Assessment $3\mathrm{.}0$: Stressing calculations$-$Using Hooke's law perform calculations for the restoration of stress in plain line

The accepted industry method of calculating stress in plain line track is derived from Hooke's law which asserts that the extension of an elastic object, such as a spring $($or rail$),$ is described by Hooke's law: i$.$e$.$ if a force is applied to a spring, the spring stretches reversibly by an amount that can be calculated $-$ the fact that the string stretches reversibly means that it will go back to its normal shape after the force has been removed.

Perform calculations for the stressing of CWR in plain line.

Expansion is calculated using the formula: $e=1000LT$

$e=$ expansion in millimetres

$L=$ length of free$*$ rail $(m),*$ note "free rail" means un$-$clipped and unrestricted to move lengthwise

$=$ coefficient of linear expansion $=0\mathrm{.}0000115$

$T=$ difference between actual temperature and $27C$ i$.$e$.-$ rail temperature$)$

Extension $(e)=$ Length of rail in metres $(L)x$ coefficient of linear expansion $()$ difference between actual temperature and $27C(T)$

Q$1)$ Calculate extension of $125$ metres of rail at $20C$

$1250\mathrm{.}01157=$

Q$2)$ Calculate extension of $275$ metres of rail at $12C$

$2750\mathrm{.}011515=$

Q$3)$ Calculate extension of $300$ metres of rail at $15C$

$3000\mathrm{.}011512=$

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