Q$4.$

A large three$-$pinned arch with a span of $100$ m and a rise of $30$ m is being designed. The pins are at the two springing points $($ie$.$ the arch supports$)$ and at mid$-$span, see Figure Q$4.$

Develop an equation of the shape of the arch, $\backslash ($ y$($x$)\backslash ),$ necessary to ensure that there are no internal moments in the arch $($ie$.\backslash ($ m$($x$)=0\backslash )),$ if the total design load on the arch is a uniformly distributed load.