GATE Civil Engineering (CE) 2019 Shift 2 Solved Paper

Question : 54 of 65

Marks: +1, -0

For a plane stress problem, the state of stress at a point P is represented by the stress element as shown in the figure.

By how much angle (θ) in degrees the stress element should be rotated in order to get the planes of maximum shear stress?

Solution:

Coordinates of

C=(\;{80-20}/{2}, \;{25-25}/{2})

=(30,0)

△ {ABC}

{BC}=80-30=50 {MPa}

{AB}=25 {MPa}

α=\tan ^{-1}(\;{25}/{50})=26.56^{∘}

∴ \;\; θ=90^{∘}-α=63.44^{∘}

Angle to be rotated

=\;{θ}/{2}=\;{63.44}/{2}=31.7^{∘}

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