A nonprismatic bar 1-2-3 of rectangular cross section (cross sectional area A) and two materials is held snugly (but without any initial stress) between rigid supports (see figure). The allowable stresses in compression and in shear are specified as σa and τa, respectively. Use the following numerical data:
(Data:

(a) If load P is applied at joint 2 as shown, find an expression for the maximum permissible temperature rise ΔTmax so that the allowable stresses are not to be exceeded at either location A or B.
(b) If load P is removed and the bar is now rotated to a vertical position where it hangs under its own weight (load intensity = w1 in segment 1-2 and w2 in segment 2-3), find an expression for the maximum permissible temperature rise ΔTmax so that the allowable stresses are not exceeded at either location 1 or 3. Locations 1 and 3 are each a short distance from the supports at 1 and 3 respectively.
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1-572/3 490 lb/ft) b2 2 E2, A2, 2 Ei, Ai,a RI Wi b2 R3