Case Study $-$ Choice of Beam Material and Dimension

A square cantilever beam presented in the figure below is used to support load

$P.$ The dimension of the square beam needs to be determined. The span of the beam is $5m$ and the load $($P$)$ need to be carried is $50kN.$

Cantilever Beam

Two materials need to be considered for the beam construction, Steel and Timber. These materials Density, Yield Strength and Young's Modulus is given in the table below.

Density, Yield Strength and Young's Modulus of Steel and Timber

$\backslash$table$[[,$Steel,Timber$],[$Density $($gm$/$cc$),7\mathrm{.}9,0\mathrm{.}8],[\backslash$table$[[$Yield Strength$],[($MPa$)]],350,40],[\backslash$table$[[$Young$\text{'}$s Modulus$],[($GPa$)]],200,10]]$

Price of Steel and Timber

$\backslash$table$[[,$Steel,Timber$],[$Price$,1\mathrm{.}5\frac{\text{\$}}{k}g,6,000\frac{\text{\$}}{m^3}$