A copper bar of rectangular cross section (b = 18 mm and h = 40 mm) is held snugly (but without any initial stress) between rigid supports (see figure). The allowable stresses on the inclined plane pq at midspan, for which θ = 55°, are specified as 60 MPa in compression and 30 MPa in shear.
(a) What is the maximum permissible temperature rise ΔT if the allowable stresses on plane pq are not to be exceeded? (Assume α = 17 × 10-6 / °C and E = 120 GPa.)
(b) If the temperature increases by the maximum permissible amount, what are the stresses on plane pq?
(c) If the temperature rise ΔT = 28°C, how far to the right of end A (distance βL, expressed as a fraction of length L) can load P = 15 kN be applied without exceeding allowable stress values in the bar? Assume that σa = 75 MPa and Ï„a = 35 MPa.