GATE 2016 ME (ME3) – Question 18

Mechanics of Materials · Transformation of stress and strain, Mohr circle · 1 mark · Multiple choice

The stress state in Figure (a) is represented in the coordinate system of Figure (b). The components $(\tau_{xx},\tau_{yy},\tau_{xy})$ are ______.

Diagram for GATE 2016 ME (ME3) question 18

$(p/\sqrt2,-p/\sqrt2,0)$
$(0,0,p)$
$(p,-p,p/\sqrt2)$
$(0,0,p/\sqrt2)$

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Correct answer: (B) $(0,0,p)$

Explanation

With principal stresses+p and−p, mean normal stress is zero. At45degrees, the transformed normal stresses vanish because cos90degrees=0; the shear magnitude is(p−(−p))/2=p. The directions in the figure correspond to **B**, a state of pure shear.