A bridge girder AB on a simple span of length L = 14 m supports a distributed load of maximum intensity q at mid-span and minimum intensity q/2 at supports A and B that includes the weight of the...

A bridge girder AB on a simple span of length L = 14 m supports a distributed load of maximum intensity q at mid-span and minimum intensity q/2 at supports A and B that includes the weight of the girder (see figure). The girder is constructed of three plates welded to form the cross section shown.

Determine the maximum permissible load q based upon (a) an allowable bending stress

_allow
= 110 MPa and (b) an allowable shear stress

_allow
= 50 MPa.