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...

(1)