from ground vibration, material character and time cost.

median values of every cost category are shown in Table 7.

trophe insurance premium rate is as follows.

successfully.

230

Figure 14.

Table 5.

Limit state costs-calculation formula.

The result is complete acceptable level for local people in Yinchuan city of western China as research sample region finally and have applied into local insurance policy

Then we can use the Eqs. (4)–(11) based data of Table 6 to calculate life-cycle seismic cost of factory buildings in selected region in consideration of random vari-

Insurance is a highly legal business. Relevant insurance matters are regulated by the laws of various countries. Generally, the calculation formula of seismic catas-

The initial unit construction cost of the building is estimated ¥1200/m2 and 10% deviation is considered in calculation. The cost of machines and nonstructural contents is supposed as ¥3000/m<sup>2</sup> and ¥300/m<sup>2</sup> respectively in research. The annual median seismic cost of structural damage of industrial buildings is ¥3419 and corresponding annual median value of non-structural damage including machine and facilities in factory buildings is ¥8505 in Figure 15. The average and

.

The annual median SLCC probability distribution of factory buildings (from left to right: Structural damage, non-structural damage and total).


#### Table 7.

LCC statistics results comparison.

$$p = \frac{\overline{L}}{1 - r - e}, e = e\_1 + e\_2 + e\_3 + e\_4 \tag{12}$$

Where p is insurance premium rate, L is expected loss rate, r is discount rate, e is additional charges rate including e<sup>1</sup> special reserve rate for claims, e<sup>2</sup> is commission rate, e<sup>3</sup> is development fund rate and e<sup>4</sup> is other fee rate. In research refer to Taiwan seismic insurance rate, e<sup>1</sup> ¼ 4%, e<sup>2</sup> ¼ 12:5%, e<sup>3</sup> ¼ 0:5%, e<sup>4</sup> ¼ 22%, r ¼ 5%.So the

insurance premium rate p ¼ 1:785, and seismic catastrophe insurance of industrial buildings is ¥15.21–15.30 Yuan/year.m<sup>2</sup> in selected sampling region of China.

References

[1] Porter KA, Kiremidjian AS, LeGrue JS. Assembly-based vulnerability of buildings and its use in performance evaluation. Earthquake Spectra. 2001; 18:291-312. DOI: 10.1193/1.1586176

DOI: http://dx.doi.org/10.5772/intechopen.84159

Interview of Natural Hazards and Seismic Catastrophe Insurance Research in China

parameters and damage indices of structures. Engineering Structures. 2001;23:698-704. DOI: 10.1016/

[9] Lagaros ND, Mitropoulou CC. The effect of uncertainties in seismic loss estimation of steel and reinforced concrete composite buildings. Structure and Infrastructure Engineering. 2013;

S0141-0296(0)00074-2

9(21):546-556. DOI: 10.1080/ 15732479.2011. 593527

International Conference on Architectural Engineering and Civil Engineering (AECE-16); Shanghai, China. 2016. DOI: 10.2991/aece-

(Paper write In Chinese)

Seismic Safety Council; 1992. pp. 102-135. DOI: 10.1193/1.2194529

16.2017.36

[10] Jian Z, Hai ZJ, Min JJ. Life-cycle seismic costs estimation and seismic insurance model for simple RC buildings in Western China. In: 2016

[11] Jian Z, Junhai Z, Pin T, Fulin Z. Seismic life-cycle loss estimation of single story factory buildings.

Earthquake Engineering & Engineering Dynamics. 2018;38(1):51-64. DOI: 10.13197/j.eeev.2018.01.51.zhuj.007.

[12] Federal Emergency Management Agency. FEMA 227: A Benefit-Cost Model for the Seismic Rehabilitation of Buildings. Washington, DC: Building

[2] Ministry of Construction P.R. China. Code for Seismic Design of Buildings (GB50011-2010). Beijing, China: China Construction Press; 2010. pp. 112-134

[3] Boore DM. Simulation of ground motion using the stochastic method. Pure and Applied Geophysics. 2001;160: 635-676. DOI: 10.1007/PL00012553

[4] Menegotto M, Pinto PE. Method of analysis for cyclically loaded R.C. plane frames including changes in geometry and non-elastic behavior of elements under combined normal force and bending. In: Symposium on the

Resistance and Ultimate Deformability of Structures Acted on by Well Defined

[5] Mander JB, Priestley MJN, Park R. Theoretical stress-strain model for confined concrete. Journal of Structural Engineering. 1988;114(8):1804-1826. DOI: 10.1061/(ASCE)0733-9445(1988)

[6] Federal Emergency Management Agency. FEMA-350:Recommended Seismic Design Criteria for New Steel Moment-Frame Buildings. Washington, DC; 2000. DOI: 10.1193/1.1572495

[7] Ghobarah A. On drift limits

associated with different damage levels. In: Proc. of the International Workshop on Performance-Based Seismic Design. Bled, CA: McMaster University; 2004. DOI: 10.1016/S0141-0296(01)00036-0

[8] Elenas A, Meskouris K. Correlation study between seismic acceleration

Repeated Loads, International Association for Bridge and Structural Engineering; Zurich, Switzerland. 1973. pp. 15-22. DOI: 10.12691/agcea-3-1-5.

114:8(1804)

233
