# The concrete sections of a certain superhighway are designed to have a length of 25.0 m. The...

## Question:

The concrete sections of a certain superhighway are designed to have a length of 25.0 m. The sections are poured and cured at 10.0{eq}^{\circ} {/eq}C.

What minimum spacing should the engineer leave between the sections to eliminate buckling if the concrete is to reach a temperature of 50.0{eq}^{\circ} {/eq}C?

## Thermal Expansion:

When the temperature of the material increases, then the molecules of the material vibrate faster, and they take more space. Due to this, the material expands on increasing the temperature and shrinks on cooling. The coefficient of linear expansion or the coefficient of one-dimensional expansion is used for the long slender bar, in which the lateral expansion or contraction is negligible.

Given data:

• {eq}L_o=\rm 25.0 \ m {/eq} is the length of the concrete section
• {eq}T_1=\rm 10.0^\circ C {/eq} is the initial temperature
• {eq}T_2=\rm 50.0^\circ C {/eq} is the final temperature
• {eq}\alpha=\rm 12\times 10^{-6} /^\circ C {/eq} is the linear coefficient of thermal expansion of the concrete

The expression for the thermal expansion of the material is given by:

{eq}\begin{align} \Delta L&=L_o \alpha \Delta T \\[0.3cm] \Delta L&=\rm 25.0 \ m\times 12\times 10^{-6} \ \frac{1}{^\circ C}\times (50.0-10.0)^\circ C \\[0.3cm] \Delta L&=\boxed{\rm 0.012 \ m} \end{align} {/eq}

Therefore, the engineer should leave the minimum spacing of 0.012 m to eliminate buckling.