GATE Mechanical Engineering (ME) 2019 Shift 2 Solved Paper

Question : 30 of 65

Marks: +1, -0

Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of 100 MPa along the length direction. Assume plane stress conditions in the plane normal to the thickness. The Young's modulus

E=200 {MPa}

and Poisson's ratio

v=0.3

are given. The principal strains in the plane of the sheet are

$(0.5,0.0)$
$(0.35,-0.15)$
$(0.5,-0.5)$
$(0.5,-0.15)$

Validate

Solution:

E_{1}=\;{σ_{1}}/{E}-µ \;{σ_{2}}/{E}=\;{100}/{200}-0.3 × \;{0}/{200}=0.5

E_{2}=\;{σ_{2}}/{E}-µ \;{σ_{1}}/{E}=\;{0}/{200}-0.3 × \;{100}/{200}=-0.15

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