A simply supported beam of uniform rectangular cross section

A simply supported beam of uniform rectangular cross section of width b and depth h is subjected to linear temperature gradient, 0° at the top and T° at the bottom, as shown in the figure. The coefficient of linear expansion of the beam material is a. The resulting vertical deflection at the mid-span of the beam is

Average change in temp = T/2
Max strain at extreme fibre

ε = α		T
		2

	M	=	f	=	E
	I		y		R

∴ R =	Ey
	y

ε =	F
	y

=	h
	αT

Deflection, δ =	L²	=	L²	×	αT	=	αTL²
	8R		8		h		8h

	αTh²	upward
	8L

	αTL²	upward
	8h

	αTh²	downward
	8L

	αTL²	downward
	8h