A simple beam AB of length L and height h (see figure) is heated in such a

Question:

A simple beam AB of length L and height h (see figure) is heated in such a manner that the temperature difference T2 - T1 between the bottom and top of the beam is proportional to the distance from support A; that is, assume the temperature difference varies linearly along the beam:
T2 - T1 = T0x

in which T0 is a constant having units of temperature (degrees) per unit distance.
(a) Determine the maximum deflection Î´max of the beam.
(b) Repeat for quadratic temperature variation along the beam, T2 - T1 = T0 x2.