Chapter 7. Finite Elements Model and Results

Transcription

1 Chapter 7 Finite Elements Model and Results 7.1 Introduction In this chapter, a three dimensional model was presented. The analytical model was developed by using the finite elements method to simulate the behavior of the masonry wall specimens under lateral loading testing. The analytical model presented the non-linear material properties, cracking and crushing of concrete, and yielding of steel. The results are compared to the experimental results obtained from the test program. The differences between the theoretical and experimental results are discussed. The ANSYS commercial finite element program was used in analyzing the behavior of the masonry wall specimens under lateral loading testing due to its ability to deal with causes of nonlinearity including material and geometrical nonlinearities. 7.2 The Proposed Model The analytical models were consisted of two main models, the control masonry wall specimen and the ferrocement masonry wall specimen as shown in Figure 7.1. The control masonry wall specimen elements were consisted of AAC bricks, two mortar plaster layers with 15mm thickness, two RC ties, a top RC beam, and a bottom RC base beam. The ferrocement masonry wall specimen elements were consisted of AAC bricks, two ferrocement plaster layers with 25mm thickness, two RC ties, a top RC beam, and a bottom RC base beam. 8

2 7.1a) Control Masonry Wall with 15mm mortar plaster layer thick. 7.1b) Ferrocement Masonry Wall with 25mm ferrocement layer thick. Figure 7.1: The three dimensional analytical ANSYS models 9

3 Each part's geometry, element type, and material properties were simulated to match the experimented specimens. Shear connectors were not simulated in the model since the elements were defined with shared nodes, which approximately give the required stiffness of the specimens. No contact conditions were specified between the ferrocement layers and the AAC blocks since the contacted elements were sharing the same surfaces, a simulation that approximately provides the specimens with required integration. The AAC blocks and the mortar joints were modeled separately, and the slippage between the mortar joints and the block was not accounted. A solid brick element "SOLID65" was used to model the block units, mortar, RC, and ferrocement as shown in Figure 7.2. The element possesses 8 nodes with 3 degrees of freedom at each node. As per ANSYS user manual, SOLID65 is used for the 3-D modeling of solids with or without reinforcing bars. The solid element is capable of cracking in tension, plastic deformation, creep, and crushing in compression. The rebar are capable of tension and compression, but not shear. They are also capable of plastic deformation and creep. The most important aspect of this element is the treatment of nonlinear material properties (ANSYS user manual, 12). Figure 7.2: The three dimensional analytical ANSYS models (ANSYS user manual, 12) For the masonry wall model, the RC base beam was not allowed to tilt, and the degrees of freedom of all nodes at the bottom face of the RC base beam were restricted in all direction to simulate the actual boundary conditions of the lateral load testing in which the bottom face is not allowed to move as shown in Figure

4 Figure 7.3: Boundary conditions of masonry wall model The main assumptions were selected based on a similar analytical model developed in AUC by Abel-Mooty (11) in autoclaved aerated concrete masonry wall strengthened using ferrocement sandwich structure (Abel-Mooty, 11). To describe the behavior of the element under cracking and crushing, a number of different parameters were required as input. The ultimate uni-axial compressive strength and the uni-axial tensile strength were input. The compressive strength is used as shown in Tables 7.1 and 7.2, while the tensile strength was taken as.1 of the compressive strength. The open and closed shear transfer coefficients were used to describe the transfer of the shearing force through the crack. Only part of the shearing force was allowed to transfer along the cracked surface, as indicated by the shear transfer coefficients. A value of.1 was used for the open shear transfer coefficient to indicate that.1 of the shearing force is transferred through an open crack whereas a value of.8 for the closed shear transfer coefficient indicated that a fraction of shearing load equal to.8 was allowed to transfer between the cracked surface. These parameters were sufficient to fully describe the concrete model of the element. Other parameters like the biaxial compressive strength were set to default and were calculated as a 1.2 of the uniaxial compressive strength 211

5 (Abel-Mooty, 11). Different material properties were set for each of the block, mortar, RC, and the ferrocement layers as shown in the next sub sections Control Masonry Wall The control masonry wall model was simulating the specimen L1 in the designation 15- Control. The dimensions of the masonry wall were mm wide and 2mm height as shown in Figure 7.3. The width dimension in the model was approximated to mm instead of 183mm in the experimental specimen because of ease of the meshing process in the model. The control masonry wall was consisted of AAC bricks with 15mm thickness and two plaster faces with thickness 15mm, so the total thickness of the masonry wall is mm. Figure 7.4: Dimensions of control and ferrocement wall model 212

6 The control wall was modeled using SOLID65 elements. The size of the element was selected to be x mm as shown in Figure 7.1a. This element size was sufficient to capture the crack pattern in the wall and also to accurately estimate the capacity of the wall. The ultimate compressive strength, modulus of elasticity and Poisson s ratio are listed in Table 7.1. Material Table 7.1: Material Properties for control wall model. Modulus of Poisson's Elements Elasticity (N/mm 2 ) Ratio Ultimate Comp. Strength (N/mm 2 ) AAC Bricks Mortar Joints and plaster RC Ties,top beam, and base beam The properties of the steel bars in the RC tie elements are: Modulus of elasticity 2x1 5 N/mm 2, Poisson s ratio.3, yield stress 413 N/mm 2. The tangential modulus which indicates the slope of the stress strain curve beyond yielding of steel is assumed as N/mm 2. Lateral load was applied in increments on the wall until nonconvergence occurs. A displacement criterion for convergence was used Ferrocement Masonry Wall The ferrocement masonry wall model was simulating the specimen L8 in the designation 15-FC-Nails. The dimensions of the masonry wall were mm wide and 2mm height as shown in Figure 7.3. The width dimension in the model was approximated to mm instead of 183mm in the experimental specimen because of ease of the meshing process in the model. The ferrocement masonry wall was consisted of AAC bricks with 15mm thickness and two plaster faces with thickness 25mm, so the total thickness of the masonry wall is mm. 213

7 The ferrocement wall was modeled using SOLID65 elements. By using SOLID65 elements, the wire mesh reinforcement in the ferrocement layer could be added as volume ratio of mortar and reinforcement. The size of the element was selected to be x mm as shown in Figure 7.1b. This element size was sufficient to capture the crack pattern in the wall and also to accurately estimate the capacity of the wall. The ultimate compressive strength, modulus of elasticity and Poisson s ratio are listed in Table 7.2. Material Table 7.2: Material Properties for ferrocement wall model. Modulus of Poisson's Elements Elasticity Ratio (N/mm 2 ) Ultimate Comp. Strength (N/mm 2 ) AAC Bricks Mortar Joints High strength mortar RC Ferrocement plaster Ties,top beam, and base beam The properties of the steel bars in the RC tie elements are: Modulus of elasticity 2x1 5 N/mm 2, Poisson s ratio.3, yield stress 413 N/mm 2. The tangential modulus which indicates the slope of the stress strain curve beyond yielding of steel is assumed as N/mm 2. Lateral load was applied in increments on the wall until nonconvergence occurs. A displacement criterion for convergence was used. 7.3 Finite Elements Results Two cases of study were developed using the ANSYS finite element model. A control plain wall made of AAC blocks was first studied followed by reinforced walls in which the ferrocement was applied on both sides. The geometric and average material properties of both masonry walls were provided as input data for the program, while the load, deflection, stress and strain distributions were the output. The lateral deformation at the far end of the wall was 214

8 plotted against the applied lateral load and comparison was made between the experimental and analytical model Control Masonry Wall After applying the lateral load on the control masonry wall, the ultimate load that caused extensive cracks in the wall was 95 kn, which matches with the experimental value of specimen L1. The maximum horizontal displacement was 2.4 mm as shown in Figure 7.5. This displacement value could be considered far less than the experimental value of 3 mm. This difference in the horizontal displacement behavior could be attributed to the slippage between the mortar joints, and the noticeable tilting of the base of the wall during the experimental testing, which was neglected in the model. Figure 7.6 shows a comparison between the displacement curve, which was obtained from the experimental results and the displacement curve, which was obtained from the modeling results. 7.5a) Control masonry wall deformed shape 215

9 Load (kn) Load (kn) Displacements (mm) 7.5b) Load-horizontal displacement relationship Figure 7.5: Displacement of control masonry wall model Displacements (mm) Model Exprimental Figure 7.6: Comparison between model and experimental Load-displacement relationship 216

10 The numerical model was able to capture the cracking pattern of the wall at failure as shown in Figure 7.7. The diagonal cracks runs across the wall. Also some vertical tensile splitting cracks appear at the RC base beam of the wall. This cracking pattern agrees with the observed experimental behavior as shown in Figure 7.8. Figure 7.7: Control wall model cracking pattern 217

11 7.8a) Diagonal crack 7.8b) Tensile splitting crack Figure 7.8: Experimental cracking pattern Ferrocement Masonry Wall After applying the lateral load on the ferrocement masonry wall, the ultimate load that caused extensive cracks in the wall was kn, which is little higher than the experimental result (168.4 kn). This difference may be attributed to the assumption of the complete interaction between the ferrocement skin layers and the AAC bricks in the finite elements model. The variation between the analytical and the experimental ultimate load was about 18%. The maximum horizontal displacement was 6.2 mm as shown in Figure 7.9. This displacement value could be considered far less than the experimental value of 3 mm. This difference in the horizontal displacement behavior could be attributed to the slippage between the mortar joints, and the noticeable tilting of the base of the wall during the experimental testing, which was neglected in the model. Figure 7.1 shows a comparison between the displacement curve, which was obtained from the experimental results and the displacement curve, which was obtained from the modeling results. 218

12 Load (kn) 7.9a) Ferrocement masonry wall deformed shape Displacements (mm) 7.9b) Load-horizontal displacement relationship Figure 7.9: Displacement of ferrocement masonry wall model 219

13 Load (kn) Displacements (mm) Model Exprimental Figure 7.1: Comparison between model and experimental Load-displacement relationship The numerical model was able to capture the cracking pattern of the wall at failure as shown in Figure The diagonal cracks runs across the wall mid width. Also some vertical tensile splitting cracks appear at the RC base beam of the wall. This cracking pattern agrees with the observed experimental behavior as shown in Figure The comparison between the results of the model and the experimental verify the validity of finite elements model for predicting the ultimate lateral load of the ferrocement masonry wall. The model could be used in the future to perform more parametric studies. 2

14 Figure 7.11: Ferrocement wall model cracking pattern 7.12a) Diagonal crack 7.12b) Tensile splitting crack Figure 7.12: Experimental cracking pattern 221

15 Failure Load (kn) 7.4 Parametric Study Effect of the Mortar Matrix Strength The effect of the mortar matrix strength on the behavior of ferrocement masonry wall under lateral loading could be investigated by changing the strength of the ferrocement mortar in the numerical model parameters and comparing the results of the different models. The use of ferrocement reinforcement with mortar strength N/mm 2 resulted in extensive cracks at ultimate lateral load kn, as discussed previously in this chapter. Decreasing the mortar strength up to N/mm 2 resulted in extensive cracks at ultimate lateral load kn. While decreasing the mortar strength up to N/mm 2 resulted in extensive cracks at ultimate lateral load kn. Figure 7.13 shows the failure load for different models with varying in mortar matrix strength. The load-displacement curves for the three models are shown in Figure Using high strength mortar in producing ferrocement masonry walls resulted in higher failure load, higher stiffness, and more ductility. Mortar strength MPa Mortar strength MPa Mortar strength MPa Figure 7.13: Failure load for different models with varying in mortar matrix strength 222

16 Load (kn) Displacements (mm) MPa MPa MPa Figure 7.14: The load-horizontal displacement curves for the different three numerical models with varying in mortar matrix strength Effect of the Ferrocement Layer Thickness The effect of the ferrocement layer thickness and consequently the overall thickness of the masonry wall on the behavior of ferrocement masonry wall under lateral loading could be investigated by decreasing or increasing the thickness of the ferrocement layer in the numerical model parameters and comparing the results of the different models. Producing ferrocement wall with 25 mm layer thickness resulted in extensive cracks at ultimate lateral load kn, as discussed previously in this chapter. Decreasing the ferrocement thickness layer up to mm resulted in extensive cracks at ultimate lateral load kn. While increasing the ferrocement thickness layer up to 3 mm resulted in extensive cracks at ultimate lateral load 3.75 kn. This insignificant increase in the failure load in despite of 223

17 Failure Load (kn) increasing the thickness layer of the ferrocement could be attributed to the fact that the ferrocement masonry wall started to separate from its RC base beam at load kn.. Figure 7.15 shows the failure load for different models with varying in ferrocement layer thickness. The load-displacement curves for the three models are shown in Figure Ferr. thick. mm Ferr. thick. 25 mm Ferr. thick. 3 mm Figure 7.15: Failure load for different models with varying in ferrocement layer thickness 224

18 Load (kn) Displacements (mm) Th. 3mm Th. 25mm Th. mm Figure 7.16: The load-horizontal displacement curves for the different three numerical models with varying in ferrocement layer thickness Effect of Increasing Layers of the Reinforcing Steel Mesh Numerical model results revealed that using double mesh reinforcement in the ferrocement masonry wall contributed to a slightly higher ultimate load than using single mesh reinforcement. Producing ferrocement masonry wall with single mesh reinforcement resulted in extensive cracks at ultimate lateral load kn, as discussed previously in this chapter. While using double mesh reinforcement in the ferrocement masonry wall resulted in extensive cracks at ultimate lateral load 2.5 kn. Figure 7.17 shows the failure load for different two models with single and double mesh reinforcement. The load-displacement curve for the double mesh reinforcement is shown in Figure

19 Load (kn) Failure Load (kn) 2 2 Single mesh reinforcement Double mesh reinforcement Figure 7.17: Failure load for different two models with single and double mesh reinforcement Displacements (mm) Figure 7.18: The load-displacement curve for the double mesh reinforcement 226