A plastic bar of rectangular cross section (b = 1.5 in. and h = 3 in.) fits snugly between rigid supports at room temperature (68°F) but with no initial stress (see figure). When the temperature of the bar is raised to 160°F, the compressive stress on an inclined plane pq at midspan becomes 1700 psi.
(a) What is the shear stress on plane pq? (Assume α = 60 × 10-6 / °F and E = 450 × 103 psi.)
(b) Draw a stress element oriented to plane pq and show the stresses acting on all faces of this element.
(c) If the allowable normal stress is 3400 psi and the allowable shear stress is 1650 psi, what is the maximum load P (in + x direction) which can be added at the quarter point (in addition to thermal effects above) without exceeding allowable stress values in the bar?

Load P for part (c) only