In a two-dimensional stress analysis, the state of stress at a point {P} is [\sigma]=[\table \sigma_{xx} , \tau_{x y} ; \tau_{x y} , \sigma_{y y}] The necessary and sufficient condition for existence of the state of pure shear at the point P, is

Correct Answer is : σxx+σyy=0

(\sigma_{x x}-\sigma_{y y})^{2}+4 \tau_{x y}^{2}=0

\sigma_{x x}+\sigma_{y y}-\tau_{x y}^{2}=0

GATE Civil Engineering (CE) 2020 Shift 1 Solved Paper

Question : 12 of 65

Marks: +1, -0

In a two-dimensional stress analysis, the state of stress at a point

{P}

[σ]=[\table σ_{xx} , τ_{x y} ; τ_{x y} , σ_{y y}]

The necessary and sufficient condition for existence of the state of pure shear at the point

P

, is

Solution:

σ_{1}=-σ_{2}

σ_{1}=\;{σ_{x x}+σ_{y y}}/{2}+

Radius

σ_{2}=\;{σ_{x x}+σ_{y y}}/{2}-

Radius

\;{σ_{ {xx}}+σ_{ {yy}}}/{2}+

Radius

=-[[\;{σ_{ {xx}}+σ_{ {yy}}}/{2}]-

Radius

]

σ_{x x}+σ_{y y}=0

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