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  1. #1
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    Exclamation a steel beam...

    A steel beam 10m long is installed in a structure at 20oC. What are the beam's changes in length at the temperature extremes of -30oC to 45oC?
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  2. #2
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    Quote Originally Posted by babygirl
    A steel beam 10m long is installed in a structure at 20oC. What are the beam's changes in length at the temperature extremes of -30oC to 45oC?
    Hello, babygirl,

    let t be the temperature of a solid in C. Then the length of it in m with respect to temperature in C is
    l_t=l_{20}+(t-20)\cdot k \cdot l_{20}=l_{20}(1+(t-20)\cdot k)

    k is a constant, describing the change of length per Kelvin. For steel it is k=11.7\cdot 10^{-6} \cdot \frac{1}{K}.
    With your problem you got:

    l_{-30}=10 m\left(1+(-50)K\cdot 11.7\cdot 10^{-6} \cdot \frac{1}{K}\right)=9.99415 m

    l_{-45}=10 m\left(1+(25)K\cdot 11.7\cdot 10^{-6} \cdot \frac{1}{K}\right)=10.002925 m

    The total change of length at a length of 10 m is:

    \Delta l=l_{45}-l_{-30}=0.008775 m=8.775 mm

    Remark: The temperature of a railroad track in Middle Europe rates from -60C up to 90C)

    Greetings

    EB
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