Young's Modulus of Aluminium Beam
Solid Mechanics Lab Report
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
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
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