# Young's Modulus of Aluminium Beam

Experiment to determine the Young’s modulus of an aluminium cantilever beam and the uncertainties in its measurement 1. Abstarct: The young’s modulus E, is a measure of the stiffness and is therefore one of the most important properties in engineering design. It is a materials ratio between stress and strain: E=σε

Young’s modulus is a unique value for each material and indicates the strength of that material as well as how it will deform when a load is applied.

2. Introduction: The Young’s Modulus can only be derived experimentally, there are no theoretical methods by which the young’s Modulus of a material can be calculated therefore in this experiment our aims were: * To calculate the Young’s modulus ,E of Aluminium from measurement of the end deflection of cantilever beam of aluminium loaded at its free end * To assess the accuracy and precision of this method by comparing the calculated value of E to the known value Eal=72.6 GPa * To measure the deflected shape of the aluminium beam for one loading condition (15N) and to compare this with the theoretical prediction of the beam bending theory for deflection of a cantilever

yx= PL32EIxL2-13xL3

3. Materials and Methods

The apparatus shown below was set up and the following equipments were used: * Dial gauge was used to measure deflection of the beam

* Magnetic clamp stand (not to affect the bending of the beam) * Solid Aluminium Beam

* 15 Weights(1N each)

* Clamp to keep it still at one end.

* Steel base

4.Results

1. Load/Deflection behaviour :Equation to calculate the young’s Modulus from the slope of deflection vs. load graph E= 4L3bd3(slope)

We measured the length (L) the width (d) and the breadth (b) of the beam 5 times and then calculated the average: Average Length/mm| Average width/mm| Average breadth/mm| 998| 25.28| 15.73|

The uncertainties of the slope, length, breadth and width were estimated using the rage...

References: The equations were obtained from the HSDM Solid Mechanics Laboratories Booklet & Solid Mechanics lecture notes

The uncertainties information and methods from “Experimental Methods” by Les Kirkup

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