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:
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
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
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... [continues]
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