Earthquake Loss for Reinforced Concrete Building Structures Before and After Fire damage

Transcription

1 Earthquake Loss for Reinfored Conrete Building Strutures Before and After Fire damage Pai-Mei LIU, Yi-Hsuan Tu and Maw-Shyong SHEU 3 ABSTRACT The purpose of this paper is to propose a rational analytial alulation for earthquake loss of RC building strutures before and after fire damage. The dynami nonlinear inremental spetrum method is used to alulate the strutural responses when ground aeleration shakes from zero and inreases gradually up to rak, yield and total ollapse of the building. One the RC building had fire damage, the ompression strength of onrete f ' and the yield strength of rebar f y would be redued orresponding to the fire envelop. Aording to the damage mode, the rak pattern and the total rak length are estimated for eah member. Before ultimate state, repair osts for epoxy injetion are alulated as earthquake loss aording to the rak length of eah member. After ultimate state, the repair osts for steel or arbon fiber jaketing are ounted as the extra loss to reover the plasti zone of eah member. In this paper, the earthquake loss for a medium-rise and a high-rise RC ommerial building in Taiwan are taken as examples for alulation before and after fire damage. Keywords: dynami nonlinear inremental spetrum method, RC building struture, struture repair ost, earthquake loss, fire damage. EVALUATION OF EARTHQUAKE LOSS Statistis are mostly used in estimate the expeted earthquake loss and earthquake insurane. An analytial method using dynami nonlinear inremental spetrum analysis (Liu, 998) that ombines seismi damage assessment and earthquake loss evaluation is disussed in this paper. Before ultimate state, raking is important for repair ost and stiffness degradation of RC members during loading stages. The most popular repair method of raked RC members is epoxy injetion. The repair ost is ounted by alulating the raking number and the raking length for epoxy injetion of eah member. After ultimate state, the plasti hinges aused by flexural raks and diagonal shear raks are repaired by using the steel or arbon fiber jaketing. The unit repair ost is based on the market prie in Taiwan. The estimation formulas for flexural and shear rak number are introdued as follows: Crak number and rak length by flexure: The flexure rak number of eah member is proposed by the formula of Oh and Kang (Oh and Kang, 98) 4.5 /3 6 s 36 0 t b A = 0 +, 0 = D b ε sa As () where s is the average raking spae of one member, D b is the diameter of the reinforing bar, ε sa (Sheu, 96) is the average strain of the longitudinal steel, 0 indiates the minimum value of raking spaing, t b is Department of Arhiteture, Kao Yuan Institute of Tehnology, Kaohsiung, Taiwan, R.O.C. pmliu@.kyit.edu.tw Department of Arhiteture, National Cheng-Kung University, Tainan, Taiwan, R.O.C. n88805@mail.nku.edu.tw 3 Department of Arhiteture, National Cheng-Kung University, Tainan, Taiwan, R.O.C. mssheu@mail.nku.edu.tw

2 the bottom over measured from the enter of lowest bar, is the distane from the extreme tension fae to the neutral axis, A is the average effetive area of onrete around eah reinforing bars and A s is the area of eah reinforing bar. Equation () indiates the flexure rak spaing is diminished as the strain grows. See Figure. flexure rak number under monotoni load Figure indiates the relationship of moment and flexure rak spaing at one onstant axial foring. When the moment inreases gradually, the rak spaing dereases quikly. As the moment inreases stage by stage, the rak spaing omes to a onstant gradually. Theoretially, the average rak number is the length of member divided by average rak spaing, but the moment is not onstant at the member like Figure 3. For solving this problem, the member was separated by plus moment and minus moment into two setions L and L. For example, as Figure 3, the length of the raking range on length L of the member is L ( M M r )/ M, M means the maximum moment at length L and M r means the raking moment. The sign s represents the average rak spaing on length L of the member and s represents the average rak spaing on length L of the same member. Therefore, s will be alulated as ( Area ) s /( M M r ) and the average rak number L M M r n at length L is. The average rak number n on length L is alulated by the same s M proess. The total rak number of this member is n = n + n. Flexure rak number under yli load The stress under yli load ould be several onditions as Figure 4. Eah member was separated as the proess desribed previously. If the moment on the separated setion of the member was both plus or minus, as Figure 4(a), the rak number is alulated based on the envelope of the moment. If the moment on the separated setion of the member is out of phase, as Figure 4(b), the rak number is the sum alulated respetively from the plus moment and minus moment. Flexure rak number under biaxial load It is proposed the loation of raking may be overlapped for % probability under biaxial load. It is alulated the rak number n x in x-axis and the rak number n y in y-axis independently. The final rak number N xy is as ( nx + n y ) max + ( nx + n y ) N xy = () The sign l represents a flexure rak length that ombines the width b of the setion of the member and two times of the distane from the extreme tension fae to the neutral axis, as Figure 5. Crak number and rak length by shear: Aording to Bazant (Bazant and Oh, 983), it indiated that the loation of the rak of the member is happened at the intersetion of the bars (see Figure 6). The rak spaing s should be the times of the distane of the joint of bars, as s = ma/, m =,,3.... So the minimum rak spaing smin of the member will be a /. In this paper, the average rak spaing s at the ultimate state was.5 times of s min, as s =.5 a/.06a (3) Shear rak number and rak length for RC walls Aording to the test data of Hwang (Hwang, 989) and Yang (Yang, 99), the rak number V V > V ) an be found from the following equation (see Figure ) ( N s at shear

3 V V N + s = N su 0. 6 (4) Vu Vu N su is the predited shear rak number at ultimate state, V is the rak shear and V u is the ultimate shear. This paper assumes every rak length is equal to the average rak length lw of 45 degree. The l w is as: l w = h w/( h + w) (5) where h is the height of the wall and w is the width of the wall. Shear rak number and rak length for olumns and beams Using the same proess of walls to alulate the shear rak number and length, aording to the test data of Sheu (Sheu, 99) and Suen (Suen, 993), the rak number N s at shear V ( V > V ) an be found from the following equation (see Figure 8) V M V M N + s = N su (6) Vu M u Vu M u V M The affeted fators that aused the rak numbers on olumns and beams are ( ) ( ). Vu M u This paper assumes the rak range at the moment when rak just happened ( V = V ) is /4 times of the depth h of the setion. It means the rak length at V = V is h / 4 beause of the rak angle is 45 degree. At the ultimate state ( V = ), the rak range was inluded all the depth of the setion. It means the rak length at Vu V = V u is h. If shear V is between V and V u, the rak length would be proportional to the shear loading. EVALUATION OF FIRE DAMAGE Using impliit numerial analysis with boundary temperature rise as Equation (), maximum temperature envelopes in every member ross-setion in the fire-damaged stories ould be alulated. T = 345 log(8t + ) () where T is temperature in, t is time in minute. One maximum temperature envelopes are found, the loation of neutral axis, the raking moment, yielding moment, ultimate moment, raking shear fore, ultimate shear fore et. must be hanged by using the orresponding stress-strain urves for those fire damaged members. The deteriorated mehanial properties of onrete and rebar after different fire damage are taken from referenes (Liu, 998). The deteriorated setional properties of any RC member after fire damage, suh as P u, V u and M u, are alulated by strain ompatibility and fore equilibrium of the setion. Finally, the seismi performane diagram of a RC building struture before and after fire damage, inluding the relationship of PGA, base shear and story drift, are alulated by dynami nonlinear inremental spetrum analysis. EVALUATION OF From the previous setion, the seismi damage situation ould be found. The type of damage ould be lassified into flexure damage, shear damage and axial fore damage. Therefore, for different type of damage the orresponding repair ost ould also be alulated. Before ultimate state, the repair ost only depended on the total length of raks. After ultimate state, if plasti hinges happened at RC olumns or beams, the repair ost must be added by hoosing the steel or arbon fiber jaketing on the plasti hinge zone. If the damage was aused by shear happened at olumns or beams, the retrofitted method is the same as that for flexure damage; If

4 the damage was happened on walls, a better way is to dismantle the wall and rebuild a new one. Table is the repair ost for different repaired items in Taiwan. EARTHQUAKE LOSS ASSESSMENT OF MEDIUM AND HIGH-RISE COMMERCIAL BUILDINGS A 0 and 0-story RC ommerial building strutures in seismi zone and on medium soil site in Taiwan are onsidered. The plans and the elevations are shown in Figure 9 and 0. These buildings were subjeted the fire damage at the first and seond stories with fire duration 60 minutes in Equation (). The earthquake repair osts are to be alulated before and after fire damage. The ollapse PGA of these two buildings are alulated by the nonlinear inremental spetrum analysis introdued in this paper. Table shows the results of ollapse PGA of the medium and high-rise building strutures before and after fire damage. The ollapse PGA after fire damage is lower than that before fire damage. The ollapse PGA is about % derease after fire damage for the medium-rise building struture and about 3% derease for the high-rise building struture. And at the same PGA stage, the roof defletion of building struture after fire damage is larger than that before fire damage. The repair ost at the every peak ground aeleration (PGA) ould be evaluated by using the previous damage assessment method before and after fire damage. Figure to 4 show the relationship between the roof displaement, the base shear, the PGA and the repair ost for different damage type of the medium and high-rise building strutures before and after fire damage. From the earthquake loss assessment, it is seen that the repair ost aused by the flexure damage on olumns and beams is about 5%; aused by RC walls is about 0% and aused by shear on olumns and beams is about 5% of the total repair ost. The repair ost is higher after fire damage than that before fire damage. The repair ost of the medium-rise building struture after fire damage is 0% to 0% more than that before fire damage; and the repair ost for the high-rise building struture is 5% to 0% more than that after fire damage. The ost of the building dismantled and rebuilt (RPC) is evaluated by the information provided from the onstrution firms in Taiwan. Let RCi be the repair ost at PGA = i. The earthquake loss rate at PGA = i ould be evaluated as LRi = RCi / RPC as shown in Figure 5. The repair ost is zero at PGA equal to zero beause the rak length is very small under dead load and live load, and ould be ignored. The repair ost is equal to the RPC when the building ollapses. It is shown in Figure 5 that the repair ost is almost proportional to the PGA before the building ollapses. Under the same PGA, the repair osts are higher in low-risk seismi zone than that in high-risk seismi zone for one building before and after fire damage. CONCLUSIONS. Repair ost of RC elements: before ultimate state, repair osts are alulated aording to the rak length. Flexural and shear rak length are alulated respetively by the semi-empirial formula proposed in this paper.. Before ollapse of the building, the earthquake loss is almost proportional to the PGA and about 5% of the total earthquake loss is due to flexural damage of beams and olumns. 3. The earthquake repair ost for the medium-rise building struture after fire damage is about 0% to 0% more than that before fire damage; and the earthquake repair ost for the high-rise building struture is about 5% to 0% more than that after fire damage. 4. Under the same PGA, repair osts are higher in low-risk seismi zone than that in high-risk seismi zone before and after fire damage. ACKNOWLEDGEMENTS This paper is supported by the Building Researh Institute, the Ministry of Interior, Taiwan, under Grant No. MOIS 86000, 996.

5 REFERENCES Bazant, Z. P. and Oh, B. H. (983), Spaing of Craks in Reinfored Conrete, Journal of Strutural Engineering, ASCE, Sept., pp. Hwang, G. S. (989), The Chang of Stiffness and Damage Assessment for Two-Story Reinfored Conrete Shearwalls Subjet to Reversed Cyli Horizontal Loadings, Master Thesis, Dept. of Arhiteture, Univ. of Cheng Kung, June, Tainan, Taiwan, R.O.C. Insurane Development Center (996), Commentary of Insurane Law, Taiwan, R.O.C., 5-58pp. Liu, Pai-Mei (998), Earthquake Insurane Rates for Medium and High-Rise RC Commerial Building Strutures before and after Fire Damages, Ph. D. Dissertation Dept. of Arhiteture, Univ. of Cheng Kung, July, Tainan, Taiwan, R.O.C., 8-3pp. Oh, B. H. and Kang Y. J. (98), New Formulas for Maximum Crak Width and Crak Spaing in Reinfored Conrete Flexural Members, ACI Struture Journal, Mar./Apr., 03-pp. Sheu, Maw-Shyong (96), A Grid Model for Predition of the Monotoni and Hystereti Behavior of Reinfored Conrete Slab-Column Connetions Transferring Moments, Ph. D. Dissertation Civil Engrg. Dept. Univ. of Wish., Seattle, Wash., U.S.A., 5-pp. Sheu, R. N. (99), Experimental Study of Improving Reinfored Conrete Short Columns, Master Thesis, Dept. of Arhiteture, Univ. of Cheng Kung, June, Tainan, Taiwan, R.O.C. Suen, Y. J. (993), Improvement of Reinfored Conrete Short Columns, Master Thesis, Dept. of Arhiteture, Univ. of Cheng Kung, June, Tainan, Taiwan, R.O.C. The Ministry of Interior (996), Building Design Code, Taiwan, R.O.C. Yang, C. F. (99), Aseismi Behaviours of Reinfored Conrete Shear Walls With Openings and Boundary Columns, Master Thesis, Dept. of Arhiteture, Univ. of Cheng Kung, June, Tainan, Taiwan, R.O.C. Table Unit ost for repairing in Taiwan Type Item Unit Unit Cost(NT$) Repairing Epoxy injetion m 000 Steel jaketing and painting m 9000 Carbon fiber jaketing and painting m 40 Dismantle of onrete m 3 400~00 Dismantle of brik m 3 00~8 Steel t 4000~00 Template m 400~0 Reasting Conrete m 3 8~000 Brik piee 4 /B Brik laying m B Brik laying m 0 :3 Mortor Brushing m 300 Painting m 0 Prestressing strut 00 Others Saffold m 80 Transportation m 3 0 Table a Collapse PGA of building strutures before fire damage Type Medium-rise ommerial building High-rise ommerial building No. CASE CASE CASE CASE PGA in x dir PGA in y dir PGA in oblique dir PGA req d by Code

6 Table b Collapse PGA of building strutures after fire damage Type Medium-rise ommerial building High-rise ommerial building No. FCASE FCASE FCASE FCASE PGA in x dir PGA in y dir PGA in oblique dir PGA req d by Code s M s0 M r L L M r M s0 / Figure 3 Moment variation of the member s 0 /4 s min ε 0 Figure Relationship between rak spaing and strain of rebars ε s Figure 4 Moment ombination under plus s and minus loads M Area s M r s Figure Relationship between moment and rak spaing Figure 5 Flexural rak

7 G F 4 E D a C B A Figure 6 Parallel raks skew to bars (a) Basement plan MEASURED CRK. Nb./PREDICT CRK. Nb Wall speimens Fit : Linear, Y=.334X-0.03 Fit : Y=0.X +.0X (V/Vu) (b) Standard floor plan F E D C B Figure Relationship between rak of walls and loads MEASURED CRK. Nb./PREDICT CRK. Nb Short & Slitted Short Columns Fit : Linear, Y=0.968X Fit : Y=0.5X +.6X (V/Vu)*(M/Mu) Figure 8 Relationship between rak of olumns and loads () Tower Plan (d) Tower Plan Figure 9 Plan of medium and high-rise ommerial building strutures

8 53.9 m 5 m m m 9@3.9 PF PF RF 0F 9F 8F F 6F 5F 4F 3F F (a) Elevation of medium-rise building F BF BF 0.8 Figure b Seismi performane and repair ost diagram in Zone of medium-rise building struture before fire damage 00 5E+ E m m 9@3.9 5 m G.L. 3@3.9 m PF PF RF 0F 9F 8F F 6F 5F 4F 3F F F 0F 9F 8F F 6F 5F 4F 3F F F BF BF (b) Elevation of high-rise building Figure 0 Elevation of medium and high-rise ommerial building strutures B3F E+ E Figure a Seismi performane and repair ost diagram in Zone of medium-rise building struture after fire damage E+ 5E+ E+8 E+8 Figure a Seismi performane and repair ost diagram in Zone of medium-rise building struture before fire damage Figure b Seismi performane and repair ost diagram in Zone of medium-rise building struture after fire damage

9 E+8 E+8 E+8 E+8 Figure 3a Seismi performane and repair ost diagram in Zone of high-rise building struture before fire damage Figure 4b Seismi performane and repair ost diagram in Zone of high-rise building struture after fire damage LOSS RATIO 0.5 CASE FCASE CASE FCASE E+8 E Figure 3b Seismi performane and repair ost diagram in Zone of high-rise building struture before fire damage Figure 5a Earthquake loss ratio of medium-rise building struture before and after fire damage Figure 4a Seismi performane and repair ost diagram in Zone of high-rise building struture after fire damage 00 E+8 E+8 LOSS RATIO CASE' FCASE' CASE' FCASE' Figure 5b Earthquake loss ratio of high-rise building struture before and after fire damage