SEISMIC EVALUATION AND ITS VERIFICATION OF STREET BUILDINGS IN TAIWAN

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1 13 th World Conerene on Earthqake Engineering Vanover, B.C., Canada Agst 1-6, 2004 Paper No SEISMIC EVALUATION AND ITS VERIFICATION OF STREET BUILDINGS IN TAIWAN Maw-Shyong SHEU 1, Tetso, KUBO 2, Hsin-Yi KUO 3 SUMMARY The irst part o this paper is to propose a rational rak path method or allation o the ltimate shear apaity or rik shear wall or RC shear wall. The load-deletion rve or rik shear wall or RC shear wall is also disssed in this part. The seond part o this paper is to propose a ast seismi evalation method or developing the perormane diagram o a low-rise RC ilding with rik shear wall or/and RC shear wall. The perormane diagram developed in this paper is a omplete hart showing the relationship among peak grond aeleration, ase shear and loor deletion. The loor response at dierent peak grond aeleration may e read diretly rom the perormane diagram, inlding the 4ollapse peak grond aeleration at ertain retrn period o earthqake. Key Words: seismi evalation, street ilding, rik wall, RC wall, seismi perormane rve INTRODUCTION The strtral system o the traditional street ildings in Taiwan is rather niqe. The width o eah nit is aot 4.5m. The depth o eah nit is rom 15m to 23m. In general, it is 3 to 4 stories in height. There is a pedestrian orridor on grond story. The grond story is sed as ommerial; the seond and aove stories are sed as residential. The seismi apaity o the traditional low-rise street ilding in Taiwan depends tremendosly on the amont o shear wall in the diretion o assessment. Bease there are lots o shear walls in the diretion perpendilar to street; t ew walls in the diretion parallel to street. So the seismi resistane in the diretion perpendilar to street is very strong t rather weak in the diretion parallel to street. Almost all the shear walls o street ildings in Taiwan were made o rik eore And then transerred to RC walls gradally de to inrease o laor ost ater Now most o the shear walls o street ilding are made o RC. The in-plane shear apaities o rik wall and RC wall are introded in this paper y a rational rak path onept. The allation o Q- rve or RC olmns and the seismi assessment method sing shear-ilding mode had een introded y She [1]. They will e introded riely herein. Three street ildings, whih ollapsed or moderately damaged in the Taiwan Chi-Chi 1 Dept. o Arhitetre, National Cheng-Kng Univ., Tainan Taiwan 2 Dept. o Arhitetre, University o Tokyo, Tokyo, Japan 3 Dept. o Civil Engrg., National Cheng-Kng Univ., Tainan, Taiwan

2 Earthqake 1999, are illstrated to veriy She s assessment method [1] in this paper. Another reinored rik street ilding designed aording to the Taiwan Bilding Code is also sed to set p the seismi perormane diagram y the assessment method in this paper. Q- CURVE OF BRICK WALL UNDER LATERAL LOAD In general, when sjet to in-plane lateral ore, rik shear wall ails y stair-step likely inlined raks. Ater many experimental and ield oservations, the inlined shear rak path might e lassiied into 3 patterns as shown in Fig.1 [2, 3]. In Fig.1, the inlined raks start rom the intersetions o ondary elements (2 intersetions in Fig.1 (a) and (); 1 intersetion in Fig.1()) and terminate at the mortar interae nearest to the entral line o wall. The horizontal raks in Fig.1 (a) and 1() go along the horizontal mortar interae. However, hal o the vertial rak in Fig.1 () goes along vertial mortar interae t the other hal o the vertial rak has to split the rik ostrting on the vertial rak path. The slope angle o inlined stair-step, θ, is dierent or dierent lay ot o the rik loks sh as Flemish ond (è _21 ), English ond (è _30 ), and strething ond (è _29 ) et. The sm o the lateral ores to aomplish a omplete inlined rak is the ltimate lateral apaity o the rik wall. The ltimate lateral apaity o rik wall is onsisted o 3 omponents: ritional strength o horizontal mortar interae, tensile strength o vertial mortar interae, and vertial splitting strength o rik lok. The ltimate strength o these 3 omponents may e allated as ollows rom regression o experimental data [2, 3].The ltimate ritional strength o horizontal mortar interae is: τ ( m ') ( m ') σ n = (1) The ltimate tensile strength o vertial mortar interae is: ( ') mt = m (2) The ltimate vertial splitting strength o rik lok is: (3) t = 0.22 ' where m ' and ' are ompression strength o mortar lok and rik lok, (MPa); σ n is the normal ompression stress ating on rik wall (MPa). The nits o τ, mt, and t are in (MPa). So the ltimate lateral apaity o rik wall in Fig.1 (a) is: Q ( W + H ) = t τ φ (4) The ltimate lateral apaity o rik wall in Fig.1 () is: mt [ W + φw tanθ + φ( H W tan )( )/ 2 ] Q = t τ θ + (5) The ltimate lateral apaity o rik wall in Fig.1 () is: Q ( W τ +. 5 H ) mt mt = t 0 φ (6) in whih t is the thikness o rik wall (mm); W and H are the net width and net height o rik wall (mm); φ is redtion ator de to onstrtion qality and tensile rittle ailre and taken as 0.9; Q is mt t

3 the horizontal ltimate apaity o rik wall in (N). The ltimate lateral deletion o rik wall at ltimate point may e allated y Ko [4] as: Q H H = Et W W W H (7) where E = 582 ' (8) and = 0.161( W / H ) or 3 sides onined rik wall; = 0.269( W / H ) wall; E is the seant modls o elastiity at ltimate point (MPa); 0.01 H. One the ltimate point (, ) or 4 sides onined rik is in (mm) and no more than Q is loated, the eqation o entire lateral load-deletion Q- rve o rik wall is regressed as polynomial: 2 3 Q = Q (9) Fig.2 shows the Q- rves o a grop o rik walls with 4 sides onined. The thikness and net height are 230mm and 3000 mm or all walls. The net width hanges rom 1000mm to 6000mm. It shows Q not neessarily proportional to W. Q is maximm when W = 3000mm. For W greater than 3000mm, the stronger vertial splitting rak path is getting smaller and transerring into weaker horizontal rition path. For W = 5000mm, the vertial splitting rak path disappears. So Q eomes minimm. One W > 5000mm, the horizontal ritional path is getting longer to provide some more additional apaity. Q- CURVE OF RC WALL RC wall is onsidered as a ig olmn or lexral strength with point o inletion loated at 0.75H. Bt its shear apaity is allated in dierent way rom general olmn. In elasti stage, Q- rve o RC wall is linear. From rak point to ltimate point, it is proposed as a logarithmi rve in this paper. The rak load Q is the minimm o lexral rak load and shear rak load. The ltimate load Q is also the minimm o lexral ltimate load and shear ltimate load. That is: ( Q Q ) Q = min, (10) s ( Q Q ) Q = min, (11) s where M r Q = (12) H Q s N H Ag ' ' Ag (13) Ag WT A = g M Q = (14) H

4 Q = Q + Q (15) s ss M r and M are the rak and ltimate ending moments o RC wall when onsidered as a ig olmn (N-mm); A g is the gross ross setional area o wall inlding ondary olmns (mm 2 ); A g ' is the gross ross-setional area o ondary olmns (mm 2 ); W T is the total width inlding ondary olmns (mm). In Eq. (15), Qss is the shear apaity ontrited y all the reinorement o wall and ondary olmns aross the diagonal rak path as shown in Fig.3 and may e allated y shear rition onept as: Q ( A + A + A ) + 0. ( A N ) ss =.324 h h wh y v1 y 48 v2 y + 0 (16) In whih A h and A wh are hoop o olmn and horizontal reinorement o wall t y 45 degree inlined path (mm 2 ); A v1 is the total vertial reinorement o wall and olmn t y 45 degree inlined path (mm 2 ); A v2 is the vertial reinorement o wall and olmns t y horizontal path (mm 2 ); yh and y are yield strength o olmn hoop and other rears (MPa); N is the normal load ating on the wall (N). The lateral deletion at rak point,, or latreral deletion at ltimate point,, is the sm o lexral deletion pls shear deletion. For lexral deletion, the point o inletion is assmed at 0.75H rom ottom o RC wall or ilding strtre. For onservative onern, o RC wall is no more than 0.015H. = + (17) s = + (18) s where 3 H Q = (19) 6.86( 0.3E I g ) 3 H Q = (20) 6.86( E I g ) = H ρ v y HWT WT ' Ag A ' I ' I g (21) 2.4HQ s = (22) 0.33E Ag 3.3HQ s = (23) E Ag In whih, ρ v is the reinorement ratio o vertial rears o wall; A ' is the ross-setional area o ondary olmns in the portion protrding rom wall (mm 2 ); I ' is the moment o inertia or A ' with respet to netral axis (mm 4 ); the nit o HW T is in (m 2 ); E is the modls o elastiity o onrete and taken as 4700 ' in (MPa).

5 The Q- rve etween the rak point o wall and the ltimate point o wall may e regressed as a logarithmi eqation [*4]: Q = ln Q Q ( ) ( ) ( ) Q ln( ) Q ln( ) ln + ln ln( ) ln( ) (24) ILLUSTRATED EXAMPLES OF STREET BUILDING From ield oservations o the damaged low-rise RC ildings [5] and rom shaking tale tests o small sale RC ilding strtres [6], it is elieved that shear-ilding model is reasonale or seismi assessment o low-rise RC ilding. The details o the assessment method had een proposed y She [1]. The proess o the seismi assessment method is introded riely as ollows: 1. Plot lateral load-lateral deletion rve or eah vertial memer, inlding eah RC olmn, eah RC wall and eah rik wall on the assessed story in the assessed diretion as shown in Fig.5; 2. Sm p all the lateral load-lateral deletion rves on the assessed story to otain the story shearstory drit rve o the assessed story as the dark rve shown in the irst qadrant o Fig Transer the story shear to ase shear. Otain the ase shear-story drit rve; 4. In order to allate the orresponding peak grond aeleration or a point on the ase shear-story drit rve, plot ilinear rve or that point y eqal energy priniple as the light rve shown in the irst qadrant o Fig.6; 5. Extend the inlining segment o the ilinear rve to ertain point to get eqivalent elasti response point, Q e, y eqal energy priniple again; 6. The orresponding peak grond aeleration or that point on the ase shear-story drit rve is: (25) a = Q / CW e where is the oeient o elasti response spetrm. C may e taken as 2.5 or onservative. W is the total weight o the strtre. 7. Keep moving the assessed point all the way on the ase shear-story derit rve, we an get the peak grond aeleration rve, as shown in the seond qadrant o Fig. 6. Fig. 6 is the perormane diagram o a ilding strtre. From this diagram, the response o ase shear and story drit an e read or dierent peak grond aeleration. The same assessment method is employed here to veriy the damage level o 3 street ildings ater the Taiwan Chi- Chi Earthqake The same assessment method is also sed to set p the seismi perormane diagram o a reinored rik street ilding designed aording to the tentative Taiwan Bilding Code. [Example 1] ollapse o a 5-story single street ilding at Tong-S Town Fig.4 shows the plan, elevation, olmn reinorement, and ollapse photo o the single ay street ilding at Tong-S Town. Fig.5 is the Q- rves in x-diretion or eah vertial RC olmn. Fig.6 is the seismi perormane diagram o this street ilding. From this diagram, the analytial ollapse grond aeleration is 0.168g. Bt the atal loal EPA o the Chi-Chi Earthqake rom reord o the Central Weather Brea (CWB) was 0.477g. [Example 2] ollapse o a 3-story row street ilding at Ch-San Town

6 Fig.7 shows the plan, elevation, olmn reinorement and ollapse photo. Fig.8 shows the seismi perormane diagram o this ilding. The analytial ollapse grond aeleration is 0.07g. Bt the atal loal EPA o the Chi-Chi Earthqake rom reord o the CWB was 0.38g. [Example 3] moderate damaged row street ilding at Dow-Lio City Fig.9 is the plan o a 3-story row street ilding loated at Dow-Lio City. Fig.10 is the seismi perormane diagram o this ilding. The analytial ollapse grond aeleration is 0.38g. The atal loal EPA o the Chi-Chi Earthqake rom reord o the CWB was 0.27g. [Example 4] demonstration or seismi perormane o a 3-story reinored rik street ilding The so-alled reinored rik ilding in Taiwan is dierent rom that in Ameria or Erope. Fig.11 is the typial plan o a 3-story reinored rik row street ilding designed aording to the tentative Taiwan Bilding Code. For this type o ilding, rik wall is laid ot irst. Two weeks later, the onrete o RC olmn, RC eam, and RC sla is pored. One onrete shrinks, the rik wall inside the RC rame will get onined ompression ore to inrease the ritional strength. Fig.12 is the seismi perormane diagram o this rik street ilding with =20.6MPa; ' =14.7MPa; ' =9.8MPa y =274MPa. It shows that i street ilding is designed aording to the desriptive rles o the tentative Taiwan Bilding Code withot any strtral analysis, the ollapse EPA o the rik ilding is aot 0.37g. ' ACKNOWLEDGMENT This joint researh is spported y the National Siene Conil o Taiwan nder Grant NSC Z and spported y the Earthqake Disaster Mitigation Researh Center at NIED, Japan. REFERENCES 1. Maw-Shyong She and Hsin-Yi Ko, Fast EQK Resistane Assessment or Shool Bildings in Taiwan, WG-1 Report, Earthqake-Resisting Tehnologies or Bilding Strtres, 3rd EQTAP Workshop, Nov , 2000, Manila, Philippines. 2. Yi-Pei Li, Seismi Evalation o Brik Bildings, Master Thesis, Dept. o Arhitetre, National Cheng-Kng Univ., Tainan, Taiwan, Jly, Yi-Hsin Chen, Seismi Assessment o RC Bildings with Inilled Brik Walls, Dotor Dissertation, Dept. o Arhitetre, National Cheng-Kng Univ., Tainan, Taiwan, Jan, Hsin-Yi Ko, Fast Seismi Evalation o RC Shool Bildings, Master Thesis, Dept. o Arhitetre, National Cheng-Kng Univ., Tainan, Taiwan, Jne, Maw-Shyong She, Shang-High Yeh, Report on Damage o Bildings ater the Chi-Chi Earthqake, 1999, Strtral Engineering, No.3, Vol.14, De., Yi-Hsan T, Maw-Shyong She, and Shi-Y X, Shaking Tale Test o One-Third Sale RC Shool Bildings, Report o National Center or Researh o Earthqake Engineering, Taipei, Taiwan, April, 2002 m

7 (a) tan θ H/W (4-side onined) () tan θ H/W (4-side onined) () Brik Wall with 3-Side Conined Fig.1 Crak Paths o Conined Brik Walls nder In-Plane Fore

8 800 W=3000mm 600 W=4000mm Q (kn) 400 W=6000mm W=5000mm W=2000mm 200 W=1000mm (mm) Fig.2 Q- Crves o Brik Walls with 4-Side Conined W T H (a) High-rise Shear Wall W T H () Low-rise Shear Wall Fig.3 Shear Crak Path o RC Walls

9 (a) Typial Strtral Plan Roo Roo Existing Bilding () Frame Elevation () Reinorement o Seond Floor Colmns Fig.4 Collapse Single Street Bilding at Tong-S

10 (d) Photo Beore Earthqake (e) Photo Ater Earthqake Fig.4 Collapse Single Street Bilding at Tong-S (ontined)

11 80 60 Story Shear (kn) S1_2FX C1 ( N=26.2t ) C2 ( N=42.8t ) C2 ( N=50.0t ) C2 ( N=25.0t ) Fig.5 Displaement (mm) Q- Crves o Eah Colmn on Seond Story 1200 a=qe/cw=0.168g 800 Story Shear (kn) Fig.6 Aeleration(g) Displaement (mm) Seismi Perormane Diagram o Tong-S Street Bilding

12 (a) Typial Strtral Plan () Frame Elevation () Reinorement o Seond Story Colmns Fig.7 Collapse Row Street Bilding at Ch-San

13 (d) Photo Ater Earthqake Fig.7 Collapse Row Street Bilding at Ch-San (ontined) 3000 a =Q e /CW=0.076g 2000 Story Shear (kn) Fig.8 Aeleration(g) Displaement (mm) Seismi Perormane Diagram o Ch-San Street Bilding

Fig.9 Row Street Bilding at Dow-Lio Ater retroit B A 20 16 12 8 4 Q(MN) Ater retroit A B 0 0.5 0.

14 Fig.9 Row Street Bilding at Dow-Lio Ater retroit B A Q(MN) Ater retroit A B PGA(g) θ(%) Fig.10 Seismi Perormane Diagram o Dow-Lio Street Bilding

Fig.11 Typial Plan o Reinored Brik Street Bilding Q (kn) 40000 30000 20000 10000 0.4 0.

15 Fig.11 Typial Plan o Reinored Brik Street Bilding Q (kn) a (g) (mm) Fig.12 Seismi Perormane Diagram o the Brik Street Bilding

The Hashemite University Department of Civil Engineering ( ) Dr. Hazim Dwairi 1

The Hashemite University Department of Civil Engineering ( ) Dr. Hazim Dwairi 1 Department of Civil Engineering Letre 8 Slender Colmns Definition of Slender Colmn When the eentri loads P are applied, the olmn deflets laterally by amont δ,, however the internal moment at midheight: