Question

# The strain measurement from a rectangular strain rosette were ε0=900×10−6,ε45=750×10−6 and ε90=300×10−6. The magnitude of minimum and maximum principal strain respectively is:

A
264.59×106,935.41×106
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B
935.41×106,264.59×106
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C
623.61×106,176.39×106
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D
176.39×106,623.61×106
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Solution

## The correct option is A 264.59×10−6,935.41×10−6 ε0=900×10−6 ε45=750×10−6 ε90=300×10−6 We know that, ε45=εx+εy2+εx−εy2 cos (2×45)+γxy2 sin (2×45) ⇒ 750×10−6=900×10−6+300×10−62+0+γxy2×1 ⇒ γxy=300×10−6 ⇒ εmax/min=εx+εy2±√(εx−εy2)2+(γxy2)2 =⎡⎣900+3002±√(900−3002)2+(3002)2⎤⎦×10−6 εmax=935.41×10−6 εmin=264.59×10−6

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