GATE Civil Engineering (CE) 2018 Shift 1 Solved Paper

Question : 64 of 65

Marks: +1, -0

A cantilever beam of length

2 {m}

with

{a}

square section of side length

0.1 {m}

is loaded vertically at the free end. The vertical displacement at the free end is 5

{mm}

. The beam is made of steel with Young's modulus of

2.0 × 10^{11} {N} \/ {m}^{2}

. The maximum bending stress at the fixed end of the cantilver is

Solution:

I=\;{(0.1)^{4}}/{12}

Deflection

δ=\;{P I^{3}}/{3 E I}

⇒ 5 × 10^{-3} {m}=\;{P(2)^{3}}/{3 × 2 × 10^{11} × \;{(0.1)^{4}}/{12}}

⇒ \;\; P=3125 {N}

Now,

\;\; M=P I \;\; =3125 × 2=6250 {Nm}

As,

\;\; \;{M}/{I}=\;{σ}/{y}=\;{E}/{R}

⇒ σ_{\max } \;\; =\;{M}/{Z}=\;{6250}/{{(0.1)^{3}}/{6}}=37.5 × 10^{6} {N} {/} {m}^{2}

\;\; =37.5 {MPa}

Go to Question:

Prev Question

Next Question