Evaluation the Overstrength of Concentrically Steel Bracing Frame Systems Considering Members Post-buckling strength

Transcription

1 Evaluation the Overstrength of Concentrically Steel Bracing Frame Systems Considering Members Post-buckling strength Mussa Mahmoudi 1 and Mahdi Zaree 2 1. Assistant Professor, Faculty of Civil Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran, m.mahmoudi@srttu.edu 2. M.S. Student in structural engineering, Faculty of Civil Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran, mahdizarebalani@gmail.com

2 Evaluation the Overstrength of Concentrically Steel Bracing Frame Systems Considering Members Post-buckling strength ABSTRACT It is acceptable inelastic deformation of structural components in seismic design. In such behavior, the strength of structures increases while plastic hinges are formed frequently in members. The strength revealed during the formation of plastic hinges is called oversterngth. Overstrength is one of the important parameter in seismic design of structures. The present study, evaluates the overstrength of the concentrically steel braced frame (CBF) systems, considering reserved strength, because of members Post-Buckling strength. To do so, static nonlinear (pushover) analysis has been performed on the buildings, having, single and two bracing bays, various stories and different brace configurations (chevron V, invert V and X bracing). It has been found out that the overstrength factor due to postbuckling effect depends on type of bracing and the height of buildings considerably. However, the number of bracing bays has a profound effect on the overstrength factor. The results indicate, the overstrength values for concentrically steel braced frame systems, proposed in seismic design codes, need to be modified. Keywords: Concentrically steel bracing frame systems, force reduction factors, Overstrength factor, Post-buckling strength, Steel structures. 2

3 1. Introduction The preliminary design of most buildings is normally based on equivalent static forces specified by the governing building code. The height-wise distribution of these static forces (and therefore, stiffness and strength) seems to be based implicitly on the elastic vibration modes. However, structures do not remain elastic during severe earthquakes and they are expected to undergo large nonlinear deformations[1]. Many seismic codes permit a reduction in design loads, taking advantage of the fact that the structures possess significant reserve strength (overstrength) and capacity to dissipate energy (ductility). The overstrength and the ductility are incorporated in structural design through a force reduction factor or a response modification factor[2]. Steel concentric braced frame (CBF) is one of the lateral load resisting systems, especially for the structures constructed in high seismic regions. Concentric braced frames are braced systems whose worklines essentially intersect at points[3]. In CBFs, the steel braces provide lateral strength and stiffness to the structural system and contribute to seismic energy dissipation by yielding in tension and buckling inelastically in compression[4]. Consequently, the cyclic axial response of the bracing members, which are expected to undergo tension deformations beyond yield and compression deformations into the post-buckling range, represents the most crucial aspect of the seismic response of a braced frame system[5]. Many researchers have attempted to identify the factors that may have contributed to the observed overstrength (Miranda and Bertero 1989, Miranda and Bertero 1989, Osteraas and Krawinkler 1989, Fishinger and Fajfar 1990, Nassar and Krawinkler 1991, Tso and Naumoski 1991, Mitchell and Paultre 1994). Osteraas and Kraeinkler[6], conducted a detailed study of overstrength concentric braced frames designed following the allowable stress design provisions with seismic loads per UBC seismic zone 4 and soil type S2. Rahgozar and Humar[7], found that the overstrength factors of CBFs. They represent that In structures having braced frames the main parameter controlling the overstrength is the slenderness ratio of the bracing members. Kim and Hyuanhoon[2], evaluated The overstrength and response modification factors of the chevron type concentric braced frames with various stories and span lengths by performing pushover analyses. DiSarno and Elnashai[8], demonstrate that in CBFs with stainless steel braces and columns the increase in overstrength is about 40% with respect to 3

4 the configuration in mild steel. Davaran and Hoveidae[9], show that type of mid-connection detail of X concentric braced frame can improve response modification factor and overstrength of system respectively 28% and 5% more than those of the system with common mid-connection detail. Previous studies do not consider the effect of bracing bays and reserve strength after buckling of the brace up to life safety structural performance level, defined in the codes. The present study focuses on the evaluation of overstrength factor of CBFs loaded by Iranian Earthquake Resistance Design Code (Standard No. 2800)[10] and designed in accordance with part 10 of Iranian national Building code, steel structure design[11], considering the brace post-buckling strength. Nonlinear static pushover analyses were carried out to obtain such behavior factor. 2. CYCLIC BEHAIVIOR OF THE BRACE Bracing members in regular buildings are expected to buckle in compression and yield in tension when subjected to reversed cyclic loading[12]. Cyclic behaviour of bracing members has been the subject of investigation by several researchers. The experimental and analytical studies illustrated the distinctive hysteretic response of axially loaded members. This is characterised by the gradual reduction in compressive resistance, as well as deterioration of stiffness in tension, with loading cycles of increasing deformation amplitude. These investigations also identified the improved stiffness and energy dissipation capabilities provided by relatively rigid end connections. In comparison with nominally pinned conditions, rigid connections cause plastic hinges to form at the member ends, in addition to that at mid-length, leading to improved inelastic performance[5]. The response of concentrically braced frames to significant earthquake loading depends strongly on the asymmetric axial resistance of the bracing members[13]. The cyclic inelastic behavior of brace members is complex due to the influence of the following physical phenomena: yielding in tension, buckling in compression, post-buckling deterioration of compressive load capacity, deterioration of axial stiffness with cycling, low-cycle fatigue fractures at plastic hinge regions, and the Bauschinger effect. These factors complicate the formulation of efficient analytical models that are capable of accurately simulating the inelastic behavior of steel braces. Nevertheless, practical and reliable analytical tools are essential for the transition from current prescriptive seismic codes to performance 4

5 based design specifications, which require accurate predictions of inelastic limit states up to structural collapse[14]. According to Ikeda and Mahin[15], frame element models, which have been used to simulate the inelastic behavior of steel braces, can alternatively be classified as finite element, phenomenological, and physical theory models. Despite the difficulty of determining input data, phenomenological models have been widely used for nonlinear seismic analyses; for example in Nilforoushan, Singh, Jain, Maison and Popov, Ikeda and Fukuta. Fig.1 shows the ideal load-deflection of steel bracing members, suggested by FEMA-356[3]. The horizontal axial represent the deflection (axial displacement ) and the vertical one shows the members internal forces (tension or compression). The yield or buckling occurs in point B. In the compression case, BC is related to elastic buckling and CE reperesent inelastic buckling. The strength happened from point B to point in which the first member reaches to life safety case is, post-buckling strength. Structural Performance Level, Life Safety, means the post-earthquake damage state in which significant damage to the structure has occurred, but some margin against either partial or total structural collapse remains. Some structural elements and components are severely damaged, but this has not resulted in large falling debris hazards, either within or outside the building. Injuries may occur during the earthquake; however, the overall risk of life-threatening injury as a result of structural damage is expected to be low. It should be possible to repair the structure; however, for economic reasons this may not be practical. While the damaged structure is not an imminent collapse risk, it would be prudent to implement structural repairs or install temporary bracing prior to reoccupancy[3]. 3. OVERSTRENGTH FACTOR Observations during many earthquakes have shown that building structures are able to sustain without damage earthquake forces considerably larger than those they were designed for. This is explained by the presence in such structures of significant reserve strength not accounted for in design[7]. Overstrength helps structures to stand against sever earthquakes safely. Overstrength also reduces the 5

6 elastic strength demand. This object is performed using force reduction factor by several codes of practice[16]. Fig.2 represents the base-shear versus roof displacement relation of a structure, which can be developed by a nonlinear static analysis. The design overstrength factor R sd and post-buckling Overstrength factor R sp are defined as follows: Vy RSd (1) V V d u RSP (2) Vy Where V d is the design base shear that building design for, V y is the base shear corresponding to the first yield observe in the frame and V u relevant to first life safety performance in structure. In this paper overstrength factor of the frames were computed using Eq.1. and Eq.2. based on analysis results.the overstrength factor shown in Eq.1. and Eq.2. are based on the use of nominal material properties. The actual overstrength factor R s should consider the beneficial contribution of some other effects[17]: R 2 S RSd.R SP.R1.R... (3) In Eq.3. R 1 is used to account for difference between actual static yield strength and nominal static yield strength. For structural steel, a statistical study shows that the value of R 1 may be taken as Parameter R 2 may be used to consider the increase in yield stress as a result of strain rate effect during an earthquake excitation. A value of 1.1, a 10% increase to account for the strain rate effect, could be used[17]. In this paper the steel type St-37 was used for all structural members. Parameters R 1 and R 2 equal to 1.05 and 1.1 were considered taking into R SM =1.155 as material overstrength factor. Other parameters can also be included when reliable data is available. These are included to the parameters such as nonstructural component contributions, variation of lateral force profile. Various codes present numerical values of the overstrength factor for CBFs; to mention a typical example, the overstrength factor for concentrically steel braced frames is equal to 2 in IBC[18], AISC[19], FEMA-450[20] and Iranian national Building code, steel structure design[11] and equal to 2.2 in UBC[21]. 6

7 4. STRUCTURAL MODELS 4.1. Design of Model Structures To evaluate the overstrength factors of concentric braced frames, five models with 3, 5, 7, 10 and 12 stories and the bay length of 5 m were designed. For this structural models three different bracing types (X, chevron V and chevron-inverted V) by single and two bracing bays were considered as per the requirement of Iranian Earthquake Resistance Design Code[8] and Iranian National Building Code, part 10, steel structure design[11] (Fig.3). The story height of the models was considered as 3.2 m. For member design subjected to earthquake, equivalent lateral static forces were applied on all the story levels. These forces were calculated following the provisions stated in Iranian Earthquake Code (Standard No. 2800)[10]. The dead and live loads of 5.5 and 2 KN/m 2, respectively, were used for gravity load. The design base shear was computed as follows, ABI V CW C (4) R In which V is base shear of structure, C is base shear ratio and W is the equivalent weight of the structure. A B is the design spectral acceleration, expressed as the fundamental period of structure T and soil type, I is the importance factor and R is the response modification factor. The importance factor of I = 1, preliminary response modification factors of R = 6 and seismic zone factor of A = 0.35 were considered for frame design. The braces were designed to sustain 100 percent of the lateral load and the beam column joints were assumed to be pinned at both ends. Allowable stress design method was used to design frame members in accordance to part 10 of Iranian national code[11]. To ensure that vertical bracing columns have enough strength to resist the forces transferred by bracing elements; Iranian Standard No.2800[10] has instruction to design vertical bracing columns for the following load combinations: (a) Axial compression according to: P DL 0.8P 2.8P P 1.7F A (5) LL E SC a 7

8 (b) Axial tension according to: The maximum lateral story displacement ( No. 2800[10] as follows: For the frames with the fundamental period less than 0.7 s: For the frames with the fundamental period more than 0.7 s: In which H is story height. 0.8PDL 2.8PE PST Fy A (6) M ) limit was selected based on the Iranian Standard Code M 0.025H (7) M 0.02H (8) 4.2. Pushover Analysis To evaluate the Overstrength factor, the inelastic pushover (static) analysis is generally used. Pushover analysis is performed by subjecting a structure to a monotonically increasing pattern of lateral forces. The selection of an appropriate lateral load distribution is an important step within the pushover analysis[22]. Pushover analyses were carried out to evaluate the buckling and post-buckling limit state by progressively increasing the lateral story forces proportional to the fundamental mode shape. The post-yield stiffness of the beams, columns and braces was assumed to be 2% of the initial stiffness. The phenomenological model presented in FEMA-356[3], was used for modeling nonlinear behavior of braces (Fig.1). The post-buckling residual compression force is set to be 20% of the buckling load as given in Tables 5 7 of FEMA-356[3]. 5. RESULTS Fig.4 through 9 show nonlinear static pushover analysis result in terms of base shear roof displacement for different bracing type (inverted V, chevronv and X type). Fig.10 and 11 shows variation of overstrength for difference type of bracing configuration. In Tables 1 through 6 design overstrength factor, post-buckling overstrength factor and overstrength factor of braced frames are shown. It can be seen that the overstrength factor decrease as the height of building increases. On the 8

9 other hand, the overstrength factors increase as the number of bracing bays increase. This is because of limitation on slendrness and allowable axial stress reduction for braces in design codes seismic provisions. Post-buckling overstrength factors have a constant value for each type of brace frame and number of bracing bays and height of building have no affect on this factor approximately. It is concluded that X shape bracing's post-buckling strength is more than chevron's one. It is due to, In X shape bracings, there is the tension member to stand against lateral load, after buckling of compression member while in chevron shapes, not. 6. CONCLUTION This paper, evaluates the overstrength of the 30 concentrically steel braced frame (CBF) systems with considering reserved strength, because of strength from brace Post-Buckling to structural life safty performance level. For this purpose static nonlinear (pushover) analysis has been performed on the buildings, having, single and two bracing bays, various stories and different brace configurations. The model structures were designed for relatively large seismic load and the beam column connections were assumed to be pinned so that the seismic load was resisted mainly by braces. The results of this study can be summarized as follows: (1) The overstrength factors increases as the structure height decreased and number of bracing bays increase. (2) Number of bracing bays and height of building have no affect on Post-buckling overstrength factors. (3) Code's seismic provisions for brace member design have a profound effect on the CBFs overstrength factor. (4) The obtained post-buckling overstrength factor for CBFs in type V, inverted V and X with single and two bracing bays are, 1.11, 1.08 and 1.28, respectively. (5) The overstrength factor for concentrically steel braced frames in type V, inverted V and X with single bracing bay are evaluated as 2.90, 3.75 and 3.10, respectively. 9

10 (6) The overstrength factor for concentrically steel braced frames in type V, inverted V and X with two bracing bay are evaluated as 3.80, 4.80 and 4.20, respectively. (7) Codes present constant value of overstrength factor for CBFs. However, the overstrength factors for these systems evaluate in this paper have different values for type of brace configurations, number of bracing bays and buildings height. So the results indicate, the overstrength factors for concentrically steel braced frame systems, proposed in seismic codes, need to be modified. REFERENCES [1] Moghaddam, H. and Hajirasouliha, I. & Doostan, A, February 2005, Optimum seismic design of concentrically braced steel frames:concepts and design procedures, Journal of Constructional Steel Research, Volume 61, Issue 2, Pp [2] Kim, J. and Hyuanhoon, C, January 2005, Response modification factors of chevron-braced frames, Journal of Engineering Structures, Volume 27, Issue 2, Pp [3] FEMA, 2000, Prestandard and Commentary for the Seismic Rehabilitation of Building. FEMA- 356, Federal Emergency Management Agency,Washington, D.C. [4] Khandelwal, K. and El-Tawil, S. & Sadek. F, March 2009, Progressive collapse analysis of seismically designed steel braced frames, Journal of Constructional Steel Research, Volume 65, Issue 3, Pp [5] Goggins, J.M. and Broderick, B.M. & Elghazouli, A.Y. & Lucas, A.S, February 2006, Behaviour of tubular steel members under cyclic axial loading, Journal of Constructional Steel Research, Volume 62, Issues 1-2, Pp [6] Ostraas, J.D. and Kraeinkler, H, June 1990, Strength and Ductility Considerations in Seismic Design, Department of Civil and Environmental Engineering Stanford University, Report No.90. [7] Rahgozar, M.A. and Humar, J.L, 1998, Accounting for overstrength in seismic design of steel structures, Can. Journal of Civil Engineering, Pp [8] DiSarno, L. and Elnashai, A.S. & Nethercot, D.A, August 2008, Seismic response of stainless steel braced frames, Journal of Constructional Steel Research, Volume 64, Issues 7-8, Pp

11 [9] Davaran, A. and Hoveidae, N, April 2009, Effect of mid-connection detail on the behavior of X- bracing systems, Journal of Constructional Steel Research, Volume 65, Issue 4,Pp [10] BHRC, 2005, Iranian code of practice for seismic resistance design of buildings: Standard no.2800, 3rd edition, Building and Housing Research Center. [11] MHUD, 2009, Iranian National Building Code (part 10): steel structure design, Tehran (Iran): Ministry of Housing and Urban Development. [12] Lee, K. and Bruneau, M, April 2005, Energy Dissipation of Compression Members in Concentrically Braced Frames:Review of Experimental Data, Journal of Structural Engineering, Vol. 131, No.4, Pp [13] Broderick, B.M. and Elghazouli, A.Y. & Goggins, J, September 2008, Earthquake testing and response analysis of concentrically-braced sub-frames, Journal of Constructional Steel Research, Volume 64, Issue 9, pp [14] Jin, J. and El-Tawil, S, May 2003, Inelastic Cyclic Model for Steel Braces, Journal of Engineering Mechanics, Vol. 129, No. 5, Pp [15] Ikeda, K. and Mahin, S.A. & Dermitzakis, S.N, 1984, Phenomenological modeling of steel braces under cyclic loading, Rep.No.UCB/EERC-84/09, Earthquake Engineering Research Center, Univ.of California, Berkeley, Calif. [16] Mahmoudi, M, 2003, The relationship between overstrength and members ductility of RC moment resisting frames, Pacific Conference on Earthquake Engineering. [17] Asgarian, B. and Shokrgozar, H.R, February 2009, BRBF response modification factor, Journal of Constructional Steel Research, Volume 65, Issue 2, Pp [18] IBC, 2000, International building code. International Code Council. [19] AISC, 2002, Seismic provisions for structural steel buildings, Chicago (IL):American Institute of Steel Construction, Inc. [20] FEMA, 2003, Recommended provisions for seismic regulations for new buildings and other structures, FEMA-450, Federal Emergency Management Agency,Washington, D.C. [21] International Conference of Building Officials, 1997, Uniform building code 1997 edition, vol. 2: structural engineering design rovisions, California. 11

12 [22] Fajfar, P, 2002, Structural Analysis in Earthquake Engineering A Breakthough of Simplified Nonlinear Methods, 12th European Conference on Earthquake Engineering. 12

13 Table 1. Overstrength factors for single bay invert-v brace frames No.story R sd R sp R sm R s Table 2. Overstrength factors for single bay V brace frames No.story R sd R sp R sm R s Table 3. Overstrength factors for single bay X brace frames No.story R sd R sp R sm R s Table 4. Overstrength factors for two bays invert-v brace frames No.story R sd R sp R sm R s Table 5. Overstrength factors for two bays V brace frames No.story R sd R sp R sm R s Table 6. Overstrength factors for two bays X brace frames No.story R sd R sp R sm R s

14 Fig.1. Generalized Force-Deformation Relation for Steel Brace Elements (FEMA-356)[3] Fig.2. General structure response 14

15 Fig.3. Configuration of model structures Fig.4. Roof displacement base shear curve for single bay invert-v brace frames Fig.5. Roof displacement base shear curve for single bay V brace frames 15

16 Fig.6. Roof displacement base shear curve for single bay X brace frames Fig.7. Roof displacement base shear curve for two bays invert-v brace frames Fig.8. Roof displacement base shear curve for two bays V brace frames 16

17 Fig.9. Roof displacement base shear curve for two bays X brace frames 5 4 Invert-V "Chevron V" "X" Overstrength Factor No.story Fig.10. Overstrength factor of single bay CBFs 7 6 Invert-V "Chevron V" "X" Overstrength Factor No.story Fig.11. Overstrength factor of two bays CBFs 17