Reinforced Concrete Beam- Column Joint: Macroscopic Super-element models

Transcription

1 Reinforced Concrete Beam- Column Joint: Macroscopic Super-element models -Nilanjan Mitra (work performed as a PhD student while at University of Washington between 1-6)

2 Need for the study Experimental UW I-8 Freeway, San Francisco, CA following Loma Prieta Earthquake in 1989 Reinforced concrete beam column joints subjected to earthquake loading Courtesy: NISEE, Univ. of California, Berkeley.

3 Loading in a joint region compression resultant (concrete and steel) shear resultant (concrete) tension resultant (steel) Earthquake Loading of Beam-Column Joint

4 Internal load distribution in a joint anchorage bond stress acting on joint core concrete compression force carried by joint core concrete

5 Macroscopic beam-column joint element models

6 Macroscopic beam-column joint element models

7 Macroscopic beam-column joint element models

8 Proposed Beam-column super-element model external node internal node zero-length bar-slip spring zero-length interface-shear spring shear panel 4-noded 1-dof element 8 bar-slip springs to simulate anchorage failure 4 interface-shear springs to simulate shear transfer failure at joint interface 1 shear-panel to simulate inelastic action of shear within joint core beam element rigid external interface plane zero-width region shown with finite width to facilitate discussion column element Note: The location of the bar-slip springs is at the centroid of the tension-compression couple at nominal strength of the beams. [Mitra & Lowes; J. Structural Eng. ASCE, 7: 133 (1): 15- ]

9 Joint element formulation: Kinematics External, Internal and Component deformation

10 Joint element formulation: Equilibrium External, Internal and Component forces Solution of element state achieved by an iterative procedure and requires solving for zero reaction in the 4 internal degrees of freedom

11 Hysteretic one dimensional material model load (d max,f(d max )) (epd,epf ) (epd 3,ePf 3 ) (epd 1,ePf 1 ) (*,uforcep.epf 3 ) (rdispp.d max,rforcep.f(d max )) (epd 4,ePf 4 ) deformation (*,uforcen.enf 3 ) (end 4,eNf 4 ) (rdispn.d min,rforcen.f(d min )) (end 1,eNf 1 ) (end,enf ) (end 3,eNf 3 ) (d min,f(d min )) Characterized by Response envelope Unload reload path Damage rules

12 Damage simulation in material model without damage with unloading stiffness damage without damage with reloading stiffness damage load load deformation ( i ) k = k δ i 1 k deformation ( dmax ) = ( dmax ) ( + δi ) i 1 d 8 6 ( fmax ) = ( fmax ) ( δi ) without damage with strength damage i 1 f i ( α ( ) ( ) ) 3 α4 1 d max δ = α + α χ load 4 d max dmax i dmin i = max., defmax defmin χ = χ = f f ( Accumulated Energy) ( No. of load cycles) deformation

13 8 6 4 without damage with all 3 damage rules Damage simulation in material model No. of load cycle criterion: rain-flow-counting algorithm load χ = du 4u max deformation Energy criterion E i χ = = E monotonic ge load history de monotonic load history de load with all 3 damages (Energy) with all 3 damages (Cyclic) deformation

14 Shear-panel calibration column shear panel Shear panel envelope calibration MCFT Diagonal compression strut Compression envelope reduction Determination of hysteretic model parameters Specimen SE8 (Stevens et al. 1987) Observed Shear stress (MPa) Typical response envelope Simulated Shear strain

15 Shear panel envelope calibration using proposed Diagonal compression strut mechanism Mander et al. (1988) concrete Column longitudinal and joint hoop steel confine the strut. Reduction in concrete to account for perpendicular tensile stress to the strut cyclic loading. Strut force is converted to panel shear stress as τ strut = f w cosα c _ strut strut strut w jnt

16 Proposed concrete compression envelope reduction 1.8 f c_obs / f c_mander.6.4. Data with ρ j > Data with ρ j = Vecchio 1986 Stevens 1991 Hsu 1995 Noguchi 199 Proposed eq. for ρ j > Proposed eq. for ρ j = Eq. for ρ j > f f ε t / ε cc c _ strut t t t ε ε ε = <.39 ε ε ε εt = ε c _ Mander cc cc cc cc Eq. for f f ρ j = c _ strut t t t ε ε ε = <.83 ε ε ε εt = ε c _ Mander cc cc cc cc

17 Comparison of MCFT and Diagonal Compression Strut model in shear-panel envelope calibration.5 τ mcft_cyclic / τ max JF BYJF BY φ τ diagonal_strut / τ max Transverse steel contribution to shear stress JF BYJF BY φ [Lowes, Altoontash and Mitra, J. Structural Eng. ASCE, 5: 131 (6) ]

18 Bar slip material model calibration column Bar-slip spring Mechanistic model :- envelope Hysteretic model calibration Strength deterioration model 1 bar-spring force (kn) slip (mm) Typical response envelope

19 Bar slip mechanistic model Assumptions for anchorage response of bond within the joint region: Bond stress uniform for elastic reinforcement, piecewise uniform for reinforcement loaded beyond yield Slip is the relative movement of reinforcement bar with respect to the joint perimeter Slip is a function of strain distribution in the joint Bar exhibits zero slip at zero bar stress l fs l d x dx f f τe πdb τ E fs slip = = s < y A b E Edb l l + l E d f b y Y db e e y τ π τ π dslip = x dx + + ( x le ) dx A b E E A l b Eh e τe l fl e y y τ l Y y = + + fs Ed E Ed b b f y Mechanistic model

20 Strength deterioration calibration for bar-slip spring maximum slip / slip with anchorage length equal to joint width BYJF BY specimen number Simulated maximum bar-slip BYJF BY specimen number Strength deterioration Is activated once slip exceeds the slip level corresponding to ultimate stress in the reinforcing bars. Is observed upon reloading, with the result that bar-slip springs always exhibit positive tangent stiffness. δ = α d d δ d d ( ) f f i max, i ult lim max, i ult

21 Steps for calibrating the joint model Calculate moment curvature of beams and columns From moment curvature analysis determine moment associated with first yield of the reinforcing bar tension-compression couple distance at nominal yield strength neutral axis depth at nominal yield strength Define joint elements parameters using joint geometry and tension-compression couple distance Determine concrete compression strut response Mander model for concrete Concrete strength reduction eq. proposed to account for perpendicular cracks and cyclic loading Hysteretic parameters defined for shear panel Determine bar-slip response Mechanistic model for bond Hysteretic parameters defined for bar-slip model Interface slip-springs are defined to be stiff and elastic

22 Model simulation Lab test Beam-Column Elements: Force based lumped plasticity element Elastic region Plastic Hinge region lateral load applied under displacement control column axial load applied under load control Fiber discretisation joint element plastic hinge length beam-column element OpenSees Model Concrete Stress-Strain (Compressive only, no tensile strength) Reinforcing Steel Stress-Strain

23 Specimen OSJ1: 3 Validation study Column shear (kn) Drift (%)

24 Validation study discussion & conclusion Failure mechanism For joints exhibiting JF (joint failure prior to beam yielding), 8% accurate. For joints exhibiting BYJF (beam yielding followed by joint failure), 89% accurate. For joints exhibiting BY (beam yielding), 94% accurate. Initial and unloading stiffness For all joints, mean of simulated to observed ranges from 1.3 to 1.6 with an average C.O.V. =.15. Post-yield tangent stiffness For joints that exhibit BYJF, mean ratio of simulated to observed is 1. with a C.O.V. =.. Maximum strength For all joints, mean of simulated to observed is 1.3 with a C.O.V. =.17. Drift at maximum strength For all joints, mean of simulated to observed is 1.1 with a C.O.V. =.7. Strength at final drift level For all joints, strength for final drift cycle is 1.4 with a C.O.V =.. Pinching ratio (ratio of strength at zero drift to maximum strength) For all joints, pinching ratio is 1.4 with a C.O.V =.1.