SSC JE Mechanical Engineering 2017 Set 1 Paper

Question : 189 of 200

Marks: +1, -0

For an element under the effect of biaxial state of normal stress, the normal stresses are on 45° plane is equal to_____.

Solution:

The normal stress at inclined plane (θ = 45°)

σ_{45°}={σ_x+σ_y}/2{σ_x-σ_y}/2\cos2θ+t_{xy}\sin2θ

where,

t_{xy}=0;2θ=90°

we get,

σ_{45°}={σ_x+σ_y}/2×{σ_x-σ_y}/2\cos90°

σ_{45°}={σ_x+σ_y}/2

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