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UNBONDED POST-TENSIONED HYBRID COUPLED WALLS Yahya C. KURAMA University of Notre Dame Notre Dame, Indiana Qiang SHEN, Michael MAY (graduate students) Cooperative Earthquake Research Program on Composite and Hybrid Structures June 24-25, 2001 Berkeley, California

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UP COUPLED WALL SUBASSEMBLAGE beam PT tendon connection region PT anchor embedded plate angle PT tendon wall region spiral cover plate concrete steel

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DEFORMED SHAPE AND COUPLING FORCES contact region gap opening V coupling = P z lblb P P V coupling dbdb z lblb

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BROAD OBJECTIVES Investigate feasibility and limitations Develop seismic design approach Evaluate seismic response RESEARCH ISSUES Force/deformation capacity of beam-wall connection region Yielding of the PT steel Energy dissipation Self-centering Overall/local stability RESEARCH PHASES Subassemblage behavior: analytical and experimental Multi-story coupled wall behavior: analytical

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ANALYTICAL WALL MODEL (DRAIN-2DX) fiber element kinematic constraint truss element wall beam wall

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MATERIAL PROPERTIES stress strain TENSION compression-only steel fiber TENSION stress strain compression-only concrete fiber TENSION stress strain compression-tension steel fiber TENSION stress strain truss element

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ANGLE MODEL bolt or PT anchor T ay seat angle at tension yielding fiber 1angle modelfiber 2 axial force TENSION def. axial force TENSION deformation axial force TENSION deformation = + Kishi and Chen (1990) T ay

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beam rotation=3.3% FINITE ELEMENT MODEL (ABAQUS)

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BEAM STRESSES (ksi)

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beam side PT anchor side CONCRETE STRESSES (ksi)

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DRAIN-2DX VERSUS ABAQUS 800 5 0 ABAQUS (rigid) ABAQUS (deformable) beam shear (kN) beam rotation (%) 0 5 d = 718 mm 1000 DRAIN-2DX (deformable) ABAQUS (deformable) b d = 577 mm b beam shear (kN) beam rotation (%) contact/beam depth 5 0 1.0 DRAIN-2DX (deformable) ABAQUS (deformable) beam rotation (%) 5 DRAIN-2DX (rigid) ABAQUS (rigid) 0 1000 beam rotation (%) beam shear (kN)

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BEAM-WALL SUBASSEMBLAGE W21x182 L8x8x1-1/8 a p = 0.65 in 2 (420 mm 2 ) l w = 10 ft l b = 10 ft (3.0 m) l w = 10 ft F f pi = 0.6 f pu

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LATERAL LOAD BEHAVIOR 0 6 -6 0 2500 -2500 L8x8x3/4 0 6 -6 0 2500 -2500 L8x8x1-1/8 beam rotation (%) beam moment (kN.m) beam rotation (%) beam moment (kN.m) 0 2500 -2500 0 6 -6 no angle beam rotation (%) beam moment (kN.m) M p M y cover plate yielding tension angle yielding decompression 6 0 3000 PT-yielding beam rotation (%) flange yld.

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PARAMETRIC INVESTIGATION Beam cross-section Wall length Beam length PT steel area Initial PT stress Angle size Cover plate size DESIGN PARAMETERS RESPONSE PARAMETERS Decompression Tension angle yielding Cover plate yielding Beam flange yielding PT tendon yielding 3000 0 6 beam moment (kN.m) beam rotation (%) analytical model bilinear estimation decompression cover plate yielding tension angle yielding PT tendon yielding beam flange yielding estimation points 8 0 3000 beam moment (kN.m) beam rotation (%) decompression cover plate yielding tension angle yielding PT tendon yielding beam flange yielding a p =560mm 2 a p =420mm 2 a p =280mm 2

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PROTOTYPE WALL W21x182 a p = 0.868 in 2 (560 mm 2 ) f pi = 0.65 f pu 10 ft 10 ft 10 ft 107 ft (32.6 m) (3.0m 3.0m 3.0 m) PLAN VIEW 20 ft 20 ft 20 ft 20 ft 20 ft 28 ft 28 ft 28 ft

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COUPLED WALL BEHAVIOR base moment (kip.ft) 02.5 120000 roof drift (%) coupled wall right wall left wall 04 roof drift (%) 120000 base moment (kip.ft) coupled wall two uncoupled walls

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CYCLIC BEHAVIOR -1.5 0 1.5 -1000 0 1000 -1.5 01.5 -1000 0 1000 -1.5 0 1.5 -1000 0 1000 base shear (kips) roof drift (%) -1000 0 1000 -303 base shear (kips) roof drift (%) base shear (kips) roof drift (%) base shear (kips) roof drift (%) 8-story precast wall w/ UP beams 6-story precast wall w/ UP beams 6-story CIP wall w/ UP beams 6-story CIP wall w/ embedded beams

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base shear, V (kips) DESIGN APPROACH 3 0 4500 roof drift, (%) 1st beam angle yielding 1st beam flange yielding wall base concrete crushing 1st beam PT tendon yielding Design EQ Survival EQ K K(R V des V des /R des sur

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MAXIMUM DISPLACEMENT DEMAND (Nassar & Krawinkler, 1991) r = s = 1/4, 1/3, 1/2 = 0.02, 0.10 Moderate and High Seismicity Design-Level and Survival-Level Stiff Soil and Medium Soil Profiles Bilinear-Elastic (BE)Elasto-Plastic (EP)Bilinear-Elastic/ Elasto-Plastic (BP) += F FF (F be, be ) k be ( r F be, be ) s k be [(1+ r )F be, be ] (1+ s )k be k be R=[c 1)+1] 1/c c= + T a b T a +1 T

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14 0 3.5 period, T (sec) 14 0 3.5 Design EQ (SAC): a=3.83, b=0.87Survival EQ (SAC): a=1.08, b=0.89 ductility demand, period, T (sec) ductility demand, DUCTILITY DEMAND SPECTRA 0 14 3.5 period, T (sec) 0 14 3.5 period, T (sec) regression BP, mean ductility demand, EP, mean BP, mean BE, mean Survival EQ (SAC): BP versus EPSurvival EQ (SAC): BP versus BE r = s = 1/3, =0.10, High Seismicity, Stiff Soil, R=1, 2, 4, 6, 8 (thin thick)

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EXPERIMENTAL PROGRAM Objectives Investigate beam M- behavior Verify analy. model Verify design tools and procedures Beam-wall connection subassemblages Ten half-scale tests (angle, beam, post-tensioning properties) W10x68 PT strand L4x8x3/4 a p = 0.217 in 2 (140 mm 2 ) l w = 5 ft l b = 5 ft (1.5 m) l w = 5 ft strong floor f pi = 0.65 f pu Elevation View (half-scale) load block

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EXPERIMENTAL SET-UP beam wall load block actuators

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SUMMARY AND CONCLUSIONS Beam Behavior Analytical models seem to work well Gap opening governs behavior Large self-centering, limited energy dissipation Large deformations with little damage Bilinear estimation for beam behavior Experimental verification Wall Behavior Level of coupling up to 60-65 percent Two-level performance based design approach ~25% larger displacements compared to embedded systems

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ONGOING WORK Subassemblage tests Design/analysis of multi-story walls Dynamic analyses of multi-story walls ACKNOWLEDGMENTS National Science Foundation (Dr. S. C. Liu) University of Notre Dame CSR American Precast, Inc. Dywidag Systems International, U.S.A, Inc. Insteel Wire Products Ambassador Steel Ivy Steel & Wire Dayton/Richmond Concrete Accessories

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University of Notre Dame Notre Dame, IN

University of Notre Dame Notre Dame, IN

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