If the temperature of a body is raised or lowered, its dimensions will increase or decrease correspondingly. The stresses developed due to thermal deformations are called thermal stresses and corresponding strains are called thermal strains.
Fig. 3.11 shows a bar of length l. If the temp of the bar is raised by Δt, the elongation δts will be given by δts = l a (Δt) where σ is the thermal coefficient of expansion.
If a wall exists at B, (Fig. 3.12) the wall will be exerting some force which will prevent the elongation.
Let δts = the elongation (or contraction) due to rise (or fall) of temperature (M) if the
rod was free to elongate.
δts = is the shortening of the rod due to the reactive force P (at B) of the wall.
Thus from consideration of deformation, we have δts = δs + δ where δ = initial gap PL between the wall B and free end of the rod. or la Δt = PL / AE + δ.
Thus P can be calculated, therefore thermal stress cr = -P /A can also be calculated from the given area of cross section of the bar i.e., A.