GATE Mechanical Engineering (ME) 2019 Shift 2 Solved Paper

Question : 65 of 65

Marks: +1, -0

A horizontal cantilever beam of circular cross-section, length

1.0 {m}

and flexural rigidity

{EI}=200

m^{2}

is subjected to an applied moment

M_{A}=1.0 {N}- {m}

at the free end as shown in the figure. The magnitude of the vertical deflection of the free end is

{mm}

(round off to one decimal place).

Solution:

When the cantilever beam is subjected to moment at the free end, then the deflection at the free end is given by

y_{(\;\text "free end "\;)}=\;{M L^{2}}/{2 E I}

So,

y_{\;\text "(free end) "\;}=\;{1 × 1^{2}}/{2 × 200}=2.5 × 10^{-3} {m}=2.5 {mm}

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