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 nonzero stress components relative to axes (x, y, z) are σxx = −90 MPa, σyy = 50 MPa, and σxy = 6 MPa.
a. Determine the principal stresses, σ1 ≥ σ2 ≥ σ3.
b. Calculate the maximum shear stress.
c. Calculate the octahedral shear stress.
d. Determine the angle between the x axis and the X axis, where X is in the direction of the principal stress σ1.
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