For each of the plane stress states listed below, draw a Mohr’s circle diagram properly labeled, find the principal normal and shear stresses, and determine the angle from the x axis to σ1. Draw stress elements as in Fig. 3–11c and d and label all details.

(a) σx = 20 kpsi, σy = −10 kpsi, τxy = 8 kpsi cw

(b) σx = 16 kpsi, σy = 9 kpsi, τxy = 5 kpsi ccw

(c) σx = 10 kpsi, σy = 24 kpsi, τxy = 6 kpsi ccw

(d) σx = −12 kpsi, σy = 22 kpsi, τxy = 12 kpsi cw