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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 realised 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.
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