For a U$-$section beam with the following dimensions: b $=130$ mm$,$ d $=160$ mm$,$ calculate the shear centre distance, e by using Equation $1$ given below.When an unsymmetrical beam is loaded, the shear force within the beam element will cause the beam

section to twist, as shown in Figure $5.$ However, if the beam is loaded at its shear centre, S as shown ir

Figure $6,$ the external applied moment $(Pe)$ will be balanced with the summation of interna

moments from the beam flanges $({\displaystyle \underset{?}{\overset{?}{}}}{M}_A=F_{f}d).$ Hence, the beam will only bend without twist.

$($v$)$

Figure $6$ The $\text{'}$U$\text{'}$ section under load through its shear centre, S

The theoretical shear centre distance, $e$ from the centre of the beam web $($shown in Figure $6($b$))$ can be

calculated using Equation $1.$

$e=\frac{b^2}{(\frac{d}{3}+2b)}$

$($Equation $1)$