Question

calculate the change in length of a 100 - ft - long steel bridge girder that will be exposed to a temperature range of - 25 to 110°f

Explanation:

Step1: Recall the formula for linear expansion

The formula for linear expansion is $\Delta L = L_0\alpha\Delta T$, where $\Delta L$ is the change in length, $L_0$ is the original length, $\alpha$ is the coefficient of linear expansion, and $\Delta T$ is the change in temperature. For steel, $\alpha = 12\times10^{-6}\,^{\circ}C^{-1}$.

Step2: Convert the length to SI units

The original length $L_0 = 100\,\text{ft}$. Since $1\,\text{ft}=0.3048\,\text{m}$, then $L_0 = 100\times0.3048 = 30.48\,\text{m}$.

Step3: Calculate the change in temperature

The temperature range is from $- 25^{\circ}C$ to $110^{\circ}C$. So, $\Delta T=T_f - T_i=110 - (-25)=135^{\circ}C$.

Step4: Substitute the values into the formula

Substitute $L_0 = 30.48\,\text{m}$, $\alpha = 12\times 10^{-6}\,^{\circ}C^{-1}$, and $\Delta T = 135^{\circ}C$ into $\Delta L = L_0\alpha\Delta T$.

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Step5: Convert the result back to feet (optional, if needed)

Since $1\,\text{m}=\frac{1}{0.3048}\,\text{ft}$, then $\Delta L = 0.0493776\div0.3048\approx0.162\,\text{ft}$

Answer:

The change in length is approximately $0.0494\,\text{m}$ (or approximately $0.162\,\text{ft}$)