The C83400-red-brass rod A B and 2014-T 6- aluminum rod B C are joined at the collar B and fix

Step 1: Calculate the change in temperature.u000AÎ”T u003D T2 u002D T1 u003D 120Â°F u002D 50Â°F u003D 70Â°Fu000Au000AStep 2: Cal

The C83400-red-brass rod A B and 2014-T 6- aluminum rod B...

The $\quad$ C83400-red-brass rod $A B$ and $2014-\mathrm{T} 6-$ aluminum rod $B C$ are joined at the collar $B$ and fixed connected at their ends. If there is no load in the members when $T_{1}=50^{\circ} \mathrm{F}$, determine the average normal stress in each member when $T_{2}=120^{\circ} \mathrm{F}$. Also, how far will the collar be displaced? The cross-sectional area of each member is 1.75 in $^{2}$.

The $\quad$ C83400-red-brass rod $A B$ and $2014-\mathrm{T} 6-$ aluminum rod $B C$ are joined at the collar $B$ and fixed connected at their ends. If there is no load in the members
when $T_{1}=50^{\circ} \mathrm{F}$, determine the average normal stress in each member when $T_{2}=120^{\circ} \mathrm{F}$. Also, how far will the collar be displaced? The cross-sectional area of each member is 1.75 in $^{2}$.

Key Concepts

Thermal Expansion

Thermal expansion is the process by which a material's dimensions change in response to a change in temperature. Each material expands (or contracts) by an amount proportional to its coefficient of thermal expansion and the temperature change, provided it is free to do so.

Thermal Stress

Thermal stress develops in a material when its natural tendency to expand or contract due to a temperature change is constrained. In such cases, the material experiences internal forces (stresses) as it is forced to conform to the imposed dimensional restrictions, which is particularly important in systems where different materials are joined together.

Compatibility of Deformations

When different structural members are connected, such as in a fixed joint, the requirement that they move together imposes compatibility conditions. This means that the overall deformation of the system must be consistent across the different materials, and any differences in free thermal expansion are balanced by the development of internal stresses.

Composite Structural Analysis

This concept involves analyzing systems composed of dissimilar materials with different thermal and mechanical properties. In composite members, each material contributes differently to the overall deformation and stress distributions based on its stiffness and coefficient of thermal expansion, making it necessary to apply equilibrium and compatibility conditions to solve for induced stresses and displacements.

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