1.a concentrated load p is applied at the end of cantilever.the crosssection of the beam is a square of side "a" and with a hole of diameter "a/2" then deflection at the tip of beam is?lengh of beam is L.

Question

1.a concentrated load p is applied at the end of cantilever.the crosssection  of the beam is a square of side "a" and with a hole of diameter "a/2" then deflection at the tip of beam is?lengh of beam is L.

MathMate · Accepted Answer

The deflection of a cantilever beam with a point load P at the end is given by
δx=PL³/(3EI)

P=point load
L=length
E=modulus of elasticity
I=area moment of inertia
all in compatible units.

The area moment of inertia for the beam in question is equal to that of the square less that of the hole.

Area moment of inertia:
I=bh³/12) (b=width, h=height)
and for a circle of radius r
Ic=πr⁴/4

For other shapes, see:
http://en.wikipedia.org/wiki/List_of_area_moments_of_inertia

So for the beam in question,
I=a⁴/12-πa⁴/1024

and the deflection can be calculated accordingly.