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.
The stress components at a point in a plate are σxx = −100 MPa, σyy = σzz = 20 MPa, σxy = σyz = 0, and σxz = −80 MPa.
a. Determine the principal stresses σ1 ≥ σ2 ≥ σ3.
b. Determine the octahedral shear stress.
c. Determine the maximum shear stress and compare it to the octahedral shear stress.
d. Determine the direction cosines of the normal to one of the planes on which the maximum shear stress acts.
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