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.

The state of plane stress is specified by the following stress components: σxx = 90 MPa, σyy = −10 MPa, and σxy = 40 MPa. Let the X axis lie in the (x, y) plane and be located at θ = π/6 clockwise from the x axis. Determine the normal and shear stresses on a plane perpendicular to the X axis; use Eqs. 2.10-2.12.

 (2.10)

 (2.11)

 (2.12)