DEFLECTION OF CANTILEVERS

 

AIM

to verify the use of simple bending theory for calculating the deflection of a cantilever 

APPARATUS

Beam bending equipment/elastic beam apparatus and support with clamping fixtures hanger clamp, hanger link, thicker steel beam, dial indicator, load writing material.

 DAIGRAM

PROCEDURE

lock that actuator arm to the left hand  end support and clamp to the thicker steel strip in the position as shown above so that it forms a cantilever.

Fix the lever clamp 0.3m from the fixed support and set up dial gauge over it. If the self-weight of the hanger and cantilever causes undue initial deflection  adjust the locking screw to rotate the clamped end clockwise, taking the cantilever as set up to be in “no load” condition, read the dial guage.

Apply load in increment of 0.5N up to about 5N, reading the dial guage  at each load. Plot the graph of deflection against load. Increase the cantilever length of 0.4m, 0.5m and 0.6m in turn and repeat the above procedure.

For one selected length of cantilever, say 0.3m change the steel strip for a strip of another material and take a new set of load-deflection readings.

Note the cross sectional dimensions of both strips.

Finally, keep the dial guage at a fixed distance from the support, find the deflection at the dial quage due to 5N load applied at different positions along the cantilever as in diagram above 

Result

From the graph obtain thhe best fit linear relationshiop between displacement  and load for the first part of the experiment using the steel strip. Campare  the gradients with the theoretical values given by:

Deflection of end load = y=           

Use the gradients to show that the deflection is proportional to L3 either by ploting a graph (e.g log y against log L) or by a tabular comparison.

Observation

comment on the accuracy of the theoretical results.

Conclusions: with what degree of accuracy can the simple theory of bending be used to predict the deflection of a cantilever?


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