Frame Structures Mark D. Denavit Jerome F. Hajjar Stanley D. - PowerPoint PPT Presentation

Seismic Safety and United States Design Practice for Steel-Concrete Composite Frame Structures Mark D. Denavit Jerome F. Hajjar Stanley D. Lindsey and Associates, Ltd. Northeastern University Atlanta, Georgia Boston, Massachusetts Tiziano Perea Roberto T. Leon Universidad Autónoma Metropolitana, Virginia Polytechnic Institute and State University Azcapotzalco, D. F., Mexico Blacksburg, Virginia Sponsors: National Science Foundation American Institute of Steel Construction Georgia Institute of Technology University of Illinois at Urbana-Champaign Proceedings of the 10th International Conference on Urban Earthquake Engineering Tokyo, Japan, March 1-2, 2013

Seismic Performance Factors for Composite Frames • NEESR-II: System Behavior Factors for Composite and Mixed Structural Systems • FEMA P695 - Quantification of Building Seismic Performance Factors Composite • Column Seismic Performance Factors:  0 = Overstrength factor – Steel Girders – R = Seismic Response Factor – C d = Deflection Amplification Factor • Two seismic force resisting systems as defined in the AISC Seismic Specification – Composite Special Moment Frames (C-SMF) using RCFT or SRC columns and steel beams – Composite Special Concentrically Braced Frames (C-SCBF) using CCFT column and steel beams and braces  o System R C d C-SMF 3.0 8.0 5.5 C-SCBF 2.0 5.0 4.5

Selection and Design of Archetype Frames = Fully Restrained Connections = Location of Braced Frame = Shear Connections Moment Frames Braced Frames

Selected Frames Moment Frames Braced Frames Design Design Conc. Bay Gravity Seismic Strength Index RCFT RCFT SRC RCFT-Cd CCFT CCFT Width Load Load ( f′ c ) 3 Stories 9 Stories 3 Stories 3 Stories 3 Stories 9 Stories a a a a a a High 20’ D max 4 ksi 1 a a a High 20’ D max 12 ksi 2 a a a a a a High 20’ D min 4 ksi 3 a a a High 20’ D min 12 ksi 4 a a a a High 30’ D max 4 ksi 5 a a High 30’ D max 12 ksi 6 a a a a High 30’ D min 4 ksi 7 a a High 30’ D min 12 ksi 8 a a a a a a Low 20’ D max 4 ksi 9 a a a Low 20’ D max 12 ksi 10 a a a a a a Low 20’ D min 4 ksi 11 a a a Low 20’ D min 12 ksi 12 a a a a Low 30’ D max 4 ksi 13 a a Low 30’ D max 12 ksi 14 a a a a Low 30’ D min 4 ksi 15 a a Low 30’ D min 12 ksi 16

Mixed Beam-Column Element • Mixed formulation with both displacement and force shape functions • Total-Lagrangian corotational formulation • Distributed plasticity fiber Shape Functions 1 Displacement formulation: stress and strain Transverse modeled explicitly at each fiber of cross section 0 • Perfect composite action 0 L assumed (i.e., slip neglected) 1 Bending Moment • Implemented in the OpenSees framework 0 0 L

Uniaxial Cyclic Constitutive Relations Steel Concrete • • Based on the rule-based Based on the bounding- model of Chang and Mander surface plasticity model of (1994) Shen et al. (1995) • Tsai’s equation used for the • Modifications were made to monotonic backbone curve model the effects of local • The confinement defined buckling and cold-forming separately for each cross process section 0 E c Stress (MPa) -20 (e ′ cc , f′ cc ) -40 -0.008 -0.006 -0.004 -0.002 0 Strain (mm/mm)

RCFT Beam-Column Validation Varma 2000 500 500 400 400 300 300 200 200 Lateral Load (kN) Lateral Load (kN) 100 100 0 0 -100 -100 -200 -200 -300 -300 Expt. Expt. -400 -400 PfB PfB -500 -500 -100 -80 -60 -40 -20 0 20 40 60 80 100 -80 -60 -40 -20 0 20 40 60 80 Lateral Displacement (mm) Lateral Displacement (mm) Test #5: CBC-32-46-10 (Varma 2000) Test #8: CBC-48-46-20 (Varma 2000) H/t = B/t = 35 H/t = B/t = 53 F y = 269 MPa F y = 471 MPa f′ c = 110 MPa f′ c = 110 MPa P/P no = 0.11 P/P no = 0.18 L/H = 4.9 L/H = 4.9

SRC Beam-Column Validation Ricles and Paboojian 1994 400 500 400 300 300 200 200 100 Lateral Load (kN) Lateral Load (kN) 100 0 0 -100 -100 -200 -200 -300 -300 Expt. Expt. -400 PfB PfB -400 -500 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 Lateral Displacement (mm) Lateral Displacement (mm) Test #4: 4 (Ricles and Paboojian 1994) Test #8: 8 (Ricles and Paboojian 1994) H = 406 mm; B = 406 mm H = 406 mm; B = 406 mm W8x40 W8x40 F y = 372 MPa F y = 372 MP 4 #9; F yr = 448 MPa 12 #7; F yr = 434 MPa f′ c = 31 MPa f′ c = 63 MPa P/P no = 0.19 P/P no = 0.11 L/H = 4.8 L/H = 4.8

Wide Flange Steel Beam Formulation Local buckling strain   based on plastic hinge L M b h F        p p f   u 1 0.405 0.0033 0.0268 0.184 1   length from regression L M t 2 t F   i max w f y analysis to mitigate localization Parameter Expression e L E   p lb s 1 Strain at Local Buckling e  Residual E L L y h i p stresses E   modeled s Local Buckling Softening Slope K lb 200 directly per fiber Local Buckling Ultimate  F 0.2 F ulb y Residual Stress   p W       1 2.0 0.05 Degradation of Plastic Modulus   p E F   y   p W Degradation of the Size of the       1 2.0 0.05    Elastic Zone F   y

WF Cyclic Local Buckling Calibration Tsai and Popov 1988 500 400 400 300 300 200 200 100 Lateral Load (kN) Lateral Load (kN) 100 0 0 -100 -100 -200 -200 -300 -300 Expt. Expt. -400 PfB PfB -500 -400 -5% -4% -3% -2% -1% 0% 1% 2% 3% 4% 5% -5% -4% -3% -2% -1% 0% 1% 2% 3% 4% 5% Beam Rotation Beam Rotation Test #2: 8 (Tsai & Popov 1988) Test #4: 10R (Tsai & Popov 1988) W21x44 W18x40 F y = 333 Mpa F y = 310 MPa h/t w = 56.3 h/t w = 50.9 b f /2t f = 7.22 b f /2t f = 5.73

Connection Regions in Special Moment Frames Nonlinear Column Zero Length Spring Element Representing the Panel Zone Shear Rigid Links Behavior Nonlinear Elastic Beam Beam Element Element Nonlinear stress-resultant-space multi-surface kinematic hardening model used for rotational spring formulation (after Muhummud 2003)

Connection Regions in Special Concentrically Braced Frames Nonlinear Moment Column Release Element Nonlinear Beam Element Rigid Nonlinear Links Brace Element Modeling assumptions established by Hsiao et al. (2012)

Subassemblage Validation Ricles, Peng, and Lu 2004 800 800 600 600 400 400 200 Lateral Load (kN) Lateral Load (kN) 200 0 0 -200 -200 -400 -400 -600 Expt. Expt. PfB PfB -600 -800 -200 -150 -100 -50 0 50 100 150 200 -200 -150 -100 -50 0 50 100 150 200 Lateral Deflection (mm) Lateral Deflection (mm) Test #2: 6 (Ricles et al. 2004) Test #3: 7 (Ricles et al. 2004) Column: H = 406 mm; B = 406 mm; t = 12.5 mm; F y = 352 MPa; f′ c = 58 MPa; P/P no = 0.18; Beam: W24x62; F y = 230 MPa; h/t w = 50.1; b f /2t f = 5.97 These specimens are strong column, strong panel zone, weak beam

Evaluation of Seismic Performance Factors Archetype frames are categorized into performance groups based on basic structural characteristics Design Design Group Period Number of Number of Gravity Load Seismic Load Number Domain C-SMFs C-SCBFs Level Level PG-1 High D max Short 6 4 PG-2 High D max Long 2 2 PG-3 High D min Short 6 4 PG-4 High D min Long 2 2 PG-5 Low D max Short 6 4 PG-6 Low D max Long 2 2 PG-7 Low D min Short 6 4 PG-8 Low D min Long 2 2

Evaluation of Seismic Performance Factors Gravity Load, Mass, Damping Design Analysis 1.4 D 1.2 D + 1.6 L + 0.5 L r 1.05 D + 0.25 L + 0.25 L r Gravity Load 1.2 D + 0.5 L + 1.6 L r etc., including live load reduction (Section 2.3, ASCE 7-10) (FEMA P695) D + 25% storage live load Mass + 10 psf for partitions Same as for design (Section 12.7.2, ASCE 7-10) Rayleigh damping defined equal to 2.5% of critical in the 1 st and 3 rd mode • • Modeling does not include: – Fracture – Connection degradation – Lateral torsional buckling

Typical Static Pushover Analysis 1000 V max = 879.3 kips 900 800 700 V 80 = 703.4 kips Base Shear (kips) 600 500  u = 50.8 in 400 300 200 V = 153.9 kips 100 0 0 10 20 30 40 50 60 Roof Displacement (in) SFRS: C-SMF, Frame: RCFT-3-1

Typical Dynamic Time History Analyses: Incremental Dynamic Analysis 18 16 14 12 S T = S MT SF 2 (g) 10 8 6 ˆ            S 5.72 g CT 4 2      1.50  S g   MT 0 0% 5% 10% 15% Maximum Story Drift SFRS: C-SMF, Frame: RCFT-3-1

System Overstrength Factor, Ω o • By the FEMA P695 methodology, Ω o should be taken as the largest Average Ω Group average value of Ω from any Number C-SMF C-SCBF performance group PG-1 5.9 2.1 – Rounded to nearest 0.5 – Upper limits of 1.5 R and 3.0 PG-2 5.3 1.9 • High overstrength for C-SMFs PG-3 7.6 2.8 – Displacement controlled design PG-4 9.9 2.7 – Current value ( Ω o = 3.0) is upper limit PG-5 6.2 1.8 and is acceptable PG-6 5.5 1.7 • Overstrength for C-SCBFs near PG-7 7.5 2.3 current value ( Ω o = 2.0) PG-8 6.5 2.2 – Higher for PG-3 and PG-4 (High gravity load, SDC D min )