Cantilever Beam Stress with Gusset

In summary, it is easy to analyze a cantilever beam of constant cross section and point loaded at the end for stress and deflection. But what about including a gusset support? There is a method to analyze this using My/I = Stress, I would be the second moment of area of the beam + gusset second moment of area, y would be the distance from the bottom of the gusset ( or top of the beam) where the centroid lies.
  • #1
edgepflow
688
1
It is easy to analyze a cantilever beam of constant cross section and point loaded at the end for stress and deflection.

But what about including a gusset support? Is there a method to analyze this?
 
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  • #2
Yes,

using My/I = Stress,

I would be the second moment of area of the beam + gusset second moment of area

y would be the distance from the bottom of the gusset ( or top of the beam) where the centroid lies.
 
  • #3
Hello edgepflow, you haven't really provided much to go on so I have drawn a steel cantilever bolted to steel stanchion as an example of how to go about it.

It is important to realize that (small) gusset plates do not change the basic global mechanics of the structure.The support vertical shear (Vj) and moment (Mj) remain the same overall, they are just achieved slightly differently with the gusset.

This is shown in the global sketch at the top.

The main sketch shows the cantilever bolted with a bolt group A to the stanchion, but also sitting on a triangular gusset.

The exact mechanics of the connection will depend upon the size of the gusset and the fixings. I have shown the gusset bolted to the stanchion with three bolts, B.

The total shear Vj is now made up of the shear reaction supplied by bolt group A plus the reaction between the gusset and the cantilever. I have shown this as a UDL, which is OK for short gussets, but better as a triangular loading for longer ones. Of course, considering the gusset as a free body the resultant of the reaction with the cantilever plus gusset self weight, equals the vertical shear in bolt group B.

The total moment Mj is similarly made from the moment exerted by the bolt group A (MA) and the moment exerted by the reaction between the gusset and the cantilever (MC). Again considering the equilibrium of the gusset the this reaction moment is equal and opposite to the moment exerted by the reaction and bolt forces between the gusset and the stanchion (MB)
 

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  • #4
Thank you for the replies.

I basically solved it the way 1988 ajk discussed. It was usefull since I was able to choose the gusset height and length so I would stay within allowable stresses. A 45 deg gusset, for example, did not pass, but a 30 deg passed.
 

1. What is a cantilever beam stress with gusset?

A cantilever beam stress with gusset is a structural element that is used to support a load at one end, while the other end is anchored to a support. The gusset is a triangular plate that connects the beam to the support, providing additional support and stability.

2. How is the stress in a cantilever beam with gusset calculated?

The stress in a cantilever beam with gusset is calculated using the bending moment equation, which takes into account the applied load, the length of the beam, and the properties of the beam and gusset material. This equation can be solved using mathematical methods or through computer simulations.

3. What factors affect the stress in a cantilever beam with gusset?

The stress in a cantilever beam with gusset can be affected by various factors such as the type and magnitude of the applied load, the length and shape of the beam, the properties of the beam and gusset material, and the design and placement of the gusset. Other external factors such as temperature and environmental conditions can also impact the stress in the beam.

4. Why is a gusset used in a cantilever beam?

A gusset is used in a cantilever beam to provide additional support and strength to the beam, as well as to prevent it from buckling or bending under the applied load. The gusset acts as a brace and transfers the load to the support, reducing the stress and strain on the beam.

5. What are the design considerations for a cantilever beam with gusset?

When designing a cantilever beam with gusset, it is important to consider factors such as the type and magnitude of the expected load, the material properties and strength of the beam and gusset, the length and shape of the beam, and the placement and design of the gusset. The design should also take into account safety factors and any potential external factors that may affect the stress and stability of the beam.

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