Question

A cantilever of length 3m is carrying a poin load of 50kn at a distance of 2m from the fixed end if I = 1 x 108 mm4 and E=2 x 105 N/mm2 find slope and deflection at the free end.

Answer 1

Thus the slope is 0.005 rad and the deflection is YB = 11.67 mm

Explanation:

Length = 3 m = 3000 mm

W = 50 KN = 50000 N

a = 2 m = 2000 mm

I = 10^8 mm^4

E = 2 x 10^5 N / mm^2

(1) Slope θB = Wa^2 / 2EI = 50000 x 2000^2 / 2 x 2 x 10^5 x 10^8

θB = 0.005 rad

(2) Deflection:

YB = 50000 x 2000^3 / 3 x 2 x 10^5 x 10^8 + 50000 x 2000^2 / 2 x 2 x 10^5 x 10^8 ( 3000 - 2000 )

YB = 11.67 mm

Thus the slope is 0.005 rad and the deflection is YB = 11.67 mm