THE EFFECTS OF HEIGHT AND LENGTH OF LINK BEAM ON RESPONSE MODIFICATION FACTORS OF ECCENTRICALLY BRACED STEEL FRAMES

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1 ISSN: CEE esearch in Civil and Environmental Engineering esearch in Civil and Environmental Engineering (1) THE EFFECTS OF HEIGHT AND LENGTH OF LINK BEAM ON ESPONSE MODIFICATION FACTOS OF ECCENTICALLY BACED STEEL FAMES Mussa Mahmoudi *, Vahid Eskandari Department of Civil Engineering, Shahid ajaee Teacher Training Universit, Tehran, Iran Kewords esponse modification factor open chevron eccentricall braced steel frames open diagonal eccentric braced steel frames length and height of link beam A B S T A C T esponse modification factor is one of the seismic design parameters to know the nonlinear performance of building structures during strong earthquakes. As such, reling on this factor, man seismic design codes lead to reduce the structural loads. The current paper tries to evaluate the response modification factors of conventional eccentric braced frames (EBFs). Since, the response modification factor depends on ductilit and over strength, the static nonlinear analsis has been performed on building models including tpe three length of link beam, with 3, 5, 7 and 1 and with different brace configurations (open chevron invert V and open diagonal bracing), Further, the linear dnamic and incremental nonlinear dnamic analsis was performed on building models under San Fernando, Cape Mendocino and Northridge strong ground motions for modification of the nonlinear static analsis results. The results indicated that the response modification factors for open diagonal eccentric braced frames were higher than the open chevron eccentric braced one. It was also found that the length of link beam and the height of buildings have had greater effect on the response modification factors. 1 INTODUCTION The structures should be designed in a wa that could resist enough against severe earthquakes and should provide comfort and peace of mind for those live there in case of minor tremors. In other words, a structure through its ductile behavior should dissipate not onl a considerable amount of imported energ but should be in a position to control the deformations and transfer the force to foundation through enough lateral stiffness in ground motions. Over the past few decades, eccentricall braced frames (EBFs) have been proved the distinctive elements of a structural tpolog suitable for satisfing different design objectives of modern performancebased seismic engineering in medium or high-rise buildings. Also, the have often been proposed as * Corresponding author ( m.mahmoudi@srttu.edu).

2 Mahmoudi et al - esearch in Civil and Environmental Engineering (1) cheaper and more valid alternative to the most common moment resisting frames (MFs) or concentricall braced frames (CBFs). Indeed, owing to the presence of bracings and links, EBFs are expected to incorporate characteristics of both high lateral stiffness and high energ dissipation capacit (Hjelmstad and Popov, 1984; oeder and Popov, 1978). These characteristics drew the attention of designers to EBFs hence, most of the codes placed the basis of seismic design of EBFs on resistance and ductilit. In other words, all designers agreed to this assumption that some part of input energ incurred b earthquake should be dissipated b plastic deformations, although considering the point that the deformations should be limited or have to be dependent upon permitted limits. It must be remembered that the final capacit of dissipated energ in ever structure depends upon factors such as: structure s seismic parameters, characteristic of earthquake records and environmental conditions of the place where a structure is located. Considering these, the response modification factor is the reflection of energ dissipation within the boundar of plastic with respect to the lack of overturning and big deformations in structure. With respect to height and length of the link beam of structure, these are of various parameters effective on the response modification factor and that in this research has been studied on EBFs. Using static pushover analsis, linear dnamic and incremental nonlinear dnamic analsis, and the effect of height and length of the link beam on ductilit reduction factor, overstrength reduction factor and response modification factor of EBFs have been studied in this research. 2 ESPONSE MODIFICATION FACTO ( FACTO) The structure's elasticit under an earthquake can create base shear force and stress which are noticeabl bigger than the real structure response. Under such circumstances, the structure can absorb quiet a lot of energ and resists when it enters the inelastic range of deformation. Overstrength is related to the fact that the maximum lateral strength of a structure generall exceeds its design strength. Hence, seismic codes reduce design loads, taking advantage of the fact that structures possess both overstrength and ductilit. In fact, the response modification factor includes inelastic performance of structure and indicates overstrength and ductilit of structure in inelastic stage (Applied Technolog Council, 1995a, b). esearchers have so far proposed different methodologies for the response modification factor which generall fall into two main groups: the European and the American methods. In this stud, one of the most important American methods, so-called Uang, has been adopted. Fig. 1 illustrates the parameters used in Uang method and are defined in the following(tasnimi and Masoumi, 26; Uang, 1991) Fig. 1 depicts variation of structural base shear versus total drift in a tpical pushover analsis. This curve is idealized as the response of bilinear elasto-plastic sstem in pursuit of seismic demand parameters including factor. The response modification factor is determined as follows:. S (1) 42

3 Mahmoudi et al - esearch in Civil and Environmental Engineering (1) eduction Factor due to Ductilit (u) Fig. 1 Definition of Nonlinear Parameters is a parameter that measures the global nonlinear response of a structure exposed to the hsteretic energ. Several proposals have been put forward for. To calculate in a nonlinear static analsis, we could appl the equation proposed b Fajfar (Fajfar, 22), the reduction factor is written as follows: T ( 1) 1 T T sec. C TC, T T sec. C (2) where, T is the fundamental period, Tc is the characteristic of ground motion equal to.5 for the soil tpe II that has been considered here based on the Iranian Earthquake esistance Design Code (Standard No. 28 and is the structural ductilit factor determined as follows: max where, max is the maximum displacement for the first life safet performance in the structure and is the ield displacement observed there. Also, V is determined using dnamic analsis method as follows: e (4) V where, V andv denote the maximum elastic earthquake force and base shear in relevance to the first e life safet performance in structural members respectivel. (3) 43

4 Mahmoudi et al - esearch in Civil and Environmental Engineering (1) Overstrength Factor ( S ) Considering some of the intermittent quake incidents, it seems building structures could take the forces considerabl larger than those designed for. The presence of significant reserved strength that was not accounted in design, explains this phenomenon (ahgozar and Humar, 1998). As a matter of fact, the overstrength helps structures stand safet not onl against sever tremors but reduces the elastic strength demand, as well. Here, this is performed using the force reduction factor (Mahmoudi, 23). The overstrength factor ( ) is defined as follows: V (5) V d Here, V is the design base shear in the building and V is the base shear in relevance to the first life d safet performance in the structure as shown before (Fig. 1). In this equation, the overstrength factor is based on the applied nominal material properties. However, the actual overstrength factor should consider the help of some other effects (Asgarian and Shokrgozar, 29):... (6) s 1 2 In the Eq. (5), 1 accounts for the difference between actual and nominal static ield strengths. Based on a statistical stud, for structural steel, the value of 1 ma be put as 1.5 (Schmidt and Bartlett, 22). During an earthquake occurrence, parameter 2 ma be used to know the ield stress under the strain rate effect. For that matter, to account the strain rate effect, a value of 1.1 (an increase of 1%) could be used (Uang, 1991). In the current stud, steel tpe St-37 has been used for all structural members. Here, parameters 1 and 2 equal to 1.5 and 1.1 are considered taking into account as material sm over strength factor. Other parameters such as nonstructural component contributions, lateral force profile variation (Asgarian and Shokrgozar, 29) could be included once a reliable data is available. 3 STUCTUAL MODELS To assess the response modification factors, reduction factors due to ductilit, and the overstrength factor, some 12 open chevron invert V eccentric braced frames (EBFs) and 12 open diagonal eccentric braced frames (EBFs) with 3, 5, 7 and 1 as well as a 5m long ba were selected. The height of ever model structure was fixed to 3.2 m. Fig. 2 shows the plan and brace configuration of the model structures. For gravit, the dead and live loads respectivel of 6.5 and 2 KN/m2 were used. To compute the seismic design base shear, parameters such as importance factor of I=1, seismic zone factor of A =.35, soil tpe II and the response modification factor 7 were considered for EBFs based on the Iranian Earthquake esistance Design Code (Building and Housing esearch Center, 25). Apart from the aforementioned Iranian Earthquake esistance Design Code (Standard No. 28) (Building and Housing esearch Center, 25), the Iranian National Building Code, part 1, steel structure design (Ministr of Housing and Urban Development, 29)was also considered while designing the models. 44

5 Mahmoudi et al - esearch in Civil and Environmental Engineering (1) (a) (b) Fig. 2 Configuration of Model Structures; (a) Plan and (b) Brace configuration Following assumptions were made for modeling of members in a nonlinear range of deformation: All braces were connected to columns b pins. For the dnamic analsis, store masses were placed in the store levels considering rigid diaphragms action. e idealized elastic-plastic behavior with strain hardening of 2% was considered for members with inelastic behavior. The P-Δ effect was considered for geometric nonlinearities. 4 PUSHOVE ANALYSIS OF MODELS AND ESULTS EVALUATION To evaluate behavior factors, the nonlinear static (pushover) analsis is performed b subjecting a structure to monotonicall increasing lateral forces with an invariant height-wise distribution. In the pushover analsis, selecting an appropriate lateral load distribution is an important step (Fajfar, 22). It was also conducted using life safet structural performance level as well as the nonlinear behavior of braces as suggested b FEMA-356 (Federal Emergenc Management Agenc, 2) (Fig. 3). As shown in Fig. 3, Q is the force at hinge that can be the moment or shear, QCE is the ield limit of these two values, Δ and θ are the displacement and rotation of the hinge, respectivel. Having the performance point in hand, the status of the structure under the effect of the maximum seismic load can now be specified. In this wa, a precise prediction can be made as what are the deformations imposed on each structural element and on the installations hence, we can do as required for strengthening them. This stud has primaril preferred FEMA- 356 code (Sabelli et al., 23) in order to define the nonlinear hinges for sections of structural elements and to assign them to the elements. Figs. 4-9 show the results of the above nonlinear static pushover analsis, in terms of base shear-roof displacement for different conventional EBFs tpe (open chevron invert V and open diagonal bracing), including three tpes of link beam length (e=l/8, e=l/4, e=l/2 and e: length of link beam, L: length beam). Figs. 1 and 11 show a variation in the response modification factor for different tpes of EBFs configuration. 45

6 Mahmoudi et al - esearch in Civil and Environmental Engineering (1) Fig. 3 Force Curve - Deformation of Nonlinear Hinges According to FEMA- 356 code 2 Base Shear(kgf) Stor 5 Stor 7 Stor 1 Stor oof Displacement (cm) Fig. 4 oof displacement-base shear curve for invert V(e=L/8) Base Shaer(kgf) Stoe 5 Stor 5 7 STOY 1 Stor oof Displacement (cm) Fig. 5 oof displacement-base shear curve for invert V(e=L/4) 46

7 Mahmoudi et al - esearch in Civil and Environmental Engineering (1) Base Shear (kgf) Stor 5 Stor 7 Stor 1 Stor oof Displacement (cm) Fig. 6 oof displacement-base shear curve for invert V(e=L/2). 2 Base Shear (kgf) Stor 5 Stor 7 Stor 1 Stor oof Displacement (cm) Fig. 7 oof displacement-base shear curve for diagonal (e=l/8) Base Shear (kgf) oof Displacement (cm) Fig. 8 oof displacement-base shear curve for diagonal (e=l/4) 3 Stor 5 Stor 7 Stor 1 Stor 47

8 esponse Modification Factor Mahmoudi et al - esearch in Civil and Environmental Engineering (1) Base Shear (kgf) 5 3 Stor 5 Stor 7 Stor 1 Stor oof Displacement (cm) Fig. 9 oof displacement-base shear curve for diagonal (e=l/2) e=l/8 e=l/4 e=l/ Store Fig. 1 esponse modification factors for invert V Fig. 11 esponse modification factors for diagonal. 48

9 Mahmoudi et al - esearch in Civil and Environmental Engineering (1) Tables 1-6 further highlight the over strength factor ( ), reduction factor due to ductilit ( ) and response modification factor () for different conventional EBFs. s Table 1 esponse modification factor of conventional EBFs that have open chevron invert-v brace with (e=l/8) sm s Table 2 esponse modification factor of conventional EBFs that have open chevron invert-v brace with (e=l/4) sm s Table 3 esponse modification factor of conventional EBFs that have open chevron invert-v brace with (e=l/2) sm s Table 4 esponse modification factor of conventional EBFs that have open diagonal brace with (e=l/8) sm s

10 Mahmoudi et al - esearch in Civil and Environmental Engineering (1) Table 5 esponse modification factor of conventional EBFs that have open diagonal brace with (e=l/4) sm s Table 6 esponse modification factor of conventional EBFs that have open diagonal brace with (e=l/2) sm s TIME HISTOY ANALYSIS OF MODELS AND ESULTS EVALUATION This stud investigates the actual behavior of frames and accurac and precision of the results in the static analsis of models under San Fernando, Cape Mendocino and Northridge quake records. To gainv, at first, three severe earthquakes (Table 7) were selected and matched them with the design spectrum. To do so, their PGA s with several tries and errors was altered in a wa that the calculated time histor resulted in the structure reaching to the following failure criteria: Based on the Iranian Earthquake esistance Design Code (Standard No. 28) (Building and Housing esearch Center, 25), the maximum inner-store drift was limited to the values.25 H and.2 H for the frames with a fundamental period less than.7 s and more than.7 s, respectivel, where H is the store height. Earthquake Name Table 7 Characteristics of selected acceleration records Distance to Year Ms PGA (g) Fault(km) San Fernando Cape Mendocino Northridge Then the incremental nonlinear dnamic analsis of the models under these scaled strong ground motion was carried out and the maximum nonlinear base shear of this time histor, V, was calculated. Finall, through linear dnamic analsis of the structure under the same scaled records, the maximum linear base shear, V e, was gained. Then the average of V and V e for each model and overstrength reduction factors, and ductilit reduction factors,, based on Equation (1) were computed. 5

11 Mahmoudi et al - esearch in Civil and Environmental Engineering (1) Table 8 Nonlinear and linear maximum base shear under scaled selected records Earthquake Name V (ton) V e (ton) San Fernando Northridge Cape endocino Table 9 Ductilit, over strength and response modification factors of the models V d (ton) ( ( ton) V ave ) V e ( ave )( ton) s sm Taking into account the above procedure, all models with open chevron invert V eccentric braced frames (EBFs) and length of link beam (e=l/8) were analzed and their final response modification factors were calculated. These converged values are shown in Tables 8 and 9. 6 CONCLUSION This paper has tried to evaluate the factors such as over strength, reduction due to ductilit, and the response modification factor of some 24 conventional EBFs considering the level of life safet structural performances. As discussed, the static nonlinear analsis was performed on building models of tpe three length of link beam (e=l/8, e=l/4, e=l/2 e: length of link beam, and L: length bracing ba), with 3, 5, 7 and 1 and different brace configurations (open chevron invert V and open diagonal bracing). The attempt was to evaluate the response modification factors of open chevron invert V eccentric braced frames (EBFs), the linear dnamic and incremental nonlinear dnamic analsis has been performed on building models including the length of link beam (e=l/8) with 3, 5, 7 and 1 under San Fernando, Cape Mendocino and Northridge strong ground motions for modification of results. 51

12 Mahmoudi et al - esearch in Civil and Environmental Engineering (1) The results of this stud can be summarized as follows: 1. It was observed that factors such as reduction due to ductilit and response modification of EBFs decrease with an increase in the height of buildings. However, the reduction factors due to ductilit are different for open chevron invert V eccentric braced frames and open diagonal eccentric braced frames. Also, the two above factors decrease with an increase in the length of link beam but there is no obvious variation on the reduction factors due to ductilit. 2. It was observed that the overstrength factors of EBFs decrease with an increase in the height of buildings. The overstrength factors also increase with an increase in the length of link beam. 3. The response modification factors for open chevron invert V eccentric braced frames with tpe three length of link beam(e=l/8, e=l/4, e=l/2) are evaluated as 6.93, 6.32 and 4.14 and for open diagonal eccentric braced frames as 8.49, 7.64 and 4.83, respectivel. 4. The identical results are also obtained for open chevron invert V eccentric braced frames with length of link beam (e=l/8) that was analzed using nonlinear static and nonlinear dnamic methods. 5. Codes give constant value of response modification factors for EBFs. However, the response modification factors, evaluated in this stud, have different values for brace configuration, the length of link beams and the height of buildings. Consequentl, results indicate that the response modification factors proposed in seismic codes need to be modified for conventional EBFs. eferences Applied Technolog Council (1995a). A critical review of current approaches to earthquake-resistant design, ed. ATC- 34. Applied Technolog Council,, edwood Cit, pp Applied Technolog Council (1995b). Structural response modification factors, ed. ATC-19. Applied Technolog Council,, edwood Cit, California, pp Asgarian, B.&Shokrgozar, H.. (29). Brbf response modification factor. Journal of Constructional Steel esearch, 65(2), Building and Housing esearch Center (25). Iranian code of practice for seismic resistance design of buildings. Fajfar, P. (22). Structural analsis in earthquake engineering break though of simplified nonlinear methods, In 12th European conference on earthquake engineering. Federal Emergenc Management Agenc (2). Prestandard and commentar for the seismic rehabilitation of building, In FEMA-356., Washington, DC. Hjelmstad, K.D.&Popov, E.P. (1984). Characteristics of eccentricall braced frames. Journal of Structural Engineering, 11(2), Mahmoudi, M. (23). The relationship between overstrength and members ductilit of rc moment resisting frames, In Pacific Conference on Earthquake Engineering. Ministr of Housing and Urban Development (29). Iranian national building code (part 1) steel structure design. ahgozar, M.A.&Humar, J.L. (1998). Accounting for overstrength in seismic design of steel structures. Canadian Journal of Civil Engineering, 25(1),

13 Mahmoudi et al - esearch in Civil and Environmental Engineering (1) oeder, C.W.&Popov, E.P. (1978). Eccentricall braced steel frames for earthquakes. Journal of the Structural Division, 14(ST3), Sabelli,., Mahin, S.&Chang, C. (23). Seismic demands on steel braced frame buildings with buckling-restrained braces. Journal of Engineering Structures, 25(5), Schmidt, B.J.&Bartlett, F.M. (22). eview of resistance factor for steel: esistance distributions and resistance factor calibration. Canadian Journal of Civil Engineering, 29, Tasnimi, A.A.&Masoumi, A. (26). Derivation of response modification factors for concrete moment resisting frames, 1st ed. Building and Housing esearch Center. Uang, C.M. (1991). Establishing r (or rw) and cd factors for building seismic provisions. Structural Engineering, 117(1),