Nonlinear Finite Element Modeling & Simulation

Transcription

1 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

2 Specimen Overview 2

3 Beam-Column-Slab Nonlinear Response Mechanism Generic floor of specimen Slab-Column Action Beam-Column Action 3

4 Beam-Column-Slab Nonlinear Response Mechanism First tensile cracks in beam occur at ~0.095% lateral drift First tensile crack 4

5 Beam-Column-Slab Nonlinear Response Mechanism First tensile cracks in slab occur at ~0.285% lateral drift First tensile crack 5

6 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

7 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

8 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

9 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

10 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

11 Concrete Material 11

12 Reinforcement Modeling 12

13 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

14 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

15 A Benchmark Example 2.0m Uniformly Loaded Concrete Slab 2.0m 15cm Structural Details 5cm 15

16 A Benchmark Example Slab Mesh and Boundary Conditions 16

17 A Benchmark Example Crack Pattern Bottom Face of Slab 17

18 A Benchmark Example Ref.: Reinforced Concrete Slabs, R. Park, W.L. Gamble Crack Pattern Bottom Face of Slab 18

19 A Benchmark Example Crack Pattern Top Face of Slab 19

20 A Benchmark Example Ref.: Reinforced Concrete Slabs, R. Park, W.L. Gamble Crack Pattern Top Face of Slab 20

21 A Benchmark Example Based on yield line theory Load Deflection Pushdown Curve 21

22 Thank you for your attention

23 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

24 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

25 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 = psi Steel02 TYP. #5 5" o.c #9 LONG. BARS Moment (kip-in) Normalized Curvature: φ*h/2 (rad) M-θ Curve under Different Axial Load Ratios

26 Column Section Analysis in OpenSees Z axis y axis z 18 TYP. #5 5" o.c. Y Axial Force (kip) #9 LONG. BARS Moment (kip-in) Column Section P-M Interaction Diagram P-M Interaction Diagram

27 Plan View for Model with Rigid Diaphragm Beam-Column Fiber Element Rigid Diaphragm Constraints Beam-Column Fiber Element

28 Plan View for OpenSees Model w/o Rigid Diaphragm Beam-Column Fiber Element Fictitious Truss Element EA = Beam-Column Fiber Element

29 Hybrid Beam w/ diaphragm w/o diaphragm Moment (kip-in) Normalized Curvature: φ*h/2 (rad) M-θ Response under Denali MCE motion

30 Hybrid Beam 16 x w/ diaphragm w/o diaphragm 12 Axial Strain (in/in) Curvature (rad/in) x 10-3 Curvature and Axial Strain Interaction under Denali MCE motion

31 DDC Beam w/ diaphragm w/o diaphragm 2000 Moment (kip-in) Normalized Curvature: φ*h/2 (rad) M-θ Response under Denali MCE motion

32 DDC Beam w/ diaphragm w/o diaphragm 0.02 Axial Strain (in/in) Curvature (rad/in) x 10-3 Curvature and Axial Strain Interaction under Denali MCE motion

33 Conventional Beam w/ diaphragm w/o diaphragm 2000 Moment (kip-in) Normalized Curvature: φ*h/2 (rad) M-θ Response under Denali MCE motion

34 Conventional Beam w/ diaphragm w/o diaphragm Axial Strain (in/in) Curvature (rad/in) x 10-3 Curvature and Axial Strain Interaction under Denali MCE motion

35 Base Column (Corner) w/ diaphragm w/o diaphragm Moment (kip-in) Normalized Curvature: φ*h/2 (rad) M-θ Response under Denali MCE motion

36 Base Column (Corner) w/ diaphragm w/o diaphragm 0.02 Axial Strain (in/in) Curvature (rad/in) x 10-3 Curvature and Axial Strain Interaction under Denali MCE motion

37 Base Column (Side) x 104 w/ diaphragm w/o diaphragm Moment (kip-in) Normalized Curvature: φ*h/2 (rad) M-θ Response under Denali MCE motion

38 Base Column (Side) 14 x w/ diaphragm w/o diaphragm 10 Axial Strain (in/in) Curvature (rad/in) x 10-3 Curvature and Axial Strain Interaction under Denali MCE motion

39 Peak Floor Acceleration Denali MCE

40 Peak Inter Drift Ratio Denali MCE