ANALYSIS OF CRITERION FOR TORSIONAL IRREGULARITY OF SEISMIC STRUCTURES

Transcription

1 3 th World Confence on Earthquake Engineing Vancouv, B.C., Canada August -6, 2004 Pap No. 465 ANALYSIS OF CRITERION FOR TORSIONAL IRREGULARITY OF SEISMIC STRUCTURES Nina ZHENG Zhihong YANG 2 Cheng SHI Zhongren Chang SUMMARY The torsion effects caused b irregularit of plan laout of seismic structures have been emphasized for seismic design in some codes. When and how to consid torsion effects is depended on the crition and relative regulations for torsional irregularit. The are some diffences between the critions from one code to anoth. In this pap, the diffences between the codes of China, USA and Europe are studied. Through analzing sies of structures with eccentricit in one and two directions, the corelation between torsion effects and the crition adopted b the diffent codes is obtained. According to the analsis results, it can be indicated that torsion effects has no dependenc relation with the crition adopted b the codes mentioned above and some regulations in the code are not reasonable. INTRODUCTION With the development of the theor of seismic design, the viewpoint is approved popularl that the torsion effects resulting from the irregular laout of the structure should be consided. The crition and some relative regulations for torsional irregularit have been put forward in Code for Seismic Design of Buildings of China (called GB for short)[], United Building Code (vsion997)(called UBC97 for short) of USA [2], while the crition for regularit of structures have been regulated in Structural codes of Europe [3] (called EC8 for short). The rationalit and practicabilit of these crition and relative regulations in these codes will be investigated in this pap. In these three codes, for structures with torsional irregularities, the torsion effects should be consided in two aspects, () The analsis models of structures should be spatial; (2) The modal analsis considing torsion coupling should be adopted for seismic design. For the structures with etreme irregularities in laouts of mass and stiffness, the torsion effects und seismic action in two directions should be consided simultaneousl. That is to sa that the crition for torsional irregularit of the seismic structures can be furth taken as the one for the irregular structures considing seismic action in two directions simultaneousl, thus the crition for torsional irregularit becomes a kestone for the selection of diffent design methods in the seismic design of the structures. College of Civil Engineing, Chongqing Univsit, Chongqing, , China 2 Committee of Construction of Nan'an District, Chongqing, , China

2 COMPARISON AND ANALYSIS OF PROVISIONS ON TORSION IRREGULARITY IN GB , UBC97 AND EC8 In GB , UBC97 and EC8, the crition for torsional irregularit of the structures is approimatel in the same form as shown in Figure. Torsional irregularit should be consided when maimum stor drift (or int-stor drift) at one end of the structure transvse to an ais ( δ 2 ) is more than.2 times the avage of the stor drifts (or int-stor drifts) at the two ends of the structure.the crition is epressed in Equation (). Figure. Graphic of torsional irregularit in GB and UBC97 δ + δ 2 δ 2 >.2 () 2 δ + δ 2 θ = δ 2 (2) 2 Whe δandδ 2 are the stor drifts (or int-stor drifts) at the two ends of the structure respectivel. θ is the paramet of the crition. Some diffences between the tms of torsional irregularit are given as following, ) δ and δ 2 can be stor drifts or int-stor drifts in GB , and the maimum θ from the two results of stor drifts and int-stor drifts should be adopted, while these can onl be int-stor drifts in UBC97 and stor drifts in EC8; 2)θ is calculated considing not onl actual eccentricit, but also accidental eccentricit of ±5 pcent of the length of the structure in UBC97 and EC8, while in GB onl actual eccentricit needs to be consided; and 3) In the code of GB , the maimum of θ is.5 while the is no similar provision in code of UBC97 and EC8. When the crition are used in practice, some problems should be pointed out, ) It is not convenient for engines to detmine θ at the beginning of the design. θ must be calculated through the global analsis of structure; 2) The relative eccentricit is usuall consided as the important factor influencing torsion effects, the relationship between θ and relative eccentricit should be studied;

3 3) Stor drifts (int-stor drifts) of diffent floors ma be diffent. So θ ma be diffent between diffent floors. It is not clear that θ of which floor should be adopted in GB , UBC97 and EC8; and 4) If θ is a prop crition for torisonal irregularit, wheth it can furth be taken as the crition for considing seismic action in two directions simultaneousl should be studied. Thefore, the are some unclearness and inconvenient in the crition of torsional irregularit. The above problems have been investigated b eample analsis b Zheng [4] and the contents are etracted he. EXAMPLE STRUCTURES ANALYSIS Although the crition for torsional irregularit looks simple, but the application of it has some confusions and it is necessar to investigate the details of it and make it eas to use. For the factors influencing torsion effects, man scholars approve the relative eccentricit is an important factor. The relationship between θ and relative eccentricit and the relationship between torsional effects are respectivel investigated b eamples analsis of structures with eccentricit in one and two directions. Based on these analses, the applicabilit of the crition will be evaluated, the supiorit of stor drift and int-stor drift to calculate θ will be evaluated and the value of θ for diffent stories will be compared. Method for analsis The eample structures are analzed through modal analsis b SAP2000. The response spectrum is adopted given b GB as shown in figure 2, he α ma is 0.6, Tg is 0.45s, η is 0.02, η 2 is and γ is The spatial model and the postulate that the floor is rigid are adopted. Three degree of freedom (two for latal translation and one for torsion rotate) for ev stor are consided and the first 5 mode shapes are combined b the complete quadratic combination method (CQC) for torsion rotate and latal translation coupling model. α η 2α ma 0.45α ma γ T α g = T η 2 αma α = γ [ η η ( T 5T g )] α ma 0 0. T g 5T g 6.0 T(s) Figure 2. Seismic effect coefficient curve Design of eample structures Two tpe of structures with torsional irregularit are designed, one with eccentricit in one direction and the oth with eccentricit in two directions. The relative eccentricit along X direction of structures with eccentricities in two directions keeps invariable when the relative eccentricit along Y direction varies from 0.0 to a value. To investigate the influence of plan size to the torsional effects, three kinds of plan sketch that the ratios of long size and short size are respectivel :, 3: and 5: (for short called correspondingl as Str., Str.3 and Str.5) are designed. All elevation laouts are regular. The structures are 5 stories and the height of the ground floor is 4.6m and the above is 3.6m each. The cross section is mm for columns and mm for beams. The cent of rigidness (C S ) of floor is located on the cent of floor and the cent of mass (C M ) is variable with the variation of mass distribution, so the total mass and total latal resisting stiffness keep invariable. He onl the plan laout of Str.3 is shown in figure 3, whe e, e are the eccentricit along and direction.

4 C Y C M CS e e X B A Figure 3. Plan laout of Str.3 For describing clearl, defining such paramets as, er = e/ r (3) 2 = e 2 + e / r (4) 2 2 r = ( a + b )2 (5) Whe er is relative eccentricit for structures with eccentricit in X direction while in two directions, r is the radius of torsion rotate of the floor. a,b are the length of structure along X and Y direction. The above information of all eample structures are shown in table. Table. Information of structures for analsis Stle of structure Numb span Structures with eccentricit in X direction Structures with eccentricit in one ~ two directions Xdirection Ydirection er Numbs 0.00~ er ~ Numb Str ~ ~0.23~ Str ~ ~0.37~ Str ~ ~0.3~ Results analsis Relationship between θ and relative eccentricit θ ( θ ) d ( θ d ) are respectivel calculated b stor drifts and int-stor drifts und earthquake action in Y(X) direction. The relationships between θ and e are shown in figure 4. (), (3) and (5) of figure 4 correspond to the structures with eccentricit in one direction, (2), (4) and (6) of figure 4 correspond to the structures with eccentricit in two directions. Based on figure 4, the following can be obtained,

5 ) θ and θ are almost same between diffent stories. θ d d are diffent from one stor to anoth, the θ of the top stor is bigg than that of the oth stories, but these diffences are not obvious. The diffences between θ d, θ d are little, which diffences is biggest in the top stor. Thefore, the diffence of stor drifts and int-stor drifts between GB , UBC97 and EC8 can be neglected for design. 2) For regular structure, θ, θ d, θ and er varies from 0 to a small value, θ ( θ θ d d are all equal, as shown in (), (3) and (5) of figure 4. When ) varies dramaticall from to a value which eceeds the limit value of torsional irregularit.2. For eample, when θ is.2, the corresponding er of Str., 3 and 5 are all less than Thus according to the crition of torsional irregularit, torsion effects should be consided for the structure with a v little eccentricit which less than That is to sa an structure ma be torsional irregular if accidental eccentricit of 5 pcent the length of the structure is consided according to UBC97 and EC8. θ θ θ er θd () Str. with eccentricit in one direction θd θd.2. er (2) Str. with eccentricit in one and two directions Figure 4. Variations of θ with er ()

6 θ.2 θd.2 θ.. er er (3) Str.3 with eccentricit in one direction θd θ θd θ (4) Str.3 with eccentricit in one and two directions.4.3 θd er. er (5) Str.5 with eccentricit in one direction Figure 4. Variations of θ with er () (continue)

7 θ θd θ θd (6) Str.5 with eccentricit in one and two directions Figure 4. Variations of θ with er () (continue) 3) Aft the quick increasing, θ of Str., 3 and 5 decrease with the increasing of er. It is contradictor to the results that Wang [5] pointed out lag relative eccentricit, lag torsion effects. The boundaries of declining points are not same for the three categories of structures, which ma attribute to the diffent sizes of the structures. The decrease ratio of θ is largest for Str.5. θ ma be less than.2 for the structure with bigg eccentricit. According to the crition, these structures are irregular and the torsion effects ma be ignored. But this is obviousl impossible. 4) As shown in (2), (4) and (6) of figure 4, with e increasing but e is constant, θ of Str. increases firstl and then decreases even less than the one of structure with onl e along X direction. When θ of Str.3 and 5 increases to some etent and the values of them are more than those of structures with e. This is to sa that one ma correspond to seval θ with the variations of the size and eccentricit of the structures. The θ of the structures with eccentricities along two directions has not good relationship with. 5) As (2), (4) and (6) in Fig. 4 shown, with eccentricit e increasing but e keeping constant, θ increases graduall. Contrasting with the phenomenon that big θ corresponds to little er of structures with eccentricit in X direction, values of θ he are all less than.. The factors influencing θ need be investigated furthmore. According to above analsis, the crition for torsional irregularit has not close relations with relative eccentricit er and. The paramet θ is not prop to represent the torsion effects of the structures and defined as the crition of torsional irregularit. The relationship between λ VX Defining λvx as following λ = V V (6) VX

8 Whe V is the shear force in X direction und earthquake action in Y direction for structures with eccentricit in X direction. V is the shear force in X direction und earthquake action in X direction. λ VX denotes the torsion effects of structures with eccentricit in X direction. For seismic design, V should not be ignored when λ VX increase to a prescribed value and the total shear in X direction should be combined b V and V no matt the structure has eccentricit in one directions or two directions, othwise the design is not safet enough. Thefore λvx can be consided as the link of torsional irregularit and considing earthquake action in two directions simultaneousl. Correlations of λvx of eample structures with eccentricit in X direction are shown in Figure5. λv θ..2.3 λv θ () Str. (2) Str λv θ (3) Str.5 Figure 5. Variations of λvx It can be seen that with the increasing of θ, λvx of diffent structures all decrease but the degrees of decrease are not same. When θ are in.3~.4, the same θ ma corresponds to seval λ VX for Str.3 and 5. And λ VX increases with the increasing of stor for Str.3 and 5. In a word, the correlation of torsion effects and the crition for torsional irregularit is not definite. This crition for torsional irregularit is not prop to decide considing earthquake action in two directions simultaneousl or not. CONCLUSIONS In this pap, the crition and relative regulations for torsional irregularit in GB , UBC97 and EC8 are compared and analzed from the theoretical and practical aspects. Through designing and analzing the sies of eample structures with eccentricit in one direction and two directions, a elementar conclusion can be drawn that the corelationships between torsion effects are not

9 definite, although the crition about θ is adopted b GB , UBC97 and EC8 for torsional irregularit. This crition is not prop to decide considing earthquake action in two directions simultaneousl or not. REFERENCES. GB , Code for Seismic Design of Buildings. (in Chinese) Beijing: China Architecture & Building Press, UBC97, Uniform building code. Intnational Confence of Building Officials (ICBO). Vol.2. Structural Engineing Design Provisions, USA, Cheng Shaoge. Structural Europe code (EC8). (in Chinese) Institute of earthquake resistant of china academ of building research, Zheng Nina. Research on the scope of structures considing seismic action in two directions simultaneousl. (in Chinese) Thesis for mast degree, Chongqing Univsit, Chongqing, China, Wang Yaowei, Huang Zongmin. Analsis on factors influencing non-linear earthquake response of structures with eccentricit. (in Chinese) Journal of Chongqing Jianzhu Univsit. 200, 23(6): 4-20.