Finite Element Analysis of Stress and Deflection of Beam

International Journal of Scientific Research and Engineering Development-– Volume 3 Issue 6, Nov-Dec 2020

Available at www.ijsred.com

ISSN : 2581-7175 ©IJSRED: All Rights are Reserved Page 646

Finite Element Analysis of Stress and Deflection of Beam for

Various Cross-sections under Central Point Loads

Abhishek Kumar Gupta1, Shalini Kumari

2 and Sawan Kumar Gupta

3

1,2 Harcourt Butler Technical University, Kanpur, India

3Ashoka Institute of Technology and Management, Varanasi, India

[email protected], [email protected] and [email protected]

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Abstract

Beam is a structural element which is subjected to transverse loading. Generally, different types of beams

such as simply supported beam, cantilever beam, fixed beam, overhanging beam etc are used in

construction and infrastructure development. In this research paper an attempt is made to used simply

supported beam with different cross section and finite element analysis on ANSYS Software 20 was

carried out to investigate the stress and deflection of structural steel beam in which various cross section is

used. Structural steel is widely used in construction area because of its excellent durability and mechanical

properties. The primary function of beam is to resist the deformation. Six different cross section of beam

which is circular section, hollow circular section, square section, hollow square section, rectangular cross

section and I-section were considered in this modelling with constant cross-sectional area and length.

Stress and deflection of simply supported beam were analysed to know the highest resistanceto

deformation at varying loads of 8kN to 14kN.

Keywords: Stress and deflection, Simply supported beam, ANSYS software, Various cross section, Loads.

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1. INTRODUCTION

In a few decades, the use of Computer Aided Engineering (CAE) for modelling and simulation analysis has

been increased because of the development of designing software and machines [1]. Beam structure are

used in many area like mechanical, civil and aerospace engineering purpose and after the application of

loads on these structural beam, damage is also seen which is undesirable and these damage in a beam are

due to presence of micro crack through which a fracture may be initiated [2, 3] Therefore, proper analysis

is required to overcome this failure.SanasamVipej et al has reported that with the use of different

arrangements of member (horizontal, vertical, square frame and ring), stiffening effects can be improved

through finite element analysis [9, 11].Yidu Bu and LerayGarderhas reported that with the help of finite

element models, 59 experiments of I-section column have been carried out covering both conventionally

RESEARCH ARTICLE OPEN ACCESS




welded and laser welded column. Experimental results are validated by finite element results which are

well satisfactory [6].Mohammed M. Eladlyhas found that by using 3D model of stainless steel beam to

column bolted joint,FEA was carried out for stiffness, ultimate moment capacity, overall moment rotation

and failure behaviour [5].J. Samuel et al. explained the experimental and numerical simulation of effects of

cold farmed steel with reinforcing bar and in this analysis, load carrying capacity, deflection, strain and

failure parameters were examined [4, 7].TapanSabuwala et al. explained the effects of blast load on steel

beam to column connection with the help of FE Analysis on ABAQUS Software and the results showed

that the criteria for steel connection subjected to loads are inadequate [2].Ou Zhao et al. have reported the

design of stainless steel square hollow section and rectangular hollow section beam column subjected to

bending moment was carried out to determine the bending performance through finite element analysis [1].

FE analysis results are composed with numerical data and after analysis it was found that finite element

analysis results was very close to numerical values.

In the present work, geometric modelling of structural steel beam for various constantcross-sectional

areaand length have been modelled. Simply supported beam with central point load was used and stress

and deflection of beam were calculated at varying point load of 8000N to 14000N to determine which

geometry of beam has much more stiffer and also able to resist more deformation.

2. FINITE ELEMENT ANALYSIS OF BEAM

FEA is a computer based analysis which is used to solve a various engineering problems with the

help of some designing software such as ANSYS Software, MATLAB, AbaqusSoftwareetc

which gives a very accurate results of problems.FEA has become a important part of designing

process in the field of automobile, civil construction, aerospace engineering etc [8].The basic

steps involved in finite element analysis are putting materials properties on software, geometric

modelling, meshing of models, applying boundary conditions, solver and post processing and

results analysis [9, 10].Modelling and meshing for various cross section members have been

done through ANSYS Software 20 which is presented in fig. 1.For FE analysis, materials

properties are required for each memberand putting these material properties on software and a

point central load of8000 N, 10000 N, 12000 N and 14000 N was applied




Fig. 1. Meshing on models.

3. RESULTS AND DISCUSSION

3.1 For Square Section

Analysis of square section for various loads are given in fig. 2 and table 1.

Fig. 2. Results analysis of deflection and stress for square section.




Table1.Results of deflection and stress for square section at various loads.

S No Load (N) Deflection (mm) Stress (MPa)

1 8000 6.52 4.09

2 10000 8.14 5.12

3 12000 9.77 6.14

4 14000 11.40 7.16

3.2 Circular Section

Results analysis for circular section are given in fig. 3 and table 2.

Fig. 3. Results analysis of deflection and stress for circular section.

Table 2. Results of deflection and stress for circular section at various loads.


1 8000 7.11 5.89

2 10000 8.89 6.23

3 12000 10.67 6.89

4 14000 24.10 7.38

3.3 Hollow Circular Section

Results analysis for hollow circular section are given in fig. 4 and table 3.




Fig. 4. Results analysis of deflection and stress for hollow circular section.

Table 3. Results of deflection and stress for hollow circular section at various loads.


1 8000 12.051 6.21

2 10000 15.064 6.78

3 12000 18.077 7.01

4 14000 21.090 7.45

3.4 Hollow Square Section

Results analysis for hollow square section are given in fig. 5 and table 4.

Fig. 5. Results analysis of deflection and stress for hollow square section.

Table 4. Results of deflection and stress for hollow square section at various loads.

S No Load (N) Deflection

(mm)

Stress (MPa)

1 8000 5.14 3.41

2 10000 6.42 4.26

3 12000 7.71 5.12

4 14000 8.99 5.17




3.5 I-section Beam

Results analysis for I-section of beam are given in fig.6 and table 5.

Fig.6. Results analysis of deflection and stress for I-section of beam.

Table 5. Results of deflection and stress for I- section at various loads.


1 8000 3.47 4.03

2 10000 4.34 5.03

3 12000 5.22 6.04

4 14000 6.08 7.04

3.6 Rectangular Section of Beam

Results analysis for rectangular section of beam are given in fig. 7 and table 6.

Fig. 7. Results analysis of deflection and stress for rectangular cross section of beam.




Table 6. Results of deflection and stress for rectangular cross section at various loads.


1 8000 3.75 4.187

2 10000 4.69 5.234

3 12000 5.63 6.281

4 14000 6.56 7.327

For various loading conditions on different cross section of beam, the results analysis for both

deflection and stress are determined and on increasing load values, both deflection and stress are

increased. From the graphs, the maximum and minimum deflectionare obtained in case of circular

cross section(CS) and I-section(IS) of beam respectively so I-section can resist more deformation than

others cross section loading and also failure will be less and maximum and minimum stress are

obtained in case of hollow circular section (HCD) and hollow square section (HSS) respectively.

0

5

10

15

20

25

30

SS CS HCS HSS IS RS

Def

lect

on

(m

m)

Cross-Section of beam

Fig 8. Deflection of beams for various cross section.

0

2

4

6

8

10

SS CS HCS HSS IS RS

Str

ess

(MP

a)

Cross-Section of beam

Fig 9. Stress of beams for various cross section.




4. CONCLUSIONS

After analysing of different cross section of beam for various loading conditions, I-section can sustain

more load followed by rectangular section, hollow square section, square section, hollow circular

section and circular section. I-section of beam will be reliable to use and also can sustain more

deformation than others cross section of beam.

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Documents

Finite Element Analysis of Stress and Deflection of Beam