18.11 : 열 변형률

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.