GATE Civil Engineering (CE) 2018 Shift 1 Solved Paper

Question : 11 of 65

Marks: +1, -0

A solid circular beam with radius of

0.25 {m}

and length of

2 {m}

is subjected to a twisting moment of

20 {kNm}

about the z-axis at the free end, which is the only load acting as shown in the figure. the stress component

τ_{x y}

at Point 'M' in the cross-section of the beam at a distance of

1 {m}

from the fixed end is

Solution:

The only non-zero stresses are

τ_{θ z}=τ_{z θ}=τ

, if

θ

90^{∘}

then

θ=y

Hence

τ_{z y}=τ_{y z}=τ_{\max }=16 {T} \/ π {d}^{3}=0.815 {MPa}

But in rest of the planes shear stresses are zero, hence,

τ_{x y}=τ_{y z}=0

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