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To compute the displacement of point **C** due to the thermal expansion of the rigid bar **ABC**, we will use the following formula for thermal expansion:

\[
\Delta L = \alpha \cdot L \cdot \Delta T
\]

where:
- \(\Delta L\) is the change in length due to thermal expansion,
- \(\alpha\) is the coefficient of thermal expansion \( (12 \times 10^{-6}/^\circ C) \),
- \(L\) is the original length of the bar (from \(A\) to \(C\)),
- \(\Delta T\) is the temperature change (60°C).

From the image, the total length of the bar \(L = AB + BC = 2\,\text{m} + 1.4\,\text{m} = 3.4\,\text{m}\).

Now, substituting the values:

\[
\Delta L = (12 \times 10^{-6}) \times (3.4\, \text{m}) \times (60^\circ C)
\]

Let me calculate the result.The thermal expansion of the bar is \( \Delta L = 0.002448 \, \text{m} \) or \( 2.448 \, \text{mm} \).

This expansion will cause point \( C \) to displace horizontally by this amount, as the bar expands.

Would you like further details on how this displacement affects the system, or do you have any other questions? 

Here are 5 related questions for deeper exploration:
1. How would the displacement change if the temperature rise was only 30°C?
2. How is the vertical displacement of point \( C \) influenced by the applied load \( P \)?
3. What would be the stress generated in the bar due to this thermal expansion if the ends were fixed?
4. How does the thermal expansion coefficient affect different materials in structural applications?
5. What happens to the overall stability of the system if \( B \) is not supported?

**Tip**: Always double-check units during calculations, as small errors can significantly impact final results in thermal expansion problems.

Compute the displacement of C if the temperature rises by 60°C.

Learn how to compute the displacement of point C in a rigid bar system due to thermal expansion when the temperature rises by 60°C. This problem involves key concepts such as thermal expansion, using the formula ΔL = α * L * ΔT. Suitable for undergraduate engineering students.

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