The bronze C 86100 pipe has an inner radius of 0.5 in. and a...

The bronze $C 86100$ pipe has an inner radius of 0.5 in. and a wall thickness of 0.2 in. If the gas flowing through it changes the temperature of the pipe uniformly from $T_{A}=200^{\circ} \mathrm{F}$ at $A$ to $T_{B}=60^{\circ} \mathrm{F}$ at $B,$ determine the axial force it exerts on the walls. The pipe was fitted between the walls when $T=60^{\circ} \mathrm{F}$.

Key Concepts

Material and Geometric Properties

The response of any structure to thermal loading depends on its material properties, such as the coefficient of thermal expansion and Young’s modulus, as well as its geometric characteristics like cross-sectional area. These properties allow for the quantification of the induced stresses and forces when a component undergoes temperature changes while being mechanically constrained.

Constrained Thermal Systems

In constrained thermal systems, such as a pipe fitted between rigid walls, the inability of the structure to expand or contract freely leads to the development of axial forces. This concept involves understanding how imposed boundary conditions interact with thermal expansion to create measurable internal loads.

Thermal Expansion

Thermal expansion is the tendency of a material to change in length, area, or volume when its temperature changes. In structures, the linear expansion coefficient quantifies the change in length per degree change in temperature, which is fundamental when predicting dimensional variations due to heat.

Thermal Stress

Thermal stress arises when a material’s free expansion or contraction is restrained, leading to internal forces. In constrained components, temperature changes generate stresses as the material is forced to conform to fixed dimensions, often resulting in compressive or tensile loads.

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