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Principal stresses at a point are 80 N/mm2 and 40 N/mm2, both tensile. The yield stess in simple tension for this material is 200 N/mm2. The value of factors of safety according to maximum principal stress theory and maximum shear stress theory, respectively, are

A
2.5 and 2.5
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B
2.5 and 5
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C
5 and 5
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D
5 and 1.67
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Solution

The correct option is A 2.5 and 2.5

σ1=80N/mm2

σ2=40N/mm2

σ3=0
According to maximum principal stress theory,

σ1σyFOs

FOS=20080=2.5
According to maximum shear stress theory

τmax,absoluteσy2×FOS

σ1σ32σy2×FOS

8002=2002×FOS

FOS=2.5


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