GATE Mechanical Engineering (ME) 2019 Shift 1 Solved Paper

Question : 52 of 65

Marks: +1, -0

Consider an elastic straight beam of length

L=10 π {m}

, with square cross-section of side

a=5

{mm}

, with Young's modulus

{E}=200 {GPa}

. This straight beam was bent in such a way that the two ends meet, to form a circle of mean radius R. Assuming that Euler-Bernoulli beam theory is applicable to this bending problem, the maximum tensile bending stress in the bent beam is ___________ MPa

Your Answer:

Validate

Solution:

The beam of length

L=10 π {m}

is bent to form a circle of mean radius

R

.
Then,

L=2 π R

⇒ 10 π=2 π R

{Or}, {R}=5 {m}

y=2.5 {mm}

[since cross section is square with side

5 {mm}

]
According to Euler-Bernoulli beam theory

\;{M}/{I}=\;{σ}/{y}=\;{E}/{R}

Using,

σ=\;{E y}/{R}=\;{200 × 10^{2} × 2.5}/{5 × 10^{2}}=100 M P a

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