Comparison of Base Shear Force Method in the Seismic Design Codes of China, America and Europe

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1 Applied Mechanics and Materials Vols (202) pp Online available since 202/May/4 at (202) Trans Tech Publications, Switzerland doi:0.4028/ Comparison of Base Shear Force Method in the Seismic Design Codes of China, America and Europe JIANG Zhinan,a, ZHAO Zhonghai 2,b Department of Architectural Engineering, East University of Heilongiang, Harbin 50086, China 2 Heilongiang Administration of Surveying, Mapping and Geoinformation, Harbin 5008, China a iangzhinan2006@63.com, b zzh_my@63.com Keywords: Seismic design code, Design response spectrum, Base shear force, Comparison Abstract. Seismic design response spectrum and earthquake action in Chinese new seismic code (GB ), ASCE/SEI7-05 and Eurcode8 were gathered in this paper. Using base shear force method of each code, the authors computed the horizontal seismic forces of a three-story reinforced concrete frame building under the same conditions. The results show that the three static methods roughly approach, while the different parameters lead to discrepancies in calculated values. Introduction New code for seismic design of building, GB , was published and has began to implement in China. Many clauses have been revised in the new code. The seismic design spectra and earthquake actions have certain differences in many countries. This paper shall make a comparison on this field in GB , ASCE/SEI7-05 and Eurocode8. Seismic Design Response Spectrum Seismic response spectrum is a curve in which the maximum elastic response of single-mass system changes with its natural vibration period in the given seismic acceleration time. For a multi-mass system, this relationship is only an approximate. However, this greatly simplifies the seismic analysis of structures. The horizontal seismic action can be converted to the equivalent lateral force. Accordingly, the action effect analysis of structures under earthquake will be converted to that under the equivalent lateral force. Thus, as long as the lateral force can be calculated, the analysis of seismic effect can be solved by static method []. Design Response Spectrum in GB [2]. Design response spectrum shall be determined from Fig.. Fig. Seismic Influence Coefficient Curve Table Maximum of Horizontal Seismic Influence Coefficient Earthquake Affection Intensity 6 Intensity 7 Intensity 8 Intensity 9 Frequently Earthquake (0.2) 0.6(0.24) 0.32 Rarely Earthquake (0.72) 0.90(.20).40 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, (ID: , Pennsylvania State University, University Park, USA-03/02/5,7:04:0)

2 2346 Progress in Structures The maximum of horizontal seismic influence coefficient α max is given in Table. The characteristic period T g shall be taken as Table 2 according to site class and design seismic group, that shall be increased 0.05s for rarely earthquake of intensity 8 and 9. Table 2 Characteristic Period Value (s) Design Seismic Group Site Class Ⅰ 0 Ⅰ Ⅱ Ⅲ Ⅳ st Group nd Group rd Group The damping adustment and shape coefficient of the response spectrum should comply with the following requirements: ) The damping ratio ξ of building structures shall select 0.05 except otherwise provided, the damping adusting coefficient of the seismic influence coefficient curve shall select.0. 2) When the damping ratio ξ of building structures is not equal to 0.05 according to relevant provisions, the damping adusting and forming parameters on the seismic influence coefficient curve shall comply with the following requirements: a) The power index of the curvilinear decrease section γ shall be determined according to Eq.(); b)the adusting factor of slope for the linear decrease section η shall be determined from Eq.(2) and it shall equal 0 when less than 0; c) The damping adustment factor η 2 shall be determined according to Eq.(3) and it shall equal 0.55 when smaller than ξ γ = ξ 0.05 ξ 0.05 ξ η = 0.02+, η2 = ξ ξ, () ~ (3) Design Response Spectrum in ASCE/SEI7-05 [3]. The design response spectrum curve shall be developed as indicated in Fig.2. Fig.2 Design Response Spectrum in ASCE/SEI7-05 This curve is determined by the expression as Eq.(4): S a T SDS , T < T0 T0 S, T T T DS 0 S = SD, TS < T TL T S T T D L 2, T > T L (4)

3 Applied Mechanics and Materials Vols S DS, S D = the design spectral response acceleration parameter at short periods and at -s period; T = the fundamental period of the structure (s); T L = long-period transition period (s) shown in figures from this code; T 0 = 0.2S D /S DS ; T s = S D /S DS ; S DS = 2 3 S MS= 2 3 F as S ; S D = 2 3 S M= 2 3 F vs ; F a, F v = the site coefficients shown in Table 3 and Table 4, respectively; S S, S = the mapped MCE spectral response acceleration at short periods and at -s period. Site Class Table 3 Site Coefficient, F a Table 4 Site Coefficient, F v Mapped MCE Spectral Response Acceleration Parameter at 0.2 Second Period Period Site Class Mapped MCE Spectral Response Acceleration Parameter at Second S s 0.25 S s = 0.5 S s = 0.75 S s =.0 S s.25 S 0. S = 0.2 S = 0.3 S = 0.4 S 0.5 A A B B C C D D E E F See Note F See Note Note: Site-specific geotechnical investigation and dynamic site response analyses shall be performed. Response Spectrum in Eurcode8(EN998-:2004) [4]. Horizontal elastic response spectrum is shown in Fig.3. Fig.3 Shape of the Elastic Response Spectrum Every stage of this curve is defined by Eq.(5). According to the ground type and magnitude, the horizontal elastic response spectrum is recommended to use Type and Type 2. If the earthquakes that contribute most to the seismic hazard defined for the site for the purpose of probabilistic hazard assessment have a surface-wave magnitude, Ms, not greater than 5.5, it is recommended that Type 2 is adopted. For the five ground types A, B, C, D and E the recommended values of the parameters S, T B, T C and T D are given in Table 5 for Type and in Table 6 for Type 2.

4 2348 Progress in Structures T ag S + ( η 2.5 ) 0 T TB TB ag S η 2.5 TB T TC Se( T) = (5) TC ag S η 2.5 TC T TD T TCT D ag S η 2.5 T 4 2 D T s T S e (T) = the elastic response spectrum; S = the soil factor; T = the vibration period of a linear single-degree-of-freedom system; a g = the design ground acceleration on type A ground; T B, T C = the lower and upper limit of the period of the constant spectral acceleration branch; T D = the value defining the beginning of the constant displacement response range of the spectrum; η = the damping correction factor, the value of η may be determined by the expression: η = 0 /( 5+ ξ) 0.55, ξ is the viscous damping ratio of the structure, expressed as a percentage. Table 5 Values of the Parameters Describing the Table 6 Values of the Parameters Describing the Recommended Type Elastic Response Spectra Recommended Type 2 Elastic Response Spectra Ground Ground S T type B (s) T C (s) T D (s) type S T B (s) T C (s) T D (s) A A B B C C D D E E Design spectrum, Sd(T), shall be defined by Eq.(6)~ Eq.(9): 2 T T TB : Sd( T) = ag S + 3 TB q 3 (6) 2.5 TB T TC : Sd( T) = ag S q (7) 2.5 TC = ag S TC T TD : Sd( T) q T (8) β ag 2.5 TCT D = ag S T 2 D T : S d( T ) q T (9) β ag Sd(T) = the design spectrum; q = the behaviour factor; β = the lower bound factor for the horizontal design spectrum, the recommended value is 0.2.

5 Applied Mechanics and Materials Vols Base Shear Force Method Regarding the calculation of seismic action, the common methods used now are generally shown as following [5] : Base shear force method Static method Push over analysis Methods of caculating Modal separateresponse spectrum procedure seismic action Dynamic method Elastic time history analytical method Elastoplastic time history analytical method This paper shall pay attention to the static method. The static method discussed in this paper is mainly base shear force method or the methods similar to it. It is called equivalent lateral force procedure in ASCE/SEI7-05, while lateral force method of analysis in Eurcode8. Base Shear Force Method in GB [2]. For the structures whose height is less than 40m, whose deformation is mainly produced by shear and whose mass and stiffness fairly distributes uniformly along the height, or the structures which could regard as a single-mass system, base shear force method can be used. When the base shear force method is used, only one degree of freedom may be considered for each story, the characteristic value of horizontal seismic action of the structure shall be determined by Eq.(0)~ Eq.(2): F Ek Gi Hi = αgeq ; Fi = FEk ( δ n) ( i=, 2 n n ) ; Fn = δ nfek (0)~(2) G H = Where F Ek = characteristic value of the total horizontal seismic action of the structure; α = horizontal seismic influence coefficient corresponding to the fundamental period of the structure; G eq = equivalent total gravity load of a structure. When the structure is modeled as a single-mass system, the representative value of the total gravity load shall be used; and when the structure is modeled as a multi-mass system, the 85% of the representative value of the total gravity load may be used; F i = characteristic value of horizontal seismic action applied on mass i; G i,g = representative values of gravity load concentrated at the masses of i-th and -th respectively; H i, H = calculated height of mass i-th and -th from the base of the building respectively; δ n = additional seismic action factors at the top of the building. Only need to consider for multi-story reinforced concrete buildings; F n = additional horizontal seismic action applied at top of the building. Equivalent Lateral Force Procedure in ASCE/SEI7-05 [3]. The structures suitable for equivalent lateral force procedure include: a) regular or irregular buildings in seismic design class B and C; b) all the light frame buildings, or regular buildings whose natural period is smaller than 3.5s, or only horizontal or only vertical irregular buildings in seismic design class D, E and F. The seismic base shear, V, in a given direction shall be determined in accordance with Eq.(3)~ Eq.(5): V = CsW ; Fx vx = C V ; V n x = F (3)~(5) i i= x C s = the seismic response coefficient which shall be determined in accordance with Eq. (6); W = the effective seismic weight; F x = The lateral seismic force (kn) induced at any level;

6 2350 Progress in Structures C C vx = vertical distribution factor which shall be determined in accordance with Eq. (7); V x = the seismic design story shear in any story; F i = the portion of the seismic base shear (kn) induced at Level i. s SDS = ; R / I C vx = w h k x x n k wi hi i= (6)~(7) S DS = the design spectral response acceleration parameter in the short period range; R = the response modification factor; I = the occupancy importance factor. w i, w x = the portion of the total effective seismic weight of the structure (W) located or assigned to Level i or x; h i, h x = the height (m) from the base to Level i or x; k = an exponent related to the structure period. Lateral Force Method of Analysis in Eurcode8 [4]. This type of analysis may be applied to buildings whose response is not significantly affected by contributions from modes of vibration higher than the fundamental mode in each principal direction.the seismic base shear force, F b, for each horizontal direction in which the building is analyzed, shall be determined using Eq.(8): b d ( ) F = S T mλ ; F i = F b si mi s m (8) ~ (9) S d (T )= the ordinate of the design spectrum at period T; T = the fundamental period of vibration of the building for lateral motion in the direction considered; m = the total mass of the building, above the foundation or above the top of a rigid basement; λ = the correction factor, the value of which is equal to: λ=0.85 if T < 2TC and the building has more than two stories, or λ=.0 otherwise; F i = the horizontal force acting on storey i, using Eq.(9); m i, m = are the storey masses computed; s i, s = are the displacements of masses mi, m in the fundamental mode shape. When the fundamental mode shape is approximated by horizontal displacements increasing linearly along the height, the horizontal forces F i should be taken as being given by Eq.(20). F i = F b zi mi z m z i, z = are the heights of the masses m i, m above the level of application of the seismic action. (20) Example Calculating This section shall calculate an example for comparing the horizontal seismic action in GB , ASCE/SEI7-05 and Eurcode8 under the same condition. A three-story reinforced concrete frame building is shown in Fig.4. Try to calculate the horizontal forces of the building under design intensity 7 with site-class Ⅰand 2 nd design seismic group. The damping ratio, ξ, of the building is 0.05.

7 Applied Mechanics and Materials Vols Fig.4 Sketch for a 3-story Reinforced Concrete Frame Building The horizontal seismic forces acting on each story and story shears computed from the seismic design codes of China, America and Europe are shown in Fig.5. a) b) c) a) According to Chinese Code b) According to American Code c) According to European Code Fig.5 The Horizontal Seismic Forces Acting on Each Story and Story Shears Using Different Codes Conclusions By comparing, we can reach the following conclusions: ) As to computed results, the value from GB is the largest, ASCE/SEI7-05 followed by and Eurcode8 minimum; 2) For shear structure, the distribution of horizontal seismic actions along the height is not strictly inverted triangle. The error on the top may reach up to 25% in long period. GB uses top additional horizontal seismic action to adust it, while American and European codes have no condition. 3) The response modification factor, R, in ASCE/SEI7-05 and the behavior factor, q, in Eurcode8 reflect the ductility of the structures, while GB has no the parameter to treat differently; 4) GB introduces a reduction factor, 0.85, in multi-mass system which reflects the difference of shear forces between multi-mass system and single-mass system. American and European codes make no reduction in this respect. 5) With regard to the distribution of the horizontal seismic force acting on each story, Chinese and American codes assign the base shear with each floor load multiplied by the distance from the floor to bottom. In Eurcode8, only when the fundamental mode shape is approximated by horizontal displacements increasing linearly along the height, the computing method is the same as Chinese and American codes, and it shall use each floor load multiplied by the displacements of each floor in the fundamental mode shape to calculate.

8 2352 Progress in Structures References [] Xiaowang Gao, Sili Gong, Jingyu Su, Fangmin Yi: Understanding and Application for Seismic Design Code of Building, China Building Industry Press, Beiing (2002).(In Chinese) [2] Code for Seismic Design of Building (GB ), China Building Industry Press, Beiing(200). (In Chinese) [3] Minimum Design Loads for Buildings and Other Structures (ASEC7-05), American Society of Civil Engineers(2006). [4] Eurocode 8: Design of Structures for Earthquake Resistance Part : General rules, seismic actions and rules for buildings, European Committee for Standardization (2004). [5] Feng Li: Comparative study on seismic analysis and design details of concrete structure in Chinese and American code, Institute of structure engineering China Acadamy of Building Research(2005). (In Chinese)

9 Progress in Structures / Comparison of Base Shear Force Method in the Seismic Design Codes of China, America and Europe /

Comparative study between the push-over analysis and the method proposed by the RPA for the evaluation of seismic reduction coefficient

33, Issue (27) 5-23 Journal of Advanced Research in Materials Science Journal homepage: www.akademiabaru.com/arms.html ISSN: 2289-7992 Comparative study between the push-over analysis and the method proposed