Comparison between Seismic Behavior of Suspended Zipper Braced Frames and Various EBF Systems

Transcription

1 Comparison between Seismic Behavior of Suspended Zipper Braced Frames and Various EBF Systems A. Niknam 1, A. Sharfaei 2 1- Assistant Professor, Civil Engineering Faculty, University of Science & Technology, Tehran, Iran 2- M. S. in Civil (Structure) Engineering, Azad University, Central Branch, Tehran, Iran Abstract Zipper frames are intended to improve on the behavior of conventional inverted-v-braced frames, which show poor performance taking place from the early buckling of braces in the lower story. A zipper frame affords better performance by forcing simultaneous buckling of all braces. In this article, seismic behaviors of zipper braced frames and three types of eccentrically braced frames are evaluated using finite element simulation. Two dimensional finite element models have been created for three-story onebay frames for various bay lengths and different arrangement of braces. Seismic response of frames subjected to near-fault ground motions (LA21) has been studied through dynamic analysis, considering nonlinearity of geometry and materials. For this purpose, SAP2000 has been used. Results have been compared and structural response of steel frames and some other parameters such as ductility of frames, maximum base shear and optimized link length have been investigated. Against other researches, in this article, the ratio of maximum shear over the weight of structure and its relation to behavior of structure has also been studied. It was found that optimized link length in EBF systems which caused to maximum ductility of frame is about 30 percent of the bay length. Moreover, the results showed that zipper frames provide desirable post buckling behavior and exhibit more ductility. Keywords: Suspended Zipper braced frames; eccentrically braced frames; near fault; dynamic analysis; 1. Introduction Steel is one of the most widely used materials for building construction. The inherent strength and toughness of steel are characteristics that are well suited to a variety of applications, and its high ductility is ideal for seismic design. To utilize these advantages for seismic applications, the design engineer has to be familiar with the relevant steel design provisions and their intent and must ensure that the construction is properly executed. The braced steel frames are extensively used in middle to high-rise buildings in highly seismic regions due to their advantages in terms of both economy and better seismic performance. These braced steel frames usually include two types: concentrically braced frames (CBFs) and eccentrically braced frames (EBFs). These brace members can be grouped into several patterns: X-type, K-type, V-type and inverted V-type etc. Steel braces are generally used as an economic means of providing lateral-load resistance to steel structures. In a traditional K braced (Chevron) frame design; the braces resist the lateral earthquake load transmitted by the beam as axial forces. The vertical resultant of two adjacent braces is null and does not affect the frame s beams. Under a strong ground motion one of the braces is expected to buckle under compression while the adjacent one is expected to yield in tension. Compared to a straight member, a buckled member has a lower capacity to carry axial compressive force while its tension capacity remains the same. In such case the vertical resultant from the two adjacent braces is not null and it is transmitted to the beam as a shear force, which makes the design of the beam very costly since the moments at the mid span are enormous and big sections are required to sustain them. In 1989 Khatib et al. suggested adding a column between the beams connected at same joints where the braces connect; this column will transmit the vertical unbalanced load to the upper floor, where it will be redistributed to its braces. As a consequence, the compression brace will be subjected to an even greater compression, triggering buckling at the second floor level. A new unbalanced vertical force would be created at the upper floor beam. If this floor is linked to the upper one, the process would repeat. The propagation of buckling and yielding to the upper floors seems similar to a zipper from which this system derived the name of zipper frame. The solution is appealing; however, the analytical results show that if all the braces at all floors are allowed to buckle, then collapse of the frame is likely to occur.[1]

2 Steel braces are generally used as an economic means of providing lateral-load resistance to steel structures. This paper discusses the ductility of eccentrically braced frames (EBFs) and Zipper braced frame. 2. THEORY FOR MODAL PUSHOVER ANALYSIS BASIC ASSUMPTIONS According to structural dynamics theory, the governing equation of the response of a structure, when it is subjected to a seismic excitation, is given by eq.1 in the general case, Where [m] is the mass matrix of the structure, [c] is the damping matrix, {s} is the influence vector and {fs} is the stiffness force. For a plane frame, the influence vector is the unit vector. Classical modal analysis for eq. 1 allows us to consider the system as uncoupled and solve it as n individual single degree of freedom (SDOF) systems. Two fundamental assumptions hold for MPA. The first one is that of the uncoupled system, and the second one is that the response of the structure is substituted by equivalent inelastic SDOF systems with known properties. In order to estimate the characteristics of the inelastic SDOF system, such as the yield point, after the computation of the structure s natural frequencies ω n and modes {Φ n }, it is subjected to lateral forces, given by eq. 2, Applying the force distribution of eq. 2 incrementally, a pushover analysis is performed developing the pushover curve of the structure (V bn -urn relationship), for its nth mode, where V bn and urn are the base shear and top roof displacement for the nth mode load pattern, respectively. The structure should be pushed just beyond the target (or expected) roof displacement for the selected mode. In order to estimate the yield point (D ny, Fsny) of the inelastic SDOF system, we perform a bilinear idealization of the pushover curve based on FEMA-273 procedure[2]. The set of eq.3 is used to convert the pushover curve of the structure to a pushover curve for the equivalent SDOF system, The period T n of the nth mode SDOF system is not necessarily equal to the nth vibration period of the structure. In order to estimate the peak inelastic displacement D no of the SDOF system for the seismic excitation under consideration, the nth equivalent one degree differential equation of motion that holds for the nth SDOF system is solved by means of non-linear direct integration time history analysis. The target roof displacement u rno of the structure is obtained from, Finally, in order to determine the total peak response for the quantity r ro, we use a modal combination rule such as complete quadratic combination (CQC) or square root of sum of the squares (SRSS). 3. DESIGN PHILOSOPHY AND METHODOLOGY a- Suspended zipper frame As mentioned previously, the full-height zipper mechanism is potentially unstable once the full-height zipper mechanism forms. To overcome this weakness, a design procedure based on preventing buckling of the topstory braces is advocated here. This procedure suppresses the formation of a complete collapse mechanism and the formation of plastic hinges in the beams. As the lateral loads increase, the compression braces will buckle, the tension braces will yield, and finally the zipper strut will yield to form the mechanism (Figure 1). 1- Phase I (Strength Design): The frame shall be designed to resist the effects of earthquake and vertical loadings from the load combinations stipulated by the Applicable Building Code without the aid of the zipper columns. 2- Phase II (Capacity Design) The frame designed in Phase I shall be modified as follows: (1) Zipper columns Zipper columns shall be added and be designed to resist the vertical unbalanced forces generated by the braces located at the level below using Py for the braces in tension and 0.3 times φcpn for the braces in compression. (2) Top-story braces 2

3 Top-story braces shall be designed to resist elastically the vertical unbalanced forces collected by the zipper columns below the top story as well as the 1.7 times the top-floor equivalent earthquake force. (3) Column Strength The required axial compressive and tensile strength shall be determined using the maximum load transferred to the column considering the capacities of the adjacent braces in combination with the Induced forces from the 1.7 times the top-floor equivalent earthquake force. (4) Beams Beams shall be considered as beam-column members stipulated at the Chapter H in the AISC LRFD Specification. The required strength shall be determined using the maximum load transferred to the beam considering the capacities of the adjacent braces.[5] Figure 1 Partial-height zipper mechanism b- Eccentrically braced frames (EBFs) Framing system with beam, columns and braces. At least one end of every brace is connected to isolate a segment of the beam called a link. Resist lateral load through a combination of frame action and truss action. EBFs can be viewed as a hybrid system between moment frames and concentrically braced frames. Develop ductility through inelastic action in the links. EBFs can supply high levels of ductility (similar to MRFs), but can also provide high levels of elastic stiffness (similar to CBFs)[3] v Link Behavior: Shear vs. Flexural Yielding Links v Link length "e" is key parameter that controls inelastic behavior (Figure 2) v Shear yielding occurs when: V = V p = 0.6 F y (d - 2t f ) t w V p = fully plastic shear capacity of link section Flexural yielding occurs when M = M p = Z F y M p = fully plastic moment of link section Static equilibrium of link e=2m/v Shear yielding will occur when V=V p and M < M p e 2M P /V P Shear yielding will occur when M = M p and V < V p e 2M P /V P Figure 2. Eccentrically braced frames 3

4 4. Modeling Assumptions Zipper brace frame Following a capacity design methodology, an inverted zipper frame was designed as the prototype structure for this project (Figure 3). It was assumed that the beam-to-column connections as well as brace-tobeam and zipper column-to-beam connections are pinned. Unfactored uniformly distributed roof dead loads of 1.69 kn/m, floor dead loads of 1.95 KN/m, and live loads of 0.40 kn/m were applied to the beams. The site is classified as site class D (soft soil) and it s mapped spectral response acceleration at short periods (Ss,) and at 1 second period (S1) are 1.5g and 0.6g respectively. The seismic weight for this braced bay is 4820 kn, which is one sixth of the entire building seismic weight. The seismic loads were calculated based on the value of R equal to 6, the value of IE equal to 1.5, and the provisions of IBC Accordingly, the seismic base shear was calculated to be 1204 kn, with the floor loads being 626 kn, 385 kn, and 193 kn from the third to first floor levels, respectively. The member sizes are listed on Table 1.[4] Table 1 Member sizes Story Type Model 3 Braces HSS10x10x5/8 2 Braces HSS7x7x3/8 1 Braces HSS7x7x3/8 3 Columns W10x77 2 Columns W10x77 1 Columns W10x77 3 Beams W8x21 2 Beams W14x82 1 Beams W12x50 3 Zipper W8x48 2 Zipper W8x24 Figure 3 Prototype zipper frame Eccentrically braced frames (EBFs) We use same section for eccentrically braced frames but using different link length. In this project, use 24, 48 and 72 inch for link length. 5. NONLINEAR STATIC ANALYSIS Operation point of structure is placed at crossing point of capacity curve of structure and necessity curve of it. And the nonlinear static analysis is used to find it. After calculating the displacement of operation point at the roof of the structure, the displacements of the same point, but at the other floor have been calculated. We use FEMA s target displacement in this project at SAP2000 ver.14. Vertical axis in the graphs is KN/lb and horizontal axis is Percent displacement of roof. 4

5 Figure 4 comparing zipper frame with EBF e=24in Figure 5 comparing zipper frame with EBF e=48in Figure 6 comparing zipper frame with EBF e=72in 6. RESULT Investigation of fig4 to fig 6, we can understand that ductility of zipper frame is more than EBF. Summary of conclusions are: link length is very important to EBF s behavior EBF is more useful than Zipper brace frame in elastic Zipper frame can resist after buckling and yielding of brace Only EBF 30% (e=72in) can ductile like zipper frame but with strength less Post- buckling behavior of zipper frame is much better than EBF For better ductile of EBF, using link length more than 20% 5

6 7. REFERENCES 1. Khatib IF, Mahin SA, Pister KS., (1998), Seismic behavior of concentrically braced steel frames, UCB/EERC-88/01. Berkeley: Earthquake Engineering Research Center, University of California 2. FEMA 273., (1997), NEHRP Guidelines for the Seismic Rehabilitation of Buildings 3. American Institute of Steel Construction (AISC), 2005, AISC Seismic. Seismic provisions for structural steel buildings. Chicago 4. Tremblay R, Tirca L. 2003, Behavior and design of multi-story zipper concentrically braced steel frames for the mitigation of soft-story response. In: Proceedings of the conference on behavior of steel structures in seismic areas.. p Leon RT, Yang CS Special inverted-v-braced frames with suspended zipper struts. In: International workshop on steel and concrete composite construction. Taipei (Taiwan) National Center for Research on Earthquake, 6