Problem $1$: A bridge girder AB on a simple span of length $L=12m$ supports the load of maximum intensity at the mid span q and zero at supports. The girder's cross$-$section is constructed of three plates to form the symmetric cross section shown.

In terms of q draw the shear force diagram and show that the maximum value is at the supports.

In terms of $q$ draw the bending moment diagram and show that the maximum value is at the mid span of the beam.

Determine the maximum permissible load $q$ based upon an allowable bending stress of $100$ MPa $.$

Determine the maximum permissible load $q$ based upon an allowable shear stress of $33$ MPa $.$

If both cases in Parts $(3)$ and $(4)$ are taken into consideration, what will be the maximum permissible load q $,$ discuss?