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 in a beam, the stress components are σxx = 20 MPa, , and σyy = σzz = σxy = σyz = 0.

a. Determine the principal stresses σ1 ≥ σ2 ≥ σ3.

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b. Determine the direction cosines of the normal to the plane on which σ1 acts.