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Question

For a case of plane stress, σx=40MN/m2,σy=0,τxy=80MN/m2. What are the principal stresses(inMN/m2) and their orientation with x and y axes?

A
σ1=80,σ2=40,θ1=30
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B
σ1=100,σ2=60,θ1=32
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C
σ1=102.5,σ2=62.5,θ1=36
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D
σ1=105,σ2=62,θ1=36
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Solution

The correct option is C σ1=102.5,σ2=62.5,θ1=36
Radius of Mohr's circle of stress,

r=(σxσy2)2+τ2xy

=(20)2+(80)2

2017MN/m2
The centre of Mohr's circle,

C=σx+σy2=40+02=20MN/m2

Major principal stress =C+r=20(1+17)

=102.5MN/m2

Minor principal stress =Cr=20(117)

=62.5MN/m2

Orientation, θ=12tan1(2τxyσxσy)=38
Although the orientaion given in the options is wrong, however the best choice will be (c).


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