A solid steel cube constrained on all six faces is heated

A solid steel cube constrained on all six faces is heated so that the temperature rises uniformly by ∆T. If the thermal coefficient of the material is α, Young's modulus is E and the Poisson's ratio is υ, the thermal stress developed in the cube due to heating is

Volumetric strain

ε V =	(1 - 2μ)	[σ_x + σ_y + σ_z]
	E

α ∆T =	(1 - 2μ)	(σ)
	E

σ =	α (∆T)E
	(1 - 2μ)

-	α(∆ T)E
	(1 - 2v)

-	2α(∆ T)E
	(1 - 2v)

-	3α(∆ T)E
	(1 - 2v)

-	α(∆ T)E
	3(1 - 2v)