Suppose we have a uniform beam that is $2\mathrm{.}80$ metres long has a flexural rigidity of $27954N{m}^2.$

Find the deflection of the beam in millimetres if the beam is under a load of $f(x)=5\mathrm{.}55(x+0\mathrm{.}61)(4\mathrm{.}782-x)\frac{N}{m}$ and is supported with fixed supports at both ends. Fill

out the table below with your answers.

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Enter as many decimal places as your calculator allows $(8$ to $10).$ Your answer must be within $+-0\mathrm{.}0005$ of the correct answer to be considered correct.