UNIVERSITY OF PADUA ITALY Dept. Civil Environmental Arch. Eng. UNIVERSITY OF CALIFORNIA BERKELEY Dept. Civil and Environmental Eng.

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1 UNIVERSITY OF PADUA ITALY Dept. Civil Environmental Arch. Eng. UNIVERSITY OF CALIFORNIA BERKELEY Dept. Civil and Environmental Eng. Cyclic Inelastic Analysis of RC Shear Walls and Plates Leopoldo Tesser and Filip C. Filippou OpenSees Days 2012, August Framework Performance based design methodology Seimic Hazard Analysis Response Analysis Damage Analysis Loss Analysis Introduction Models Implementation Analyses Conclusions 1/36 1

2 Framework Performance based design methodology Seimic Hazard Analysis Response Analysis Damage Analysis Loss Analysis Introduction Models Implementation Analyses Conclusions 1/36 Background Introduction Models Implementation Analyses Conclusions 2/36 2

3 Experimental Investigations Maier and Thϋrlimann 1985 Stevens et al Mansour and Hsu 2005 JNES 2006 Introduction Models Implementation Analyses Conclusions 3/36 Recent Tests by NEES Univ. of Michigan Univ. of Illinois Univ. of Minnesota Univ. of CA Berkeley Introduction Models Implementation Analyses Conclusions 4/36 3

4 Existing Models They can be subdivided in two categories: Plane stress models for all types of RC elements Fiber beam models for particular RC members Some incorporated in commercial software Plane stress FE models seem to have issues of accuracy for general RC stress states, computational efficiency for large scale, or robustness Fiber beam models with shear appear to be limited to cases of moderate shear demand Introduction Models Implementation Analyses Conclusions 5/36 Objectives of the Current Work The current work aims at developing an efficient membrane and plate model for the simulation of RC structural elements under cyclic loads with the following features: general and suitable for several types of RC elements under high shear with normal force and bending moment accurate and computationally efficient to be suitable for the earthquake analysis of large structures plastic and damage evolution laws describe plastic strain and stiffness degradation at the material level The membrane and plate model is implemented in a general purpose platform so that it can be combined with other finite elements, such as beam or column elements, for modeling an entire structure Introduction Models Implementation Analyses Conclusions 6/36 4

5 Experimental Evidences in Uniaxial Conditions Tension Compression Introduction Models Implementation Analyses Conclusions 7/36 Envelope 1 Introduction Models Implementation Analyses Conclusions 8/36 5

6 Envelope Damage σ = (1 d) Eε Residual Strength 1.7 Introduction Models Implementation Analyses Conclusions 9/36 Cyclic Loading σ = ( 1 d) E( ε ε p ) Residual Strain Introduction Models Implementation Analyses Conclusions 10/36 6

7 Features of the Presented Model The features of the presented concrete constitutive law are: it is a general three dimensional law that can be used with all types of finite elements both tensile and compressive damage modes are taken into account by means of two scalar damage parameters a simplified plasticity evolution law represents the residual strains for all stress states it uses a straight forward algorithm for material state determination The material parameters are calibrated once from experimental data and used consistently in applications (no parameter tuning ) The 3d concrete law is constrained to a plane stress state for the RC membrane element The out of plane stress of the 3D concrete law is condensed out for use with the RC plate element Introduction Models Implementation Analyses Conclusions 10/36 Plastic Damage Concrete Model Separate scalar damage parameters for tension and compression; these arre coupled under multi axial stress states Tension Gopalaratnam and Shah 1985 Compression Sinha et al Introduction Models Implementation Analyses Conclusions 11/36 7

8 Crack Width Crack width [μin] Crack width [μin] The correlation between average concrete tensile strains, tensile damage parameter and crack width can be derived from experimental measurements The correlation holds only for micro cracks; this may be suitable for structural durability studies For the estimation of large crack widths under seismic excitations the reinforcing steel strains should be used Introduction Models Implementation Analyses Conclusions 12/36 Multi Axial Conditions The concrete constitutive law is developed in three dimensions and can be used with all types of finite elements For the analysis of RC shear walls the most significant biaxial stress state is tension compression Non dimensional stress σ/fc Kupfer et al / / / Non dimensional strain ε/ε c0 1/0 Numerical Experimental ratio of minimum to maximum principal stress Introduction Models Implementation Analyses Conclusions 13/36 8

9 RC Membrane Model The 3d concrete law is constrained to a plane stress state Concrete Uniaxial Steel layer Introduction Models Implementation Analyses Conclusions 14/36 RC Membrane Model The 3d concrete law is constrained to a plane stress state Uniaxial steel constitutive relations Reinforced Concrete Filippou et al. (1983) Introduction Models Implementation Analyses Conclusions 15/36 9

10 RC Plate Model The out of plane stress of the 3d concrete law is condensed numerical integration over the thickness: e.g. 7 mid points Insertion of reinforcing layer at actual locations e.g. 2 reinforcement nets Introduction Models Implementation Analyses Conclusions 16/36 Correlation with experiments The material parameters are calibrated once from experimental data on the concrete material and used consistently in the correlation studies (no parameter tuning ) Introduction Models Implementation Analyses Conclusions 17/36 10

11 RC Panels Mansour and Hsu (2005) α = 45 Test CA2: α = Shear Stress [MPa] Experimental Numerical Shear Strain [-] Introduction Models Implementation Analyses Conclusions 18/36 RC Panels vertical vs. horizontal strain and vertical normal stress vs. strain Vertical Strain [-] Experimental Numerical Horizontal Strain [-] Vertical Normal Stress [MPa] Experimental Numerical Vertical Strain [-] Introduction Models Implementation Analyses Conclusions 19/36 11

12 Mansour and Hsu (2005) RC Panels α = 90 Test CE3: α = 90 Introduction Models Implementation Analyses Conclusions 20/36 RC Panels vertical vs. horizontal strain and vertical normal stress vs. strain Introduction Models Implementation Analyses Conclusions 21/36 12

13 RC Beams w/o Shear Reinforcement Leonhardt and Walter 1962 Introduction Models Implementation Analyses Conclusions 22/36 Shear Failure d + d Introduction Models Implementation Analyses Conclusions 23/36 13

14 Flexural Failure T10 d + d Introduction Models Implementation Analyses Conclusions 24/36 RC Planar Shear Walls RC Panel with boundary elements (Maier and Thϋrlimann 1985) d Height: 1200 mm 47 in Aspect ratio: 1 Thickness: 100 mm 4 in Vertical reinforcement ratio: 1.16% Horizontal reinforcement ratio: 1.03% Axial load: 416 kn 94 kips Introduction Models Implementation Analyses Conclusions 25/36 14

15 RC Plates RC Plates under combined in plane and lateral loads (Ghoneim and MacGregor 1994) Compressed layer d Size: 72 in 1829 mm Thickness: 2.65 in 67.4 mm Isotropic reinforcement ratio: 0.77% in two grids In plane biaxial compression: 1400 psi 9.8 MPa Transverse load carrying capacity: 1440 psf 69 kpa Tensed layer d + Introduction Models Implementation Analyses Conclusions 26/36 RC U shaped Shear Wall (1) U shaped shear wall (Pégon et al., JRC Ispra, 2000) Height: 3.6 m 11 ft 10 in Axial load: 2MN 450 kips Dimension in mm Introduction Models Implementation Analyses Conclusions 27/36 15

16 RC U shaped Shear Wall (2) d kn 1 kips Introduction Models Implementation Analyses Conclusions 28/36 RC Box Shear Wall (1) Box shaped shear wall (Japan Nuclear Energy Safety Organization 2006) Height: 1.0 m 3 ft 3 in Axial load: 670 kn 150 kips Dimension in mm Introduction Models Implementation Analyses Conclusions 29/36 16

17 RC Box Shear Wall (2) d kn 1 kips Introduction Models Implementation Analyses Conclusions 30/36 RC Box Shear Wall (2) d + d Introduction Models Implementation Analyses Conclusions 30/36 17

18 Conclusions (1) Excellent agreement with correlation studies was observed for different specimens concrete cylinders and prisms under cyclic loads (uniaxial stress states) concrete prisms under combined tension and compression RC panels under cyclic shear loads (uniform stress state) beams without shear reinforcement (complex stress states) planar, U and box shaped RC shear walls under axial force and cyclic lateral loads (complex stress states) The tensile and compressive damage parameters of the concrete constitutive law permit the interpretation of observed experimental behavior in regard to accumulated structural damage failure mechanisms tensile cracks location and orientation micro cracks width concrete compression strut location and orientation Introduction Models Implementation Analyses Conclusions 31/36 Conclusions (2) Neglecting the dowel action and bond slip of reinforcing bars does not seem to affect the agreement of the model with the experimental data regarding strength. However, some discrepancy in unloading and reloading is evident the dowel action of the reinforcement is statistically significant in affecting the unloading stiffness the more the orientation of the reinforcing bars deviates from the principal stress directions The robustness and consistency of the proposed RC membrane and plate model over a range of structural elements under different stress states holds significant promise for its use as reliable tool for the simulation of structural systems under earthquake excitations Introduction Models Implementation Analyses Conclusions 32/36 18

19 Current Work (1) Influence of bond slip and Bond degradation T10 Introduction Models Implementation Analyses Conclusions 33/36 Current Work (2) Shear Deficient Columns d Introduction Models Implementation Analyses Conclusions 34/36 19