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Beam Bending and Superposition

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Beam Bending and Superposition

Page 1 of 9
School of Mechanical and
Aerospace Engineering
Ashby Building
Stranmillis Road
Belfast
BT9 5AH

Stage 1 Laboratory Report

Beam Bending and Superposition

Author
TutorProf. Menary
Semester1
Date28/11/2011

Summary

An investigation into beam bending and superposition. Being able to analyse how beams bend is an essential tool for all engineers. By using mathematics and material properties, engineers are able to compute structural deformation thus verifying a structures fitness for use. In this experiment a simply supported beam of aluminium is loaded with point forces in three different cases. A clock gauge is positioned in the middle of the beam to measure the deflection. The results of a complex arrangement of forces can be deduced by the superposition of more simple cases. Superposition is possible only when the response of the structure is linear, e.g. when deflection is directly proportional to the applied load. Also the experimental and theoretical deflections of the beam will be compared and a percentage error obtained. There was a second test performed in this investigation demonstrating the influence the 2nd moment of area, also known as the second moment of inertia, had on the load carrying capacity of the beam. The results from test 1 show that it is possible to deduce the deflection of the beam when loaded with point forces by superposition. Results from test 2 show that the deflection of a beam is influenced greatly by its moment of inertia, i.e. with a greater value of inertia there is a smaller deflection.

Contents
Page
Nomenclatureii
Introduction1
Apparatus and Procedure5
Results6
Discussion10
Conclusions11
References11
Bibliography11
.

Nomenclature

Symbols:
EYoung’s Modulus (Pa)
LLength of beam (m)
bBreadth of beam (mm)
dDepth of beam (mm)
ISecond moment of inertia (m4)
FForce (N)
δ Deflection (mm)

Introduction

Due...