assignment 8 v2

8/13/2019 Assignment 8 v2

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Atn zgrAhmet Uur Birinci 12.12.2013

ME 482 ASSIGNMENT 8

INTRODUCTION

The main aim of the assignment is to investigate a uniformly loaded and simply

supported beam. The beam is made of steel, it is 0.5m in length and the cross section is 50

mm deep by 10 mm wide. The uniform load is a pressure of 2 N/mm2.

The main objectives are; to find out the effects of type of supports, namely pin-pin,

pin-roller, to study the effect of placement of supports, namely neutral axis, bottom fibers and

to compare structural and continuum elements.

ANALYSIS OF THE MODEL

Preliminary Analysis (Beam Theory):


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Finite Element Analysis

The material is steel with 210 MPa Youngs modulus and 0.3 Poissons ratio.For the pin supports, pinned boundary condition is applied; for the roller supports,

displacement boundary condition in y-direction is applied.

For continuum elements, 75 elements gave out 0.733 mm deflection, 250 elements

gave out 0.776 mm deflection. The mesh was considered to be converged at 250 elements.

For beam elements, 25 elements gave out 0.743 mm deflection, 50 elements gave out

0.744 mm deflection. The mesh was considered to be converged at 50 elements.

Maximum bending stress, maximum deflection and the reaction at supports were

investigated for CPS8R, B23 and B22 elements. The cases where pin-roller and pin-pin

supports are applied at neutral axis and at the bottom were considered. The reaction force was

scaled by multiplying by 10 to account for the 2D modeling of the beam. The results were

compared with beam theory solutions.

Deflection for 75 elements

Deflection for 250 elements


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Stress for CPS8R pin-pin supports at neutral axis

Stress for B23 pin-pin supports at the bottom

Stress for B23 pin-roller supports at the bottom


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Table.1 Maximum Stress, Maximum Deflection and Reaction Force Values

RF (N)

Beam Theory 150 0.744 5000

Pin-Roller

CPS8R

n.a 150 0,763 5000B23n.a 150 0,744 5000

B22n.a 150 0,763 5000

CPS8RBottom 150 0,776 5000

B23Bottom 150 0,744 5000

B22Bottom 150 0,763 5000

Pin-Pin

CPS8Rn.a 150 0,763 5000

B23n.a 150 0,744 5000

B22n.a 150 0,763 5000

CPS8R

Bottom 99 0,372 5000, 10750*B23Bottom 50 0,298 5000, 12500*

B22Bottom 50 0,316 5000, 12500*

* The reaction forces in x and y-direction respectively.

Table.2 Shear Stress Effect

Pin-RollerNeutral Axis

CPS8R 10 1 1,02

5 1,008 1,132 0,94 5,45

1 0,92 47,1

B23 10 1 1

5 1 1

2 1 1,2

1 1 1

B22 10 1 1,02

5 1 1,11

2 1 1,94

1 1 3,55


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CONCLUSIONS

Pin-pin supporting can give the same results as pin-roller supporting if the pins are

applied at the neutral axis. If the pins are applied at the bottom, stress concentration occurs at

the pins, this results in less stress at the outer fibers.All the cases except for the pin-pin support at the bottom give out the same maximum

bending stress with the beam theory. Maximum deflections are also accurate considering the

beam theory solution to be true.

For L/h = 10 and L/h = 5, all three elements give results consistent with the beam

theory. For L/h < 5, beam theory fails to function. Beam elements give close results to the

beam theory but the continuum elements give very different results for the maximum

deflection. It is better to use continuum elements for L/h < 5.

assignment 8 v2

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