Project ForgeStrength of Materials
Stress & Strain
GATE 2014
Medium
The state of stress at a point is given by σx=−6 MPa, σy=4 MPa, and τxy=−8 MPa. The maximum tensile stress (in MPa) at the point is __________.
8.43 MPa(± 0.1 accepted)
Explanation
Maximum principal stress σ1 = (σx+σy)/2 + √(((σx−σy)/2)²+τxy²) = (−6+4)/2 + √(((−6−4)/2)²+(−8)²) = −1 + √(25+64) = −1+√89 ≈ −1+9.434 ≈ 8.43 MPa.
Source: GATE ME 2014 (Session 1 / Set-1) (2014)
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