Full-Scale Structural and Nonstructural Building System Performance during Earthquakes & Post-Earthquake Fire A Joint Venture between Academe, Industry and Government Nonlinear Finite Element Modeling & Simulation Xiang Wang, Hamed Ebrahimian, Jose I. Restrepo, Joel P. Conte
Specimen Overview 2
Beam-Column-Slab Nonlinear Response Mechanism Generic floor of specimen Slab-Column Action Beam-Column Action 3
Beam-Column-Slab Nonlinear Response Mechanism First tensile cracks in beam occur at ~0.095% lateral drift First tensile crack 4
Beam-Column-Slab Nonlinear Response Mechanism First tensile cracks in slab occur at ~0.285% lateral drift First tensile crack 5
Beam-Column-Slab Nonlinear Response Mechanism Negative yield line in slab Plastic hinge in beam Ultimate design lateral drift ~3% Elongation of beam is resisted but not prevented by slab action 6
Beam-Column-Slab Nonlinear Response Mechanism Flexural yield lines??? Slab will effectively contribute to lateral nonlinear response behavior of frame.??? Slab can neither be modeled as Rigid Diaphragm nor as Linear Elastic Plate/Shell. 7
DIANA DIANA is a well proven and tested general FE software package with a reputation for handling difficult technical problems related to modeling and assessment activities in concrete, steel, soil, rock and soil-structure interaction. Developed since 1972 by Delft University of Technology in the Netherlands. Extensive material, element and procedure libraries. Linear and nonlinear (material, geometry, contact) capabilities. Full 2D and 3D modeling features. 8
Why DIANA? Need to simulate slabs as nonlinear RC plate/shell OpenSees and Perform 3D do not have a nonlinear RC shell element DIANA provides nonlinear RC shell elements with embedded reinforcements 9
DIANA General Overview Analysis Types Solution Procedures Material Models Elements Powerful GUI Linear Static Analysis Direct and iterative solvers Elasticity Truss and Beam Elements Nonlinear Static Analysis Automatic load and time stepping Smeared Crack Models Plane Stress/Strain Elements Plate Bending Elements Dynamic Analysis (Linear and Nonlinear) Incrementaliterative methods Plasticity Flat/Curved Shell Elements Phased Analysis Continuation methods and line search technique Interface nonlinear models Solid Elements Interface Elements Parameter Estimation Automatic substructuring Others Embedded Reinforcement Flow Elements Others Others 10
Concrete Material 11
Reinforcement Modeling 12
Approach in Getting Up to Speed with the Use of DIANA Linear Elastic Models of RC Plates and Shells Model benchmark problems Compare with other FE software Nonlinear RC Slab Models Compare with closed-form solutions based on yield line theory (limit analysis) Nonlinear RC Frame Models Model benchmark problems Compare with other FE software (OpenSees) Nonlinear Frame-Slab Models Model benchmark problems Nonlinear Frame-Wall- Slab Models Model benchmark problems Modeling and Simulation of Test Specimen 13
A Benchmark Example Nonlinear RC slab analysis problem Closed-form solution (for strength) is available based on yield line theory (Ref.: Reinforced Concrete Slabs, R. Park, W.L. Gamble) 2.0x2.0x0.2m RC square slab All edges simply-supported Uniformly loaded, loading increased incrementally Uniformly reinforced at bottom, both directions, r=0.524% 8 node, quadratic curved shell element E c = 26.2GPa, f c = 30MPa, f t = 2.93MPa Total strain rotating crack, brittle in tension and ideal in compression behavior for concrete E s = 210GPa, f y = 400MPa Von Mises with ideal plasticity for Steel Forced-based push-down analysis Modified Newton iteration method Energy based convergence criteria 14
A Benchmark Example 2.0m Uniformly Loaded Concrete Slab 2.0m 10@10cm 15cm Structural Details 5cm 15
A Benchmark Example Slab Mesh and Boundary Conditions 16
A Benchmark Example Crack Pattern Bottom Face of Slab 17
A Benchmark Example Ref.: Reinforced Concrete Slabs, R. Park, W.L. Gamble Crack Pattern Bottom Face of Slab 18
A Benchmark Example Crack Pattern Top Face of Slab 19
A Benchmark Example Ref.: Reinforced Concrete Slabs, R. Park, W.L. Gamble Crack Pattern Top Face of Slab 20
A Benchmark Example Based on yield line theory Load Deflection Pushdown Curve 21
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Element Background The curved shell elements, based on isoparametric degenerated solid approach by introducing two shell hypotheses: Straight-normals : normals remain straight, but not necessarily normal to the reference surface. Transverse shear deformation is included according to the Mindlin Reissner theory. Zero-normal-stress: the normal stress component in the normal direction of a lamina basis is forced to zero. Quadratic 8-noded curved shell element. 3-point integration in thickness direction according to the Simpson rule. 23
Embedded Reinforcement (Standard) No degrees of freedom of their own. The strains in the reinforcements are computed from the displacement field of the mother elements (perfect bond). The total area of the grid is divided in several particles. Each particle contributes to the stiffness of the element. Mother Element Reinforcement Grid 24
Column Section Analysis in OpenSees Concrete strength (cover) Concrete strength (core) Rebar yield strength f c = 5000 psi Concrete02 1.3f c = 6500 psi Concrete02 f y = 60000 psi Steel02 TYP. #5 TIES @ 5" o.c. 12000 10000 18 26 10 #9 LONG. BARS Moment (kip-in) 8000 6000 4000 2000 0.0 0.1 0.2 0.3 0.4 0 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 Normalized Curvature: φ*h/2 (rad) M-θ Curve under Different Axial Load Ratios
Column Section Analysis in OpenSees Z 3000 2500 axis y axis z 18 TYP. #5 TIES @ 5" o.c. Y Axial Force (kip) 2000 1500 1000 500 26 10 #9 LONG. BARS 0 0 2000 4000 6000 8000 10000 12000 Moment (kip-in) Column Section P-M Interaction Diagram P-M Interaction Diagram
Plan View for Model with Rigid Diaphragm Beam-Column Fiber Element Rigid Diaphragm Constraints Beam-Column Fiber Element
Plan View for OpenSees Model w/o Rigid Diaphragm Beam-Column Fiber Element Fictitious Truss Element EA = Beam-Column Fiber Element
Hybrid Beam 5000 4000 w/ diaphragm w/o diaphragm 3000 2000 Moment (kip-in) 1000 0-1000 -2000-3000 -4000-5000 -0.05-0.04-0.03-0.02-0.01 0 0.01 0.02 0.03 0.04 0.05 Normalized Curvature: φ*h/2 (rad) M-θ Response under Denali MCE motion
Hybrid Beam 16 x 10-3 14 w/ diaphragm w/o diaphragm 12 Axial Strain (in/in) 10 8 6 4 2 0-2 -3-2 -1 0 1 2 3 4 Curvature (rad/in) x 10-3 Curvature and Axial Strain Interaction under Denali MCE motion
DDC Beam 6000 4000 w/ diaphragm w/o diaphragm 2000 Moment (kip-in) 0-2000 -4000-6000 -0.05-0.04-0.03-0.02-0.01 0 0.01 0.02 0.03 0.04 0.05 Normalized Curvature: φ*h/2 (rad) M-θ Response under Denali MCE motion
DDC Beam 0.03 0.025 w/ diaphragm w/o diaphragm 0.02 Axial Strain (in/in) 0.015 0.01 0.005 0-0.005-3 -2-1 0 1 2 3 4 Curvature (rad/in) x 10-3 Curvature and Axial Strain Interaction under Denali MCE motion
Conventional Beam 6000 4000 w/ diaphragm w/o diaphragm 2000 Moment (kip-in) 0-2000 -4000-6000 -0.05-0.04-0.03-0.02-0.01 0 0.01 0.02 0.03 0.04 0.05 Normalized Curvature: φ*h/2 (rad) M-θ Response under Denali MCE motion
Conventional Beam 0.035 0.03 w/ diaphragm w/o diaphragm 0.025 Axial Strain (in/in) 0.02 0.015 0.01 0.005 0-0.005-3 -2-1 0 1 2 3 4 Curvature (rad/in) x 10-3 Curvature and Axial Strain Interaction under Denali MCE motion
Base Column (Corner) 10000 8000 w/ diaphragm w/o diaphragm 6000 4000 Moment (kip-in) 2000 0-2000 -4000-6000 -8000-0.05-0.04-0.03-0.02-0.01 0 0.01 0.02 0.03 0.04 0.05 Normalized Curvature: φ*h/2 (rad) M-θ Response under Denali MCE motion
Base Column (Corner) 0.03 0.025 w/ diaphragm w/o diaphragm 0.02 Axial Strain (in/in) 0.015 0.01 0.005 0-0.005-3 -2.5-2 -1.5-1 -0.5 0 0.5 1 1.5 Curvature (rad/in) x 10-3 Curvature and Axial Strain Interaction under Denali MCE motion
Base Column (Side) 0.8 1 x 104 w/ diaphragm w/o diaphragm 0.6 0.4 Moment (kip-in) 0.2 0-0.2-0.4-0.6-0.8-1 -0.05-0.04-0.03-0.02-0.01 0 0.01 0.02 0.03 0.04 0.05 Normalized Curvature: φ*h/2 (rad) M-θ Response under Denali MCE motion
Base Column (Side) 14 x 10-3 12 w/ diaphragm w/o diaphragm 10 Axial Strain (in/in) 8 6 4 2 0-2 -3.5-3 -2.5-2 -1.5-1 -0.5 0 0.5 1 1.5 Curvature (rad/in) x 10-3 Curvature and Axial Strain Interaction under Denali MCE motion
Peak Floor Acceleration Denali MCE
Peak Inter Drift Ratio Denali MCE