Modeling of Bridge Piers with Shear-Flexural InteractionAssessment of Bridges
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Proposed Axial-Shear-Flexure Interaction (ASFI) Scheme
Primary Curves and Hysteretic Models Considering Combined Actions
Generation of Primary Curve Family
Stress Level Index & Two-stage Loading Approach
Model Verification
Limitations and Known Issues
Arrival Time of Vertical Ground Motion
Vertical-to-Horizontal PGA Ratio
Introduction
Motivation
Bridge columns are subjected to combined actions of axial, shear and flexure forces due to structural and geometrical constraints (skewed, curved etc.) and the multi-directional earthquake input motions.
Axial load variation can directly impact the ultimate capacity, stiffness and hysteretic behavior of shear and flexure responses.
Accurate seismic demand assessment of bridges needs to realistically account for combined actions.
Objectives
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(Ozcebe and Saatcioglu 1989)
Shear displacement can be significant -- even if a RC member is not governed by shear failure (as is the case in most of RC columns).
Inelastic shear behavior -- RC members with higher shear strength than flexural strength do not guarantee an elastic behavior in shear deformation.
Coupling of Axial-Shear-Flexural Responses
(ElMandooh and Ghobarah 2003)
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MCFT
Derivation of Flexural and Shear Primary Curves
Discretize RC member into small pieces. For each piece of RC element, estimate M-φ and τ-γ relationship by Modified Compression Field Theory (MCFT, Vecchio and Collins 1986).
M
Δs
V
Δm
M
θ
M
S-UEL
F-UEL
δ=Σ { φi*dy*yi + γi*dy }
Flexural deformation Shear deformation
Sections with different M/V ratio (level of shear-flexural interaction) demonstrate different mechanical properties and behaviors
Section with higher M/V ratio:
Larger moment capacity
Smaller shear capacity
V
N
dy
yi
M
Unloading & reloading stiffness depend on:
Primary curve (Kelastic, Crack, & Yield)
Cracked? Yielded?
Axial load ratio
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Proposed Axial-Shear-Flexure Interaction (ASFI) Scheme
Primary Curves and Hysteretic Models Considering Combined Actions
Generation of Primary Curve Family
Stress Level Index & Two-stage Loading Approach
Model Verification
Limitations and Known Issues
Arrival Time of Vertical Ground Motion
Vertical-to-Horizontal PGA Ratio
Ultimate capacity and stiffness increase with compressive axial load level.
Yielding displacement is almost fixed, regardless of applied axial load.
Cracking point is getting smaller as axial force decreasing, implying the column being relatively easy to be cracked.
Kunnath et al.
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(ii) crackyield: interpolation
(iii) yieldultimate: interpolation
(iv) ultimatefailure: constant residual strength ratio
Objective: Generating the primary curves related to various axial load levels from a given primary curve subject to an initial axial load
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a
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n% critical points, predicted from equations
loading
deflection
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Assumption:
Effective stress level of a loaded column at fixed ductility is independent of axial load.
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Equivalent
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Proposed Axial-Shear-Flexure Interaction (ASFI) Scheme
Primary Curves and Hysteretic Models Considering Combined Actions
Generation of Primary Curve Family
Stress Level Index & Two-stage Loading Approach
Model Verification
Limitations and Known Issues
Arrival Time of Vertical Ground Motion
Vertical-to-Horizontal PGA Ratio
TP-033
TP-034
Height
Diameter
TP-032
TP-031
TP-031
TP-032
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TP-033
TP-034
TP-031
TP-032
TP-033
TP-034
Dynamic Validation with Fiber Section Model
Proposed ASFI model in general produces larger displacement demand than the fiber section model.
Vibration frequencies of the two models agree with each other indicating reasonable prediction on the tangent stiffness of the proposed ASFI model.
Considering only the SFI can yield good prediction on the displacement demand.
ABAQUS ASFI Model
OpenSees Fiber Model
Limitations and Known Issues
Estimation on post-peak stiffness of primary curve family may not be adequate.
May converge at an incorrect solution for systems with yielding platform.
May converge at an inconsistent deformed configuration for softening systems.
Use of full stiffness matrix can somehow improve the above-mentioned convergence issues, however, it is an asymmetric matrix which offsets most of the advantages.
V
Δs
M
θ
Proposed Axial-Shear-Flexure Interaction (ASFI) Scheme
Primary Curves and Hysteretic Models Considering Combined Actions
Generation of Primary Curve Family
Stress Level Index & Two-stage Loading Approach
Model Verification
Limitations and Known Issues
Arrival Time of Vertical Ground Motion
Vertical-to-Horizontal PGA Ratio
(a) H: WN22; V: WN22 (b) H: WN22; V: NO4
(a) Horizontal: WN22 (Tp=0.488s);
Vertical: WN22 (Tp=0.138s)
Vertical: NO4 (Tp=0.322s)
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(a) H: WN22; V: WN22 (b) H: WN22; V: NO4
(a) Horizontal: WN22 (Tp=0.488s);
Vertical: WN22 (Tp=0.138s)
Vertical: NO4 (Tp=0.322s)
tVpeak – tHpeak = -0.1s
Larger PGAV/PGAH ratio tends to have larger influence on force demand.
No significant correlation exists with drift demand.
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Axial load considerably affects the lateral responses of RC columns.
Primary curves of the same column under different axial loads can be predicted very well by applying the normalized primary curve and parameterized critical points.
Mapping between loading branches corresponding to different axial load levels is made possible by breaking the step into two stages: constant deformation stage and constant loading stage.
Model verification shows that the proposed method is able to capture the effects of axial load variation on the lateral responses of RC columns.
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The research presented here was funded by National Science Foundation through the Network for Earthquake Engineering Simulation Research Program, grant CMMI-0530737, Joy Pauschke, program manager.
Thank You!
Plastic Hinge Models
Using equivalent springs to simulate shear and flexural responses of columns at the element level
Empirical and approximate
Difficult to couple together the axial, shear, and flexural responses
Numerical instability in the adopted hysteretic models may induce convergence problem
Fiber Section Formulation
Coupling the axial-flexural interaction
Rotation of principal axes in concrete (as large as 30°) due to the existence of shear stress is not considered
Elastic or rigid beam
Deficiencies of Current Models
Non-linearity in shear deformation is not accounted for.
Material damage (strength deterioration and pinching) due to cyclic loading is not considered.
Axial-Shear-Flexural interaction is not captured.
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Similar trends are observed except post-yield response.
Fiber Section Model overestimates initial stiffness.
Fiber Section Model underestimates axial load effects.
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Column of Bridge#4 (H/D=2.5, P/P
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Test TP-021
nonLinear M-
predicted by equations
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