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Study on Two Way Reinforced Concrete Slab Using Ansys with Different Boundary Conditions and Loading
Civil Engineering (CE)
Anna University
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1 Abstract —This paper presents the Finite Element Method (FEM) for analyzing the failure pattern of rectangular slab with various edge conditions. Non-Linear static analysis is carried out using ANSYS 15 Software. Using SOLID65 solid elements, the compressive crushing of concrete is facilitated using plasticity algorithm, while the concrete cracking in tension zone is accommodated by the nonlinear material model. Smeared reinforcement is used and introduced as a percentage of steel embedded in concrete slab. The behavior of the analyzed concrete slab has been observed in terms of the crack pattern and displacement for various loading and boundary conditions. The finite element results are also compared with the experimental data. One of the other objectives of the present study is to show how similar the crack path found by ANSYS program to those observed for the yield line analysis. The smeared reinforcement method is found to be more practical especially for the layered elements like concrete sla bs. The value of this method is that it does not require explicit modeling of the rebar, and thus a much coarser mesh can be defined.
Keywords — ANSYS, cracking pattern, displacements, RC Slab, smeared reinforcement.
I. INTRODUCTION RADITIONALLY the reinforced concrete structures were designed using empirical methods based on experience or conducting experimental investigations on real structures. While this method yields a high degree of accuracy, it is always very expensive and time-consuming. With the introduction of advanced computers, Finite Element Analysis became a popular tool to analyze and design complicated structures. In this study, the finite element analysis software ANSYS was employed to model the two-way reinforced concrete slab in order to determine the failure pattern and load displacement behavior when subjected to different boundary conditions and loading.
II. FINITE ELEMENT MODELING A rectangular reinforced concrete slab is discretized into quadrilateral brick elements. The nonlinear analysis is conducted using Ansys commercial finite element program [1], [2]. The smeared reinforcements are used at the bottom as a tensile reinforcement. A. Physical Model The geometry of the full concrete slab of size 2x3 m is shown in Fig. 1. The slab has been designed for service load
Ahmed Gherbi is with the University of Mouloud Mammeri of Tizi- Ouzou, Algeria (e-mail: lahlou_d@yahoo).
of 18 kN/m 2 which is broken into load steps in order to capture the ultimate response of the specimen. The slab thickness is 200 mm. Concrete cover 25 mm is used, and reinforcement adopted is 8 mm diameter bar @ 250mm c/c.
Fig. 1 Physical model B. Reinforced Concrete Model An eight-node solid element (SOLID65) was used to model the concrete [6], [7]. The solid element has eight nodes with three degrees of freedom at each node Fig. 2 (a) – translations in the nodal x, y, and z directions. Eight Gaussian integration points are used to recover nodal displacements and stresses Fig. 2 (b). Fig. 2 below shows the solid 65 element used by ANSYS in order to capture the cracking and crushing state in addition to the plastic deformation of the concrete slab. C. Steel Reinforcements The reinforcements in concrete slab can be modeled by two methods. A discrete method where the reinforcing is simulated as strut or beam elements connected to the solid elements. This method is more suitable for simple concrete models like beams (Fig. 2 (a)). A smeared method (used in this paper) where the reinforcements are introduced as a volume ratio which is defined as the rebar volume divided by the total element volume. The rebar element effectively sits on top of the existing concrete elements, and thus uses the same nodes as the underlying concrete elements (Fig. 2 (b)). Cracks can also be idealized into either the discrete type or the smeared type. D. Finite Element Discretization A solid concrete slab model shown in Fig. 1 is descretized with a 3D finite element model as shown in Fig. 4. The hole model is meshed at once with an hexahedral shaped elements along with a smartsizing control featured by Ansys. The stress
Study on Two Way Reinforced Concrete Slab Using
ANSYS with Different Boundary Conditions and
Loading
A. Gherbi, L. Dahmani, A. Boudjemia
T
International Journal of Civil and Environmental Engineering Vol:12, No:12, 2018
Open Science Index, Civil and Environmental Engineering Vol:12, No:12, 2018 waset/Publication/
and strains are then calculated after applying the load and boundary conditions to the finite element model [9]. A slab is composed of two regions; a concrete element without
reinforcement (Fig. 5) and a concrete element with a smeared reinforcement (Fig. 6).
(a)
(b) (c) Fig. 2 SOLID65: 3D reinforced concrete solid (ANSYS 15)
Fig. 3 Discrete vs. smeared element for concrete reinforcing
Two real constant sets for SOLID65 element are created. First one does not have volume ratio (the volume ratio is defined as the rebar volume divided by the total element volume) for the reinforcement, the second one does. Then, two separate volumes adjacent to each other and one under the other are created (Fig. 1). The glue operation used by ANSYS redefines the input volumes so that they share areas along their common boundaries. Before meshing, we choose the first real constant set for the upper one and the second set for the other as mesh attributes (Fig. 4).
III. NONLINEAR SOLUTION STRATEGY Nonlinear solution technique and overall nonlinear solution strategy to be adopted are very important for nonlinear pre and post-yielding analyses of concrete members. The load is applied gradually by dividing it into a series of increments an d
adjusting the stiffness matrix at the end of each increment. The ANSYS program [1], [2], [4] uses Newton-Raphson equilibrium iterations for updating the model stiffness. Newton-Raphson equilibrium iterations provide convergence at the end of each load increment within prescribed tolerance limit. In this study, Full Newton-Raphson option with Sparse Direct Solver was used for speed and robustness of the solution.
Fig. 4 Finite element model
IV. FAILURE CRITERIA FOR CONCRETE ANSYS non-linear concrete model is based on William Warnke failure criteria. Two input strength parameters are needed to define a failure surface for the concrete. Once the failure is surpassed, concrete cracks if any principal stresses
International Journal of Civil and Environmental Engineering Vol:12, No:12, 2018
Open Science Index, Civil and Environmental Engineering Vol:12, No:12, 2018 waset/Publication/
(a) All sides simply supported (b) All sides fixed Fig. 9 Load–deflection response of the concrete slab
The crack pattern found by ANSYS program (Figs. 10 and 12) has confirmed Johansen's hypothesis [7] that the location of appropriate yield lines (Figs. 11 and 13) in a two-way reinforced concrete slab follows exactly the same pattern as the crack propagation. The crak formation in the slab starts to develop after oneset of yielding of the reinforcements. The yield line pattern caused by the crack formation reaches its maximum length at failure. A. Case 1: All Sides Simply Supported At load step 6 (Fig. 10 (a)), the total uniformly distributed load acting on the slab is 6 kN/m 2. Until this loading, slab behaves elastically. The deformation is small, and up to this point, the Hooke’s law is valid. The slab reaches its ultimate collapse load in between 10-12 kN/m 2 and the transverse deflection suddenly increases as the load step increases from 10 to 12. The collapse of slab can also be confirmed by the study of cracking pattern which has been generated in the highly stressed elements just as the ultimate load has been reached. Figs. 10 (a)-(d) are enlisted below showing the difference in the crack patterns from load step 6 to 12. It is conspicuous in the figure that a complete fracture has occurred at load step 1 2 as the cracks (explicitly representing the yield lines) have reached to the boundaries of the slab. Figs. 11 (a)-(c) represent the corresponding yield line pattern given from the literature [7], [10].
(a) No cracks
(b) First cracking at the bottom face
(c) Further cracking
(d) Cracking at failure Fig. 10 Cracking patterns by ANSYS
International Journal of Civil and Environmental Engineering Vol:12, No:12, 2018
Open Science Index, Civil and Environmental Engineering Vol:12, No:12, 2018 waset/Publication/
(a) First yielding (b) Further development of yield lines
(c) Collapse mechanics formed Fig. 11 Yield lines patterns for a simply supported slab [7]
(a) No cracks
(b) First cracking at the top face
(c) Further cracking (top and bottom face)
(d) More cracks formation
(e) Cracking at failure Fig. 12 Cracking patterns by ANSYS B. Case 2: All Sides Fixed The sequential failure patterns in the case of all sides fixed slab are shown in Figs. 12 (a)-(e) from the load step 8 to 18. The failure pattern occurs at the highly stressed region (center of slab) and at the fixing support. The failure pattern follows the same pattern as in the simply supported slab with additional cracks at edge of the fixed slab [10].
International Journal of Civil and Environmental Engineering Vol:12, No:12, 2018
Open Science Index, Civil and Environmental Engineering Vol:12, No:12, 2018 waset/Publication/
Study on Two Way Reinforced Concrete Slab Using Ansys with Different Boundary Conditions and Loading
Course: Civil Engineering (CE)
University: Anna University
