W 850 N/m 300 mm -2.5 m-

A simple log bridge in a remote area consists
of two parallel logs with planks across them (see figure).
The logs are Douglas fir with an average diameter
300 mm. A truck moves slowly across the bridge,
which spans 2.5 m. Assume that the weight of the
truck is equally distributed between the two logs.
Because the wheelbase of the truck is greater than
2.5 m, only one set of wheels is on the bridge at a
time. Thus, the wheel load on one log is equivalent to
a concentrated load W acting at any position along
the span. In addition, the weight of one log and the
planks it supports is equivalent to a uniform load of
850 N/m acting on the log.
Determine the maximum permissible wheel load W
based upon (a) an allowable bending stress of 7.0 MPa
and (b) an allowable shear stress of 0.75 MPa.