Young Modulus Experiment

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  • Topic: Young's modulus, Pascal, Moment of inertia
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  • Published : November 7, 2012
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Experiment 1: Young Modulus
Title:Bending of beam and coefficient of elasticity.
Objective: To study the relationship between load, span, width, height and deflection of a beam, places on two bearers and affected by a concentrated load at the centre.
:To ascertain the coefficient of elasticity for aluminium, brass and steel. Results:
Measurement of test specimen
(a) For beam material – Steel
| Length, L (mm)| Thickness, h (mm)| Width, b (mm)|
1st reading| 650| 3.15| 18.97|
2nd reading| 650| 3.11| 19.03|
3rd reading| 650| 3.12| 18.97|
Average reading| 650| 3.13| 18.99|

(b) For beam material – Aluminium
| Length, L (mm)| Thickness, h (mm)| Width, b (mm)|
1st reading| 650| 3.25| 19.15|
2nd reading| 650| 3.21| 19.23|
3rd reading| 650| 3.21| 19.18|
Average reading| 650| 3.22| 19.19|

(c) For beam material – Brass
| Length, L (mm)| Thickness, h (mm)| Width, b (mm)|
1st reading| 650| 3.31| 19.05|
2nd reading| 650| 3.34| 19.20|
3rd reading| 650| 3.35| 19.09|
Average reading| 650| 3.33| 19.11|
Two simple supports end.
(a) Deflection of test specimen [ Beam material-Steel ]

Mass(gram)| Load (N)| Deflection #1 (mm)| Deflection #2 (mm)| Deflection #3 (mm)| Average Deflection (mm)| 100| 0.981| 0.35| 0.45| 0.48| 0.43|
200| 1.96| 0.85| 0.88| 0.85| 0.86|
300| 2.94| 1.30| 1.32| 1.38| 1.33|
400| 3.92| 1.74| 1.80| 1.81| 1.78|
500| 4.91| 2.20| 2.24| 2.25| 2.23|

(b) Deflection of test specimen [ Beam material-Aluminium ]

Mass(gram)| Load (N)| Deflection #1 (mm)| Deflection #2 (mm)| Deflection #3 (mm)| Average Deflection (mm)| 100| 0.981| 1.18| 1.15| 1.16| 1.16|
200| 1.96| 2.43| 2.54| 2.40| 2.46|
300| 2.94| 3.72| 3.67| 3.72| 3.70|
400| 3.92| 4.98| 5.08| 5.10| 5.05|
500| 4.91| 6.07| 6.20| 6.15| 6.14|

(c) Deflection of test specimen [ Beam material-Brass ]

Mass(gram)| Load (N)| Deflection #1 (mm)| Deflection #2 (mm)| Deflection #3 (mm)| Average Deflection (mm)| 100| 0.981| 1.02| 0.97| 0.90| 0.96|
200| 1.96| 1.80| 1.78| 1.74| 1.77|
300| 2.94| 2.67| 2.78| 2.66| 2.70|
400| 3.92| 3.49| 3.57| 3.52| 3.53|
500| 4.91| 4.37| 4.41| 4.37| 4.41|

One fixed end and one simple support end.
(a) Deflection of test specimen [ Beam material-Steel ]

Mass(gram)| Load (N)| Deflection #1 (mm)| Deflection #2 (mm)| Deflection #3 (mm)| Average Deflection (mm)| 100| 0.981| 0.26| 0.23| 0.27| 0.25|
200| 1.96| 0.48| 0.45| 0.47| 0.47|
300| 2.94| 0.69| 0.70| 0.70| 0.70|
400| 3.92| 0.97| 0.88| 0.88| 0.89|
500| 4.91| 1.15| 1.12| 1.12| 1.13|

(b) Deflection of test specimen [ Beam material-Aluminium ]

Mass(gram)| Load (N)| Deflection #1 (mm)| Deflection #2 (mm)| Deflection #3 (mm)| Average Deflection (mm)| 100| 0.981| 0.60| 0.67| 0.69| 0.65|
200| 1.96| 1.28| 1.19| 1.20| 1.22|
300| 2.94| 1.80| 1.80| 1.82| 1.81|
400| 3.92| 2.37| 2.43| 2.45| 2.42|
500| 4.91| 2.97| 2.98| 3.01| 2.99|

(c) Deflection of test specimen [ Beam material-Brass ]

Mass(gram)| Load (N)| Deflection #1 (mm)| Deflection #2 (mm)| Deflection #3 (mm)| Average Deflection (mm)| 100| 0.981| 0.47| 0.42| 0.48| 0.46|
200| 1.96| 0.90| 0.86| 0.86| 0.87|
300| 2.94| 1.30| 1.28| 1.30| 1.29|
400| 3.92| 1.73| 1.70| 1.71| 1.71|
500| 4.91| 2.14| 2.14| 2.13| 2.14|

Calculations:
* Two simple supports end
To calculate the moment of inertia :
I = bh312
I = Moment of Inertia ( m4 )
b = Width of beam ( m )
h = Thickness of beam ( m )
To determine the beam Young modulus :
E = Fδ(L348I)
E = Young modulus ( Pa )
F = Force/load applied ( N )
δ = Deflection ( m )
L = Beam length ( m )
I = Moment of Inertia ( m4 )...
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