Designing a Beam from Shear Force & Bending Moment Diagram

In summary, the conversation discusses designing the cross section of a beam to carry a uniformly distributed load. The beam is supported by four ropes, and the shear and bending moment diagrams are provided. The suggested solution involves choosing a material with a yield stress of 414MPa and a rectangular cross section with a ratio of height to breadth of 2:1. The calculations result in a beam with dimensions of 18.9cm x 9.4cm, but the possibility of shear and deflection is also mentioned.
  • #1
lazypast
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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 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.
 

Attachments

  • BM SF.jpg
    BM SF.jpg
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  • #2
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.
 

1. What is a shear force and bending moment diagram?

A shear force and bending moment diagram is a graphical representation of the internal forces and moments present in a beam. It shows the variation of these forces and moments along the length of the beam.

2. How do I create a shear force and bending moment diagram?

To create a shear force and bending moment diagram, you will need to first determine the magnitude and direction of the external loads acting on the beam. Then, you can use equations and equations of equilibrium to calculate the internal forces and moments at different points along the beam. Finally, plot these values on a graph to create the diagram.

3. Why is it important to design a beam from a shear force and bending moment diagram?

The shear force and bending moment diagram provides valuable information about the internal forces and moments in a beam, which are crucial for ensuring the structural integrity and safety of the beam. By designing a beam based on this diagram, engineers can ensure that the beam can withstand the expected loads without failing.

4. What factors should be considered when designing a beam from a shear force and bending moment diagram?

When designing a beam from a shear force and bending moment diagram, it is important to consider the material properties of the beam, such as its strength and stiffness, as well as the expected loads and the beam's geometry. Other factors that may need to be taken into account include the beam's supports and any potential points of failure.

5. Are there any limitations to designing a beam from a shear force and bending moment diagram?

While a shear force and bending moment diagram provides valuable information, it is important to note that it is based on simplifying assumptions and does not take into account factors such as material fatigue or dynamic loading. Therefore, it should be used in conjunction with other design methods and engineering judgement to ensure the safety and reliability of the beam.

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