To determine The failure (yielding) has occurred on the basis of the maximum shear stress theory. Explanation Given information: The components of plane stress at a critical point on a thin steel shell are σ x = 70 MPa, σ y = − 60 MPa , and τ x y = 40 MPa . Calculation: Consider the yield stress for the steel is σ Y = 250 MPa . Find the principal stresses in complex system as shown below. σ 1 , 2 = σ x + σ y 2 ± ( σ x − σ y 2 ) 2 + τ x y 2 (1) Here, σ x is the normal stress in x direction, σ y is the normal stress in y direction, and τ x y is the shear stress. Substitute 70 MPa for σ x , − 60 MPa for σ y , and 40 MPa for τ x y in Equation (1). σ 1 , 2 = 70 + ( − 60 ) 2 ± ( 70 − ( − 60 ) 2 ) 2 + 40 2 = 10 2 ± 4 , 225 + 1 , 600 = 5 ± 76

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Chapter 10.7, Problem 10.75P

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The failure (yielding) has occurred on the basis of the maximum shear stress theory.

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