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 = 80 MPa, σyy = 60 MPa, σzz = σxy = 20 MPa, σxz = 40 MPa, and σyz = 10 MPa.
a. Determine the stress vector on a plane normal to the vector i + 2j + k.
b. Determine the principal stresses σ1 ≥ σ2 ≥ σ3.
c. Determine the maximum shear stress.
d. Determine the octahedral shear stress.
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