Problem 5.90

The free body diagram is

I shall assume that the beam's weight can be neglected, as I did in an earlier problem.

The shear at A is 74.25 kN and it's constant from A to B.

The 75 kN force drives the shear down by that amount, to 74.25 - 75 = - 0.75 kN. This is constant from B to C.

From a mental free body at the right end, and reversing the sign, V_D =-72.75 kN.

The shear is a linear relationship from C to D because of the rectangular load.

I drew the moment vs x plot from knowing the end values (zero) and the areas under the various portions of the shear plot. The maximum moment is 66.825 kN-m.

The stress is given by

Section moduli for two channels with the same c and moment of inertia I are additive. Thus, theS for one channel that we must design for is half; 176 x 10³  mm³. From Appendix C, the shapes that will satisfy this are:

C200 x 27.9
C230 x 22