18.11:
Thermal Strain
A homogeneous rod with a uniform cross-section, resting freely on a horizontal surface, expands when heated.
The expansion is proportional to the temperature change and the rod's length, governed by the material’s coefficient of thermal expansion in unit per degree Celsius. It indicates the material’s expansion or contraction per degree of temperature change.
The elongation of the rod due to the temperature change is due to the thermal strain. Contrary to typical strain scenarios, no stress is associated with this thermal strain as the rod is not constrained.
If the homogeneous rod is constrained at both ends, it experiences a temperature rise but cannot elongate due to the restraints, inducing stress without strain on the rod.
To estimate the load and stress from this temperature change, remove one of the supports in the rod, allowing it to elongate freely.
After determining the extent of this hypothetical elongation, apply a force to the detached end, simulating the reaction the support would have provided. Ensuring the total deformation equals zero, the load and stress on the rod are calculated.
18.11:
Thermal Strain
Thermal strain is a concept that arises when we consider how temperature changes affect structures. Unlike the conventional assumption that structures remain constant under load, real-world scenarios often involve temperature fluctuations that can significantly impact these structures. Consider a homogeneous rod with a uniform cross-section resting freely on a flat horizontal surface. If the rod's temperature increases, the rod elongates. This elongation is proportional to the temperature change and the rod's original length.
The proportionality constant in this relationship is a material-specific characteristic known as the coefficient of thermal expansion. It represents the amount by which a unit length of a material will change for each degree of temperature change. The coefficient can be expressed in units per degree Celsius.
As the rod deforms due to the temperature change, it results in elongation. The deformation is associated with thermal strain. It is important to note that stress is not necessarily related to thermal strain. It distinguishes thermal strain from mechanical strains, which usually involve associated stresses. Understanding thermal strain is essential in designing and analyzing structures subjected to temperature changes. The thermal strain must be ensured for the safety and integrity of structures under different environmental conditions. It can significantly affect the performance and lifespan of various structures.