Static Analysis of Mild Steel Cantilever Beam by Finite Element Modeling

Ajay Kumar Choubey1*

1Research Associate, Central Institute of Agricultural Engineering, Bhopal-462038

*Corresponding Author : a1ja1y@yahoo.co.in

ABSTRACT

A beam is a structural member. In this paper a two dimensional Finite Element (FE) model for Mild Steel material as beam has been developed to study. This research work aims to analyze the static analysis of an isotropic rectangular beam with boundary condition and different types of point load. For this, commercially available Finite Element software ANSYS 12.0.1 has been used. Simulation results are critically studied and salient conclusions have been drawn. The outputs of finite element simulation are used to investigate the effect of point load on product integrity and mechanical properties. Key words: Cantilever beam, FEM, Mild Steel.

1. INTRODUCTION

Finite element analysis is an effective method of determining the static performance of structures for three reasons which are saving in design time, cost effective in construction and increase the safety of the structure. [1] Beams are one dimensional structural element that can sustain transverse loads by the development of bending, twisting and transverse shearing resistances in the transverse sections of the beam. [2] The present work deals with the analysis of an isotropic cantilever beam being considered as a plane stress condition. This paper deals with FEA of isotropic beam under various boundary conditions and loadings. Throughout the analysis, the master element which is quadrilateral elements, are used. Later, experiments have been conducted for same, using ANSYS. Finally, results have been checked with exact results.

2. Problem Description This is a simple, structural analysis of a cantilever beam. The left side of the cantilever beam is fixed while there is a point load of 100N. The objective of this problem is to demonstrate ANSYS Workbench, finding von-Mises stress and total deflection throughout the beam.

3. Finite Element Modeling:

A 2-D deep drawing model has been developed to simulate for Mild Steel using the ANSYS 2.10.1 Software. PLANE 82 element type is use for beam material. Cantilever beam is modeled in ANSYS software using 8node brick element. The finite element (FE) model is shown in Fig. 1.

Figure 1 : FEM Model

Table 1: Geometrical Parameters

Parameters Value Length of Beam 90 mm Width of Beam 10 mm Height of Beam 5 mm

4. Material Properties of Mild Steel The material properties of Mild steel as shown in below table:

Material Used

Young’s modulus

(E)

Poisson’s Ratio (ν)

Density (ρ)

Mild Steel 210 GPa 0.3 7850 kg/m3

5. Results & Discussion

Point load or concentrated load of 50 N to 200 N are applied on a cantilever beam with same dimension and calculate the total displacement and von-Mises stress.

Table 2 :Value of Maximum Total Displacement &

von-Mises stress of cantilever beam

S. No. Point

Load Total Displacement

Von-Mises Stress

1. 50 0.464E-03 0.950E+08 2. 100 0.928E-03 0.190E+09 3. 200 0.001857 0.380E+09 Fig. 2 shows the effect of point loads on von-Mises stress. It is seen that when the point load increases from 50 N to 200 N, the von-Mises stress increases.

Figure 2 : von-Mises Stress at Different Point Load

Figure 3 : Total Displacement

Fig. 3 shows the effect of point load on displacement. It is seen that when the point load increases, the displacement increases.

Figure 4 : von-Mises stress at 50 N Point Load

(Max. Stress = 0.950E+08 and Min. Stress =1250N)

The Figure 4 shows the FE simulation of cantilever beam in terms of von-Mises stress.

Figure 5 : von-Mises stress at 100 N Point Load (Max. Stress = 0.190E+09 and Min. Stress =2499N)

Figure 6 : von-Mises stress at 200 N Point Load (Max. Stress = 0.380E+09 and Min. Stress =4999N)

CONCLUSIONS

Through the simulation of the cantilever beam of mild steel, the following conclusions are drawn: (i) It is found that von-Mises stress and total displacement increases from 50 to 100 N value of point load. (ii) Maximum displacement occurs at the free end. And at fixed end there is no displacement. Figure 6 as showing total displacement.

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