Designing a Beam from Shear Force & Bending Moment Diagram

[lazypast]

Homework Statement

We need to design the cross section of a beam to make it suitable to carry a uniformly distributed load. The beam is held up by 4 ropes which are shown on my diagram as R. In the same attached picture I have the shear diagram and the bending moment diagram for this beam.

Homework Equations

σ(Bending)=My/I
I=(bh^3)/12

The Attempt at a Solution

If I choose a material with a yield (I assume the applied stress shouldn't exceed the yield) of 414MPa.
The max bending moment is 232kNm.

So y/I = 414/0.232 = 1780

I chose a rectangular cross section, as this resists bending in 1 plane well, with a ratio of height to bredth of 2:1
I=bh^3/12=(h/2)(h^3)/12 = h^4/24
y=h/2

∴y/I = 12/h^3

h=(12/1780)^1/3=18.9cm

So the beam is 18.9cm x 9.4cm.
Edit: I amended the calculations because I realized I had used MN for bending moment (should be kN).

But finally, I think the beam would be safe to carry this load with the cross section of dimensions given above. But shear wasn't considered. Anyone care to input? Would be appreciated.

 

[pongo38]

In the first place, are the reactions correct? If the supports are ropes, then they will stretch and possibly alter the distribution of reactions if their lengths vary. Have you assumed the reactions are equal? I notice that the total downward vertical load does not balance the total upward forces from the ropes. Had you checked this? Shear could be a problem, but what is equally likely is deflection. When you use the word 'safe'. I notice you used the yield stress in your calculations but without a safety factor applied.