(a) Briefly explain why thermal stresses may be introduced into a structure by rapid heating or cooling. (b) For cooling, what is the nature of the surface stresses? (c) For heating, what is the nature of the surface stresses?

Thermal expansion and contraction are phenomena occurring naturally in materials as they react to changes in temperature. When a material is subjected to an increase in temperature, the kinetic energy of its particles increases, causing them to move apart slightly and the material to expand. This is known as thermal expansion. Conversely, when the temperature decreases, the particles' kinetic energy diminishes, and they get closer together, leading to thermal contraction.

For instance, metal bridges have expansion joints to accommodate the expansion and contraction caused by changes in temperature throughout the year. Without these joints, the bridge could suffer from structural damage due to the induced stresses. Similarly, railway tracks and pipelines are constructed with consideration for these effects to avoid warping or fracturing.

Understanding these concepts is crucial in the design and analysis of structures to ensure they can withstand the thermal stresses caused by temperature changes without failing.

When materials undergo thermal expansion or contraction, they may experience two primary types of stresses: compressive and tensile. Compressive stress is a result of forces that attempt to reduce the volume of a material, effectively squeezing it. Tensile stress, on the other hand, occurs when forces attempt to elongate or stretch the material.

Imagine a steel rod fixed at both ends. If the rod is heated, it will try to expand, but the fixed ends will restrict its movement, resulting in compressive stress along the length of the rod. On the flip side, if the rod is cooled, it will attempt to contract. However, since it is fixed, it cannot shrink, which introduces tensile stress because the structure is being pulled from each end.

This illustrates why it's vital for engineers to calculate the expected thermal expansion or contraction of a material when designing structures, to ensure that the induced stresses will not exceed the material's strength and cause failure.

A temperature gradient occurs when there is a difference in temperature across a material, leading to differential thermal expansion or contraction. This non-uniformity can be significant in large structures or materials with different rates of thermal conductivity. For example, a concrete wall exposed to sunlight may have a warmer surface while remaining cooler on the inside, creating a temperature gradient.

When temperature gradients occur, one part of the material can be expanding while another part is static or contracting, which results in internal stress known as thermal stress. In engineering applications, these gradients must be considered because they can cause buckling, cracking, or other forms of structural failure if not properly managed.

Materials with high thermal conductivity experience smaller temperature gradients and hence less induced stress. On the other hand, materials with low thermal conductivity may see larger temperature gradients causing greater internal stresses, making the choice of material and design critical for the longevity and safety of structures.