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.
Using transformation equations of plane stress, determine σXX and σXY for the X axis located 0.15 rad counterclockwise from the x axis. The nonzero stress components are given in Problem 2.19.
Problem 2.19
In Problems 2.18 through 2.21, the Z axis for the transformed axes coincides with the z axis for the volume element on which the known stress components act.
The nonzero stress components are σxx = −90 MPa, σyy = 50 MPa, and σxy = 60 MPa. Determine the principal stresses and maximum shear stress. Determine the angle between the X axis and the x axis when the X axis is in the direction of the principal stress with largest absolute magnitude.
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