A cantilever of rectangular cross-section has a
length of 50 cm. its breadth is 3 cm and
thickness 0.6 cm. a weight of 1 kg is attached at
the free end. The depression produced is 4.2 cm.
calculate Young’s modulus of the material of the
bar. (g=9.8m/sec
2
)
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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
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