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.
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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
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