Structural Nonlinear Analysis of a Shear Wall Panel

Transcription

1 Structural Nonlinear Analysis of a Shear Wall Panel analys: linear static. constr: suppor. elemen: cq16m ct12m pstres. load: force node. materi: elasti isotro. option: direct units. post: binary ndiana. pre: dianai. result: cauchy displa extern force green reacti strain stress total.

2 Outline 1 Description 1.1 Model specification 2 Finite Element Model 2.1 Units 2.2 Geometry definition 2.3 Properties 2.4 Boundary conditions 2.5 Loads Vertical load Applied deformation 2.6 Meshing 3 Structural linear static analysis 3.1 Analysis commands 3.2 Results Total displacement DtXYZ Vertical stress SYY 4 Structural nonlinear analysis 4.1 Analysis commands 4.2 Results In-plane principal stress SXX Reinforcement plastic strain EpYY Crack width Ecw Load-displacement curve Structural Nonlinear Analysis of a Shear Wall Panel 2/33

3 1 Description This example presents the modeling of the shear wall panel in Figure 1. The shear wall is made by a central panel, two columns on the side and a loading plate on the top where a vertical pressure q and the horizaontal load u are applied. The structure will be modeled using plane stress elements and adopting the Total Strain based rotating crack model as constitutive material behavior for the concrete centaral panel and side columns. A linear elastic material model is used for the modeling of the top loading plate. First we will build and check the model using a linear elastic analysis. Then, we will perform a nonlinear analysis while considering a monotonic increase of the horizontal load u. Besides the visualization of the contour plot of displacement, stress and strain fields, we will display in the load-displacement curve associated to this problem. q u ρ y ρ x ρ y y x Figure 1: Shear wall panel with grid reinforcement Structural Nonlinear Analysis of a Shear Wall Panel 3/33

4 1.1 Model specification The geometry and the layout of the reinforcements are shown in Figure 2. The reinforcing steel bars will be modeled using grid reinforcement layers. The concrete and steel material properties are in Table 1. A q = N/mm 700 u = 1-30 mm 240 ρ x = 1.03 mm/m 2 ρ y = 1.16 mm/m 2 ρ y = 4.64 mm/m 2 y x B Linear concrete Young s modulus N/mm 2 Poisson s ratio 0.15 Nonlinear concrete Young s modulus Poisson s ratio 30E N/mm 2 Tensile strength Ultimate strain N/mm 2 Compressive strength 27.5 N/mm 2 Reinforcement steel Young s modulus 200E3 N/mm 2 Yielding stress 574 N/mm 2 Ultimate strength Ultimate strain ε su N/mm 2 Figure 2: Geometry and reinforcements layout of the shear wall panel (dimensions in mm) Table 1: Concrete and steel properties Structural Nonlinear Analysis of a Shear Wall Panel 4/33

5 2 Finite Element Model For the modeling session we start a new project for structural analysis [Fig. 3]. The dimensions of the domain for the 2D model are set equal to 10 m. We will use quadratic quadrilateral finite elements. Main menu File New [Fig. 3] Figure 3: New project dialog Structural Nonlinear Analysis of a Shear Wall Panel 5/33

6 2.1 Units We choose millimeter for the unit Length, ton for Mass and Newton for Force. Geometry browser Reference system Units [Fig. 4] Property Panel [Fig. 5] Figure 4: Geometry browser Figure 5: Property Panel - Units Structural Nonlinear Analysis of a Shear Wall Panel 6/33

7 2.2 Geometry definition We create a sheet for the panel, a second one for the left column and a third one for the loading plate. The coordinates to be used for these geometries are in Table 2. Main Menu Geometry Create Add polygon sheet (X3) [Fig. 6] [Fig. 7] [Fig. 8] Viewer Viewpoints Top View panel left column loading plate Table 2: panel, left column and loading plate coordinates Figure 7: Add left column sheet Figure 6: Add panel sheet Figure 8: Add loading plate sheet Figure 9: View of the model Structural Nonlinear Analysis of a Shear Wall Panel 7/33

8 We create the right column by copying and translating the left column shape. Main Menu Geometry Modify Array copy [Fig. 10] [Fig. 11] Geometry browser Shapes Right click ( ) left column 1 Rename right column [Fig. 12] [Fig. 13] Figure 12: Geometry browser Figure 10: Create right column shape Figure 11: View of the model Figure 13: Geometry browser Structural Nonlinear Analysis of a Shear Wall Panel 8/33

9 The reinforcements are modelled as 2D layers with the same geometry of the embedding shapes. Therefore, we can generate the reinforcement layers by duplicating the panel, left column and right column sheets. Geometry browser Geometry Shapes Select panel, left column and right column Right click ( ) Duplicate [Fig. 14] Geometry browser Shapes Right click ( ) panel 1 Rename grid reinforcement panel [Fig. 15] [Fig. 16] Geometry browser Shapes Right click ( ) left column 1 Rename grid reinforcement left column [Fig. 15] [Fig. 16] Geometry browser Shapes Right click ( ) right column 1 Rename grid reinforcement right column [Fig. 15] [Fig. 16] Figure 14: Duplicate shapes Figure 15: Geometry browser Figure 16: Geometry browser Structural Nonlinear Analysis of a Shear Wall Panel 9/33

10 2.3 Properties We assign the element class and the material and geometrical properties to the panel. We use regular plane stress finite elements with a thickness of 100 mm as shown in Figure 2. The material is nonlinear as described in Section 1.1. Main Menu Geometry Analysis Property assignments [Fig. 17] Property assignments Add new material [Fig. 18] [Fig. 21] Property assignments Add new geometry [Fig. 22] Figure 17: Property assignments to panel Figure 18: Add new material nonlinear concrete Figure 19: Edit material nonlinear concrete Structural Nonlinear Analysis of a Shear Wall Panel 10/33

11 Figure 20: Edit material nonlinear concrete Figure 21: Edit material nonlinear concrete Figure 22: Edit panel geometry Structural Nonlinear Analysis of a Shear Wall Panel 11/33

12 We assign the element class and the material and geometrical properties also to the left column and the right column. As shown in Figure 2, their thickness is 400 mm. Here, we do not need to add a new material, since we will assign to the left column and the right column the same material used for the panel. Main Menu Geometry Analysis Property assignments [Fig. 23] Property assignments Add new geometry [Fig. 24] Figure 23: Property assignments to left column and right column Figure 24: Edit left column and right column geometry Structural Nonlinear Analysis of a Shear Wall Panel 12/33

13 Then, we assign the element class and the material and geometrical properties to the loading plate. A new material is here created for the linear concrete as described in Section 1.1. As shown in Figure 2, the thickness is 700 mm. Main Menu Geometry Analysis Property assignments [Fig. 25] Property assignments Add new material [Fig. 26] [Fig. 27] Property assignments Add new geometry [Fig. 28] Figure 25: Property assignments to loading plate Figure 26: Add new material linear concrete Figure 27: Edit material linear concrete Figure 28: Edit loading plate geometry Structural Nonlinear Analysis of a Shear Wall Panel 13/33

14 Finally, we assign the material and geometrical properties to the steel reinforcements. We start from assigning the properties to the grid reinforcement in panel. During the assignement of the material properties we need to specify the strain-stress diagram at yielding based on the material properties in Table 1. Main Menu Geometry Analysis Reinforcement property assignment [Fig. 29] Shape assignment Add new material [Fig. 30] [Fig. 31] [Fig. 32] Shape assignment Add new geometry [Fig. 33] Figure 29: Property assignments to grid reinforcement in panel Figure 30: Add new material steel Figure 31: Edit material steel Structural Nonlinear Analysis of a Shear Wall Panel 14/33

15 Figure 32: Edit material steel (strain-stress diagram at yielding) Figure 33: Edit grid reinforcement in panel geometry Structural Nonlinear Analysis of a Shear Wall Panel 15/33

16 Then, we assign the material and geometrical properties to the grid reinforcement in left column and the grid reinforcement in right column. Compared to the grid reinforcement in panel, only the geometry changes while the material properites are the same. Main Menu Geometry Analysis Reinforcement property assignment [Fig. 34] Shape assignment Add new geometry [Fig. 35] Figure 34: Property assignments to grid reinforcement in left column and grid reinforcement in right column Figure 35: Edit grid reinforcement in left column and grid reinforcement in right column geometry Structural Nonlinear Analysis of a Shear Wall Panel 16/33

17 2.4 Boundary conditions We support the bottom edge of the model in the X and Y -directions. Main Menu Geometry Analysis Attach support [Fig. 36] [Fig. 37] Figure 36: Apply symmetry boundary conditions Figure 37: Bottom contraints Structural Nonlinear Analysis of a Shear Wall Panel 17/33

18 2.5 Loads Vertical load We apply a vertical distributed load N/mm to the top edge of the loading plate. Main menu Geometry Analysis Attach load [Fig. 38] [Fig. 39] Figure 38: Apply vertical nodal force Figure 39: Vertical distributed load Structural Nonlinear Analysis of a Shear Wall Panel 18/33

19 2.5.2 Applied deformation To apply a prescribed deformation in the center node of the loading plate, we need to create a node at this location. We first generate a vertex at the center of the loading plate, that we will later imprint on the loading plate itself. Main Menu Geometry Create Add point body [Fig. 40] Main Menu Geometry Modify Projection of shapes [Fig. 41] [Fig. 42] Figure 40: Create point body Figure 41: Imprint point body on loading plate Figure 42: Imprinted point on loading plate Structural Nonlinear Analysis of a Shear Wall Panel 19/33

20 To apply a prescribed displacement in a node in, we first constrain the displacement of the node and then apply a finite deformation. Main Menu Geometry Analysis Attach support [Fig. 43] Main Menu Geometry Analysis Attach load [Fig. 44] [Fig. 45] Figure 43: Constrain center node of loading plate Figure 44: Apply prescribed deformation Figure 45: View prescribed deformation Structural Nonlinear Analysis of a Shear Wall Panel 20/33

21 2.6 Meshing We set the mesh properties such that the elements size is 50 mm. Then, we generate the mesh. Main Menu Geometry Analysis Set mesh properties [Fig. 46] Main Menu Geometry Analysis Generate mesh [Fig. 47] Figure 46: Mesh properties Figure 47: Finite element mesh Structural Nonlinear Analysis of a Shear Wall Panel 21/33

22 3 Structural linear static analysis 3.1 Analysis commands We will first perform a linear elastic analysis for a quick assessment of the model. Main Menu Analysis New Analysis Analysis browser Right click ( ) Analysis1 Rename Linear [Fig. 48] Analysis browser Right click ( ) Linear Add command Structural linear static [Fig. 49] [Fig. 50] Main Menu Analysis Run Analysis Figure 48: Analysis window Figure 49: Add command Figure 50: Analysis tree Structural Nonlinear Analysis of a Shear Wall Panel 22/33

23 3.2 Results Total displacement DtXYZ First we will create a contour plot for the total displacement DtXYZ for the two load cases (top pressure and displacement). Results browser Output linear static analysis Nodal results Displacements DtXYZ [Fig. 51] [Fig. 52] Results browser Case displacement [Fig. 53] Figure 51: Results browser - DtXYZ Figure 52: Displacement DtXYZ top pressure Figure 53: Displacement DtXYZ displacement Structural Nonlinear Analysis of a Shear Wall Panel 23/33

24 3.2.2 Vertical stress SYY Then, we display the contour plot of the vertical stress SYY. Results browser Output linear static analysis Element results Cauchy Total Stresses SYY [Fig. 54] Results browser Case top pressure [Fig. 55] Results browser Case displacement [Fig. 56] Figure 54: Results browser - SYY Figure 55: Displacement SYY top pressure case Figure 56: Displacement SYY displacement case The positive stresses induced by the displacement are higher than the tensile strength of the concrete. Therefore, in the nonlinear analisys we will observe cracks forming in the panel and in the left and right column. Structural Nonlinear Analysis of a Shear Wall Panel 24/33

25 4 Structural nonlinear analysis 4.1 Analysis commands Now, we perform a nonlinear structural analysis where the horizontal displacement is incrementally increased. Main Menu Analysis New Analysis Analysis browser Right click ( ) Analysis2 Rename Nonlinear [Fig. 57] Analysis browser Right click ( ) Nonlinear Add command Structural nonlinear [Fig. 58] [Fig. 59] Figure 57: Analysis window Figure 58: Add command Figure 59: Analysis tree Structural Nonlinear Analysis of a Shear Wall Panel 25/33

26 The existing default execute block will be used to apply the vertical load on the structure. Therefore, the exucute block command will be renamed top pressure. Then, a new execute block is added to the nonlinear analysis to take into account of the horizontal displacement. This second execute block will be renamed displacement. Analysis browser Nonlinear Structural nonlinear Right click ( ) new execute block Rename top pressure [Fig. 60] Analysis browser Nonlinear Right click ( ) Structural nonlinear Add Execute step - Load steps [Fig. 61] Analysis browser Nonlinear Structural nonlinear Right click ( ) new execute block Rename displacement [Fig. 62] Figure 60: Rename execute block Figure 61: Add new execute block Figure 62: Rename execute block Structural Nonlinear Analysis of a Shear Wall Panel 26/33

27 The horizontal displacement will be applied 30 times. During these steps we set the maximum number of iterations to 50 and the convergence norm to energy together with a convergence tolerance equal to Analysis browser Nonlinear Structural nonlinear displacement Load steps [Fig. 63] Analysis browser Nonlinear Structural nonlinear displacement Equilibrium iteration [Fig. 64] [Fig. 65] Figure 63: Load steps Figure 64: Equilibrium iteration Figure 65: Convergence norm Structural Nonlinear Analysis of a Shear Wall Panel 27/33

28 We select the desired output results listed in Table 3 and we run the analysis. Analysis browser Nonlinear Structural nonlinear Right click ( ) Output Edit properties Properties - OUTPUT Result User selection Results Selection [Fig. 66] Properties - OUTPUT Result Modify Results Selection [Fig. 67] [Table 3] [Fig. 68] Main menu Nonlin Run analysis Figure 67: Results selection Figure 66: Output properties Global displacements Global total stresses Global plastic strain Crack width Reaction forces DISPLA TOTAL TRANSL GLOBAL STRESS TOTAL CHAUCHY GLOBAL STRAIN PLASTI GREEN GLOBAL STRAIN CRKWDT GREEN PRINCI FORCE REACTI TRANSL GLOBAL Table 3: Required output data Figure 68: Output properties Structural Nonlinear Analysis of a Shear Wall Panel 28/33

29 4.2 Results In-plane principal stress SXX We will create a contour plot for the in-plane principal stress at load step 2 and 31. Results browser Nonlinear Output Element results Cauchy Total Stresses Right click ( ) SXX Show in-plane principal components [Fig. 69] Results window Case Load-step 2, Load-factor , displacement [Fig. 70] Results window Case Load-step 31, Load-factor , displacement [Fig. 71] Figure 69: In-plane principal stresses Figure 70: In-plane stress SXX - load-step 2 Figure 71: In-plane stress SXX - load-step 31 Already at step 2, some of the concrete in the panel already cracks since the tensile exceeds the tensile strength (see Table 1). At step 31, also the compressive stresses reached the tensile strength of the concrete. Structural Nonlinear Analysis of a Shear Wall Panel 29/33

30 4.2.2 Reinforcement plastic strain EpYY We will display the contour plot for the reinforcement plastic strain EpYY at load step 2 and 31. Results browser Nonlinear Output Reinforcement results Reinforcement plastic strains EpYY [Fig. 72] Property editor Contour plot settings Color scale limits Specified values [Fig. 73] Property editor Contour plot settings Specified values Minimum value [Fig. 73] Property editor Contour plot settings Specified values Maximum value 0.04 [Fig. 73] Results window Case Load-step 2, Load-factor , displacement [Fig. 74] Results window Case Load-step 31, Load-factor , displacement [Fig. 75] Figure 72: Reinforcement plastic strain EpYY Figure 73: Contour plot limits Figure 74: Reinforcement plastic strain EpYY - load-step 2 Figure 75: Reinforcement plastic strain EpYY - load-step 31 At step 2 the plastic strain is about 0 everywhere, thus the steel reinforcemnts are not yielded. However, as shown at step 31, due to the increasing of the horizontal displacement the reinforcements yield. Structural Nonlinear Analysis of a Shear Wall Panel 30/33

31 4.2.3 Crack width Ecw1 We will display the contour plot for the crack width Ecw1 at load step 2 and 31. Results browser Nonlinear Output Element results Crack-widths Ecw1 [Fig. 76] Property editor Contour plot settings Specified values Minimum value 0 [Fig. 77] Property editor Contour plot settings Specified values Maximum value 2.6 [Fig. 77] Results window Case Load-step 2, Load-factor , displacement [Fig. 78] Results window Case Load-step 31, Load-factor , displacement [Fig. 79] Figure 76: Crack width Ecw1 Figure 77: Contour plot limits Figure 78: Crack width Ecw1 - load-step 2 Figure 79: Crack width Ecw1 - load-step 31 As shown in Figure 78, the formation of cracks in the concrete starts from the bottom left corner due to the tension induced by the horizontal load yy increasing its value, the cracks width increases, especially in the left column where the tension is higher (see Figure 79). Structural Nonlinear Analysis of a Shear Wall Panel 31/33

32 4.2.4 Load-displacement curve Finally, we will make a load-displacement curve. For this model, the load is actually a prescribed displacement at the center of the loading plate. Therefore, a load-displacement diagram should actually plot the reaction force versus the displacement of this center node. Results browser Nonlinear Output Nodal results Reaction forces Right click ( ) FBX Show table [Fig. 80] Chart view Node and element selection nodes [Fig. 81] [Fig. 82] Figure 80: Show table Figure 81: Node selection Figure 82: Load-displacement curve Figure 82 shows that the elastic threshold is reached as soon as the horizontal displacement is applied. Then, the stiffness of the wall decreases due to the formation of cracks in the concrete, until a constant slope is reached since the load is undertaken by the hardening steel reinforcements. Structural Nonlinear Analysis of a Shear Wall Panel 32/33

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