Many of the problems for Sections 2.1-2.4 require the determination of principal stresses...

Many of the problems for Sections 2.1-2.4 require the determination of principal stresses and maximum shear stress, as well as the location of the planes on which they act. These quantities are required input in design and failure criteria for structural and mechanical systems.

At a point on the flat surface of a member, load-stress relations give the following stress components relative to the (x, y, z) axes, where the z axis is perpendicular to the surface: σxx = 240 MPa, σyy = 100 MPa, σxy = −80 MPa, and σzz = σxz = σyz = 0.

a. Determine the principal stresses using Eq. 2.20 and then again using Eqs. 2.36 and 2.37.

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b. Determine the principal stresses using Mohr’s circle and show the orientation of the volume element on which these principal stresses act.

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c. Determine the maximum shear stress and maximum octahedral shear stress.

 (2.20)

 (2.36)

 (2.37)