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International Journal of Mechanical Engineering and Technology (IJMET) Volume 6, Issue 7, Jul 2015, pp. 21-28, Article ID: IJMET_06_07_004

Available online at

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ISSN Print: 0976-6340 and ISSN Online: 0976-6359

© IAEME Publication

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NUMERICAL STUDY ON STRESS

ANALYSIS OF CURVED BEAMS

D. Bharadwaj

M. Tech. CAD/CAM Student,

Sreenidhi Institute of Science &Technology, Hyderabad, India

A. Purushotham

Professor, Sreenidhi Institute of Science &Technology, Hyderabad, India

ABSTRACT

The static analysis of naturally curved beams with closed thin walled cross

section has many important applications in mechanical, civil and aeronautical

engineering. Many of the curved beams subjected to bending moment find in

real life applications .Due to bending moment, tensile stresses developed in

one portion of the section and compressive stresses in other portion of cross

section. The analytical computation to determine these stresses are more

complex, therefore in this paper we attempted the determination of stresses

and deflection of curved beams when it is subjected to bending moment with

the help of ansys software. The result obtained from ansys software is

validated with the simplified stress equations of curved beams developed by

the other researchers. The material selected for curved beams for simulation

studies is isotropic ductile material. The geometry of curved beams is

described with central included angle in this paper. The work carried out

exhaustively covers the estimation of stresses in quarter circle beam, semi

circle beam, three quarter circle beam and full circle beam. The methodology

adopted for simulation model briefed out step by step in this paper for further

studies of other researchers

Key words: Beams, Stress and Deflection

Cite this Article: Bharadwaj, D. and Purushotham, A. Numerical Study on

Stress Analysis of Curved Beams. International Journal of Mechanical

Engineering and Technology, 6(7), 2015, pp. 21-28.

http://www.iaeme.com/IJMET/issues.asp?JTypeIJMET&VType=6&IType=7

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1. INTRODUCTION & LITERATURE SURVEY

The determination of stress and displacement in a rectangular cross section curved

beam will play very important role in many structural problems. Many researchers

D. Bharadwaj and A. Purushotham


attempted previously with the help of simple beam theory adopted for straight beams.

In 1968 Gaydon [1] has discussed the problem of rectangular cross section curved

beam with boundary loadings. His work was totally on analytical complex expression.

Sarma et al (1975) [2] simplified the expressions developed by previous authors some

extent by adopting Eigen function for the solution of stress problems of curved beams

[3, 4]. Dym, C. L. and Williams [5] proposed stress and displacement expressions for

curved arcs which are more suitable to write finite element equations in 2011. ERIK

PERSSON [6] utilized MATLAB/CALFEM software’s to determine stress and

deflections of structures made up of curved beams. He also compared the results with

the analytical expressions developed by previous authors to simplify the problem of

stress analysis of curved beams of rectangular cross section; we developed ansys FEA

modeling in this paper. This work helps researchers to determine stresses quickly as

per their requirement of beam size and material.

The paper is organized in the following manner: section 2 describes the geometry

of the beam and load condition on it. It also covers the finite element model of curved

beam. Section 3 discusses the results obtained from the ansys simulation study made

on the curved beam with different loading condition. Conclusions are finally drawn in

the section 4.

2. GEOMETRY AND FEA MODELING OF CURVED BEAMS

The cross section selected for curved beam is a rectangle having width: 40 m height:

20 mm. The outer and the inner diameter of curved beam are respectively 310 mm

and 300 mm. The material used for curve beam is carbon steel of young’s modulus

2*105 MPa and poison ratio 0.3. The geometry of curved beam in ansys software. The

sequential steps used to form geometry of curved beam are given below:

Step: 1 we need to select create option

Step: 2 we need to select Areas

Step: 3 we have to select annulus circle

Step: 4 after selecting annulus circle we need to select rectangle

Step: 5 we will get the required curved beam

If we follow above steps the curved beam geometric model appears as shown in

Figure 1.

The FEA model of the curved beam is worked out with the following sequential

steps in ANSYS:

Step: 1 choose the element type solid quadnode82

Step: 2 real constants are default

Step: 3 apply material properties by giving young’s modulus and Poisson ratio

Step: 4 sectioning width: 40 depth: 20

Step: 5 follow the modeling steps given above

Step: 6: Adopt meshing mesh tool smart size

The FEA model obtained with the above steps is shown in the Figure 2.

Numerical Study on Stress Analysis of Curved Beams


Figure 1 Semi circular arc before meshing

Figure 2 Mesh model of semi circle arc

3. RESULTS AND DISCUSSIONS

In this section the numerical study on deflection and stresses developed in circular arc

rings subjected to different loading is covered. There are eight different arcs of rings

considered for the study. The rectangular cross section beam is selected with the

dimension 40 mm and 20 mm. Figure 3 shows the ansys numerical results on four

different circular beams whose circular included angles are 180°,360°,90° and 270°.

Here every circular plate was loaded with 5 N force. It is found that semi circular

beam experienced maximum stress value up to 100 MPa while three fourth circled

beams encountered less stress value 47 MPa. Figure 4 shows the numerical results of

stresses and deflections of the four circular beams that are taken for simulation study

earlier example. Here the load taken on the model is 10 N, but here the numerical

studies shows the maximum stress induced is in full circular beam.

Set of Figures shown in Figure 5 predicts the stress and deflection values of four

different circular plates when they are subjected to the bending load of 15 N.Here also



the maximum stresses are induced in a plate where circular arc included angle is 360

degrees.

Figure 3 stress and deflection values of various curved beams with load 5 N.




Similarly the simulation studies are run on all four circular beams with the load 20

N and the obtained results are shown in Figure 6 here the maximum stresses are

developed in full circle beam having the value 176 MPa.

The simulation studies are also worked out by changing arc included angle from

zero degrees to 270 degrees for different loads ranging from 5 N to 20 N.The results

are included in the form of graphs shown in fi

Figure 7 Variation of stresses with the change of included arc angle of beams.

The stress ratio are also caluculated as the ratio between maximum stress to

minimum stress on every curved beam when loads are changed from 5 N to 20 N.The

results of the variation of the stresses are shown in the Figure 8.

The variation of stress ratio with the arc included angle is shown in the Figure 9. It

is observed from this Figure that the stress ratio in all loading conditions on various

curved beams found to be more than two and less than three.It implies that the

bending stresses increses to minimum twice of the nominal stresses induced in

straight beam.It is also found that the maximum stress ratio is on semi circular curved

beam.

50 100 150 200 250 300 350 40080

100

120

140

160

180

200

220

240

260

280

Angle of arc , Degrees

Str

ess,

MP

a

Load :20N

50 100 150 200 250 300 350 40090

100

110

120

130

140

150

160

170

180

angle of arc,Degrees

str

ess M

PA

load:15N

50 100 150 200 250 300 350 40040

50

60

70

80

90

100

angle of arc,Degrees

str

es

s

MP

A

Load:5N

50 100 150 200 250 300 350 40020

30

40

50

60

70

80

90

100

110

Angle of arc,Degrees

Str

es

s M

PA

Load:10N


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Figure 8 variaton of stresses with different loads on four curved beams

Figure

4. CONCLUSIONS

After realizing the difficulty for the

beam by different authors, this paper finds numerical solutions to get stresses and

deflections in a curved beam with the help of ansys software. The magnitude of

curvature of the beam is described with arc

developed, by changing curved angles from 0

analysis on curved beam following conclusions are made.

to be maximum when a circular arc being subjected to a

analysis is carried out on semi circular beam subjected to similar load conditions as

that of other circular beams, it is found that maximum stress values are developed

than the other cases. 3)The stress factor that is the ratio of ma


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variaton of stresses with different loads on four curved beams

Figure 9 variation of stress ratio arc angles

After realizing the difficulty for the estimation of stresses and deflections in curved



curvature of the beam is described with arc angle and various ansys models are

developed, by changing curved angles from 0° to 90°

to 180°

to 270°. After the ansys

analysis on curved beam following conclusions are made. 1)The stress values found

to be maximum when a circular arc being subjected to a bending load.



3)The stress factor that is the ratio of maximum stress to

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variaton of stresses with different loads on four curved beams

estimation of stresses and deflections in curved



angle and various ansys models are

. After the ansys

1)The stress values found

bending load. 2)When



ximum stress to



minimum stress also calculated for full circle, semi circle, quarter circle, three fourth

circular beams. when loads fluctuates from 5 N to 20 N. It is found that the stress

factor 4.1 which is high in the case of load condition 10 N. The procedure adopted in

this paper for modelling various types of circular beam. It is helpful to test

numerically the stress values of various shapes of curved beams.

ACKNOWLEDGEMENTS

The authors thank the Head of the Mechanical Engineering, Principal and Director

Sreenidhi Institute of Science and Technology (SNIST) Hyderabad for their support

and permission to carry out this research thesis work.

REFERENCES

[1] Gaydon, F. A. The rectangle under general equilibrium loading in generalized

plane stress. Proc. R. Soc. A, 283, 1968, pp. 356

[2] Sarma, P. V. B. A. S., Ramachandra Rao, B. S. and Gopalacharyulu, S.

Eigenfunction, 1975.

[3] Solution for plane stress problems of curved beams. Int. J. Engng. Sci., 13. pp.

149–59.

[4] Debnath, V. and Debnath, B. Deflection and Stress Analysis of A Beam on

Different Elements Using Ansys APDL. International Journal of Mechanical

Engineering & Technology IJMET, 5(6), 2014, pp. 70–79.

[5] Dym, C. L. and Williams, H. L. Stress and Displacement estimates for Arches.

Journal of Structural Engineering, 137(1), 2011.

[6] Persson, E. Stress and strength analysis of curved glulam beams with box cross

section Masters Dissertation LUND University, 2012.

numerical study on stress analysis of curved · pdf fileand deflection of curved beams when it...

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