Question

Calculate the Young's modulus in the cantilever depression method used. The length of cantilever beam is 1m which is suspended with a load of 150 gm. The depression is found to be 4×10^-2m. The thickness of the beam is 5×10^-3m and breadth of the beam is 3×10^-2 m.
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Answer 1

Answer:

Length of cantilever, L=50cm=0.5m

Deflection at the end w(L)=15mm

Find: Deflection w(x) at 30cm from rigid end.

Depression at a point in a cantilever beam with load at one end is given by,w(x)=

6EI

Px

2

(3L−x)

We have,

w(L)

w(x)

=

3EI

PL

3

6EI

Px

2

(3L−x)

w(0.5m)

w(0.3m)

=

3EI

P(0.5)

3

6EI

P(0.3)

2

(3(0.5)−0.3)

This gives, w(0.3m)=6.48mm