Recall that the Influence function $($or Green's function$),G(x,)$ is a solution to the differential equation $\frac{d^{4}y}{d{x}^4}=\frac{(x-)}{EI(x)}$ and thus gives the deflection of a beam under a point load coming from a $1N$ force at $x=.$

You can use this fact, combined with what you know about constants and integration, to use the Influence function to find the deflection for any point load $($not just a point load from a $1N$ force$).$

Question

Suppose we have a uniform beam that: is $4\mathrm{.}57$ metres long, has a flexural rigidity of $34677N{m}^2,$ and is supported with simple supports at both ends.

Find the Influence function of the beam for the beam and use it to find the folowing deflection of the beam in millimetres at various points on the beam under different point loads, according to the table, below. Fill out the table with your answers.

Answer

$\backslash$table$[[$Point Force and Location,$x-$coordinate,Deflection $(mm)$