GATE Mechanical Engineering (ME) 2020 Shift 2 Solved Paper

Question : 54 of 65

Marks: +1, -0

A cantilever of length I, and flexural rigidity EI, stiffened by a spring of stiffness

{k}

, is loaded by a transverse force

P

, as shown.

The transverse deflection under the load is

Solution:

-\;{P L^{3}}/{3 E I}+\;{R_{S} L^{3}}/{3 E I}=\;{-R_{S}}/{K}

R_{S} \;{1}/{K}+\;{L^{3}}/{3 E I}=\;{P L^{3}}/{3 E I}

=\;{-P L^{3}}/{3 E I}+\;{R_{S} L^{3}}/{3 E I}=\;{-P L^{3}}/{3 E L}

\;{R_{S}}/{1} \;{P L^{3}}/{3 E I} ×(\;{3 E I K}/{3 E I+K L^{3}})

δ=\;{P L^{3}}/{3 E I+K L^{3}}

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