Inelastic Torsional Response of Steel Concentrically Braced Frames

Transcription

1 Inelastic Torsional Response of Steel Concentrically Braced Frames R. Comlek, B. Akbas & O. Umut Gebze Institute of Technology, Gebze-Kocaeli, Turkey J. Shen & N. Sutchiewcharn Illinois Institute of Technology, Chicago-IL, USA SUMMARY: Concentrically braced frames (CBFs) are considered to one of the most cost-effective structural systems to resist lateral loads in steel buildings. The main advantages of these systems are their efficiency in meeting lateral stiffness and strength requirements with minimum steel tonnage, and simplicity in design calculations. However, CBFs have limited energy dissipation capacity and low redundancy due to the likelihood of premature brace fracture under cyclic loading in addition to the brittle failure of brace connections. The main objective of this study is to investigate the accidential torsional response in low-rise steel CBFs due to the difference in design strength of braces. For this purpose, inelastic torsional response of a -story building having perimeter CBFs under strong earthquake ground motions in investigated in detail. Keywords: Torsional response, concentrically braced frames, strength and ductility. INTRODUCTION Concentrically braced frames (CBFs) are considered to one of the most cost-effective structural systems to resist lateral loads in steel buildings. The main advantages of these systems are their efficiency in meeting lateral stiffness and strength requirements with minimum steel tonnage, and simplicity in design calculations. However, CBFs have limited energy dissipation capacity and low redundancy due to the likelihood of premature brace fracture under cyclic loading in addition to the brittle failure of brace connections. Braces are the main-load carrying elements in CBFs and their axial force-deformation relation is substantially different from moment-rotation behaviour in moment resisting frames. Torsional irregularities in a building whose structural system consists of CBFs is not only due to the difference between the centers of rigidity and mass, but also due to the difference in strength of braces. The main objective of this study is to investigate the accidential torsional response in low-rise steel CBFs due to the difference in design strength of braces. For this purpose, inelastic torsional response of a -story building having perimeter CBFs under strong earthquake ground motions in investigated in detail. The plan of the building is symmetrical and 5ft x 5ft with a story height of ft for the second and third stories and 8 ft for the first story. The building consists of five-bay frames in two orthogonal directions spaced at ft. The columns are assumed to be pinned to the ground. All the connections of frame to column, brace to girder, and girder to column are assumed to be pin connections. The strength of the braces are assumed to be varying for each perimeter CBF up to %. Seven spectrum-compatible earthquake ground motions are selected for the nonlinear dynamic time history analyses. Analyses are carried out using Perform D () computer program. The buckling behaviour of braces is modelled using strut component. The results are presented in the form of axial stress-strain in brace members, plastic hinge rotations, pushover curve and drift ratio.

2 . DESCRIPTION OF THE BUILDING The plan of the building is symmetrical and 5ft x 5ft with a story height of ft for the second and third stories and 8 ft for the first story. The building consists of five-bay frames in two orthogonal directions spaced at ft. The columns are assumed to be pinned to the ground. All the connections of frame to column, brace to girder, and girder to column are assumed to be pin connections. The strength of the braces are assumed to be varying for each perimeter CBF up to %. Seven spectrum-compatible earthquake ground motions are selected for the nonlinear dynamic time history analyses. Analyses are carried out using Perform D () computer program. The buckling behaviour of braces is modelled using strut component. The results are presented in the form of axial stress-strain in brace members, plastic hinge rotations, pushover curve and drift ratio. See Table and Figure for the sizes. And also see the variations. Blank line pt Figure. Plan and elevation of the -story frame Table.. Case definitions of the study Case No Strength Variation Applied Frame Applied Case-.F y Frame- -,, Figure Case-.F y Frame-, -,, Case-.F y Frame-,, -,, Case-4.F y Frame-,,,4 -,, Case-5.F y Frame- - Case-6.F y Frame-, - Case-7.F y Frame-,, - Case-8.F y Frame-,,,4 - Table.. Member sizes of the building Braced Un-braced Brace Bay Bay Members Girders Girders Braced Bay Columns Un-braced Bay Columns Exterior Columns Columns not on the perimeter Girders not on perimeter Roof HSS7 7 / W4 6 W 44 W 4 W 4 W 4 W 5 W 55 nd HSS8 8 / W4 5 W 44 W 4 W 4 W 4 W 5 W 55 Floor st HSS 5/8 W6 95 W 44 W 65 W 65 W 4 W 7 W 55 Floor

3 Designed with SS = 5% g, S = 8% g; Dead load = 8 psf(lb/ft) and live load = 5 psf(lb/ft). AISC 4-5 and ASCE 7-5. Rigid diagram assumption might be used. Or we define a master node in the mass center (the geometrical center of the plane, neglecting 5% accidental mass eccentricity), and all nodes at the columns are slaved nodes. Girders (the beams directly connected to columns) need to be included with pin connection for now (we will consider semi-rigidity in the next phase). Floor Beams (beams supported by girders) need not to be included. Masses (from 8 psf dead load) are lumped at all joints based on tributary area of each column. Only perimeter frames will contribute carrying lateral forces, i.e. interior frames will only carry gravity loads in this phase. To prevent interior frames carrying lateral forces, the flexural rigidity of all interior members will be set to zero. That is, the beam-to-column connections are assumed to be pin. The plastic hinges will be defined for the braces and girders on the braced bays. There will be one axial plastic hinge location on the braces (in the middle). For the girders on the braced bay, P-M plastic hinge will be defined in the middle... Earthquake Ground Motion In this study, four ground motions (LA, LA8,, ) was selected so that the seismic response of each of the three frames would range from moderate to severe, and the story drifts be evaluated based on the response of the frames. These ground motions were used in FEMA- sponsored research project on steel moment frames damaged in the 994 Northridge Earthquake. These ground motions were identified as having a % Probability of exceedence in 5 years by SAC, a consortium conducting the FEMA-sponsored project. Mean response spectrum of the ground motions matches the 997 NEHRP design spectrum, modified from soil type of SB SC to soil type SD and having a hazard specified by the 997 USGS maps. Figure presents the normalized response spectra of these ground motions. 4. Pseudo Acceleration/Peak Ground Acceleration... La La La5 La6 La6 La7 La Period Blank line pt Figure. Normalized response spectrum of the ground motions (n=5%)

4 . NONLINEAR ANALYSES Three typical steel moment resisting frames with 4-, 9-, and -stories, representing typical low-, medium-, and high-rise steel buildings, as shown in Figures,, and, are selected for this study. The frames were designed based on the seismic design requirements in ASCE 7-5 (5) and AISC 4-5 (5) (Shen et al. ). All buildings are considered to be regular structures. The 4-story building has plan dimensions of 6.6m x 54.9m with four 9.5m bays and six 9.5m bays in the two orthogonal directions, respectively, and a typical story height of.96m (Figure ). The columns are assumed to be fixed at the ground level. The 9-story building has plan dimensions of 45.75m x 45.75m and consists of five bays of framing in both orthogonal directions spaced at 9.5m on center (Figure ). The building has a basement level (Level B in Figure b). The typical story height is.96m except at the Ground and B Levels where it is 5.5m and.65m, respectively (Figure b). The - story building has plan dimensions of 6.m x 6.m and consists of five 6.m bays and six 6.m bays of framing in the two orthogonal directions, respectively (Figure ). The building has two basements levels (Levels B and B). The typical story height is.96m, except at the Ground B and B Levels where it is 5.5m and.65m, respectively (Figure b). The columns are assumed to be pinned at the lowest basement level for the 9- and -story buildings respectively, although they run continuously through the Ground Level framing. Stress (MPa) Strain Blank line pt Figure. Mathematical models for non-linear brace elements 4. ANALYSES RESULTS Inelastic dynamic time history analyses were conducted to study inelastic response of the three frames. The frames were modeled as beam and column elements with potential plastic hinges at their ends. The interaction between the axial force and bending moment was considered in columns. A 5% strain hardening ratio was assumed in the plastic hinges. P-Δ effects were always included in the timehistory analyses. Modal analyses were conducted prior to time-history evaluations and indicated that the fundamental period of vibration of the 4-, 9-, and -story frames is.8 sec.,.6 sec., and.4 sec. for ASCE 7-5 frames and.787 sec,.4 sec, and.75 sec for TEC (7) frames, respectively. Base shear vs. roof displacement for the 4-story, 9-story and -story frames are given in Figures 5, 6, and 7, respectively. Maximum plastic hinge rotation at the story levels for the 4-story, 9- story and -story frames are given in Figures 8, 9, and, respectively. drift ratios at the story levels for the 4-story, 9-story and -story frames are given in Figures,, and, respectively. Figures show that seismic demand is quite less for the frames designed according to the TEC (7) requirements. The ratio of design base shear (design strength) to the yielding strength is also given in Table 4. Deflection amplification factors for each ground motion with respect to ASCE 7-5 (5)

5 and TEC (7) design are given in Tables 5 and 6, respectively. Results indicate that deflection amplification factors are lower for TEC (7) design, but for both design codes they are lower than 8. It should be pointed out the ground motions used in this study have higher probability of exceedence (%) than design ground motions (% probability of exceedence). 4 Reference 4 Case Blank line pt 4 Case-,, Case-5 Blank line pt Case-6,7, Blank line pt Figure 4. Mathematical models for non-linear response history analysis Authors may choose how they wish to format the table layout. Use Times New Roman pt for Table Authors may choose how they wish to format the table layout. Use Times New Roman pt for Table Authors may choose how they wish to format the table layout. Use Times New Roman pt for Table

6 Reference Blank line pt Case- Case-,, Case-5 Blank line pt Case-6,7, Blank line pt Figure 5. Mathematical models for non-linear response history analysis Authors may choose how they wish to format the table layout. Use Times New Roman pt for Table Authors may choose how they wish to format the table layout. Use Times New Roman pt for Table Authors may choose how they wish to format the table layout. Use Times New Roman pt for Table

7 8 Reference Case Blank line pt 8 Case-,, Case-5 Blank line pt Case-6,7, Blank line pt Figure 6. Mathematical models for non-linear response history analysis Text after the figure. 5. CONCLUSIONS This paper studied the inelastic response of low-, medium-, and high-rise steel moment resisting frames designed for different story drift limitations. Desing story drift is generally computed using the equal displacement rule. The analysis results obtained from this study indicate that the notion of "equal displacement" would be acceptable for a structure with its design base shear close to yielding strength. It might be too conservative for flexible structure such as special moment resisting frames where yielding strength is noticeably larger than design base shear. However, the story drift limitation, the ratios of actual inelastic displacement demand to design displacement demand and elastic displacement demand to yielding displacement demand should be further studied for special moment frames.

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