If we clamp the ends of a rod rigidly to prevent expansion or contraction and then change the temperature, tensile or compression stresses called thermal stresses develop. The rod would like to expand or contract, but the clamps won’t let it. The resulting stresses may become large enough to strain the rod irreversibly or even break it. Concrete highways and bridge decks usually have gaps between sections, filled with a flexible material or bridged by interlocking teeth (Fig. 15-8), to permit expansion and contraction of the concrete. Long steam pipes have expansion joints or U-shaped sections to prevent buckling or stretching with temperature changes. If one end of a steel bridge is rigidly fastened to its abutment, the other end usually rests on rollers.
To calculate the thermal stress in a clamped rod, we compute the amount the rod would expand (or contract) if not held and then find the stress needed to compress (or stretch) it back to its original length. Suppose that a rod with length 4, and cross-section area A is held at constant length while the temperature is reduced (negative l:!.T), causing a tensile stress. The fractional change in length if the rod were free to contract would be For a decrease in temperature, l:!.T is negative, so F and F/A are positive; this means that a tensile force and stress are needed to maintain the length. If l:!.T is positive, F and F/A are negative, and the required force and stress are compression.
If there are temperature differences within a body, non-uniform expansion or contraction will result and thermal stresses can be induced. You can break a glass bowl by pouring very hot water into it; the thermal stress between the hot and cold parts of the bowl exceeds the breaking stress of the glass, causing cracks. The same phenomenon makes ice cubes crack when dropped into warm water. Heat-resistant glasses such as Pyrex have exceptionally low expansion coefficients and high strength.