EXAMPLE $2$

A simply supported beam has an effective span of $8m$ and supports characteristic dead $(g_k)$ and live $(q_k)$ loads of $15kN{m}^{-1}$ and $10kN{m}^{-1}$ respectively. Determine suitable dimensions for the effective depth and width of the beam.

From Table $3\mathrm{.}17,$ span$/$effective depth ratio for a simply supported beam is $12.$ Hence effective depth, $d,$ is

$d=\frac{\text{s}\text{p}\text{a}\text{n}}{12}=\frac{8000}{12}$~~$670mm$

Total ultimate load $=(1\mathrm{.}4g_k+1\mathrm{.}6q_k)$ span $=(1\mathrm{.}415+1\mathrm{.}610)8=296kN$

Design shear force $(V)=\frac{296}{2}=148kN$ and design shear force, $v,$ is

$v=\frac{V}{bd}=\frac{148{10}^3}{670b}$

Assuming $v$ is equal to $1\mathrm{.}2Nm{m}^{-2},$ this gives a beam width, $b,$ of

$b=\frac{V}{dv}=\frac{148{10}^3}{6701\mathrm{.}2}=185mm$

Hence a beam of width $185mm$ and effective depth $670mm$ would be suitable to support the given design loads.

After designing the size of the beam, reinforce the beam and check for deflections