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### Mechanics of Materials

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# Mechanics of Materials

By | September 2012
Page 1 of 10
Experiment 7: Deflection of beams (Effect of beam length and width)

1.OBJECTIVE
The objective of this laboratory experiment is to find the relationship between the deflection (y) at the centre of a simply supported beam and the span, width.

2.MATERIALS - APPARATUS
Steel Beams, Deflection measuring device, 500g weight

3.INTRODUCTORY INFORMATION
The deflection of a beam, y, will depend on many factors such as: -

• The applied load F (F=m•g).
• The span L.
• The width of the beam b, and its thickness h.

Other factors such as position, method of loading, the material of which the beam is made will also influence the deflection.

If we wish to find the relationship between y and one of the possible variables it is necessary to keep all the other possible variables constant throughout the experiment.

1. Length calculation
In this experiment the same beam is used throughout and the centrally applied point load is kept constant.

Thus keeping all possible variables other than the deflection y and the span L constant we may investigate the relationship between y and L.

Let y[pic]Ln where n is to be found
Then y = k•Ln where k is a constant
Taking logarithms:
log y = n log L + log k which is in the straight line form (y = mx + C). Thus plotting logy against log L will give a straight-line graph of slope “n” and “k” may be determined.

2. Width calculation

In this experiment beams of the same material but of different width are used. The span and loading are kept the same for each beam. Hence keeping all possible variables other than width and deflection constant the relationship between y and b is determined.

Let y[pic]bn where n is to be found.
Then y = k•bn where k is a constant.
Taking logarithms,
log y = n log b + log k which is in the straight line from : (y = mx + C). Thus plotting logy against log b will give a straight line of slope “n” and “K” may be determined. 4.1PROCEDURE (Length calculation)...

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