Cantilever Beam Stress with Gusset

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Discussion Overview

The discussion revolves around the analysis of stress and deflection in a cantilever beam that incorporates a gusset support. Participants explore methods for evaluating the structural mechanics involved when a gusset is added to the system.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes that analyzing a cantilever beam with a gusset support requires a different approach than a simple cantilever beam with a point load.
  • Another participant suggests using the formula My/I = Stress, where I includes the second moment of area of both the beam and the gusset, and y is the distance from the bottom of the gusset to the centroid.
  • A third participant provides a detailed explanation of how the gusset affects the overall mechanics, stating that while the gusset does not change the global mechanics significantly, it alters how shear and moment are distributed in the structure.
  • This participant describes the mechanics of the connection, emphasizing that the shear and moment reactions are influenced by the gusset's size and the configuration of the bolts.
  • Another participant shares their experience of solving a similar problem, indicating that they adjusted the gusset dimensions to remain within allowable stress limits, noting that different angles of the gusset led to different outcomes regarding stress compliance.

Areas of Agreement / Disagreement

Participants express varying approaches to analyzing the cantilever beam with a gusset, and while some methods are discussed, there is no consensus on a single method or solution. The discussion remains unresolved regarding the best approach to take.

Contextual Notes

Participants highlight the importance of considering the size and configuration of the gusset and its impact on the overall mechanics, but specific assumptions and limitations in their analyses are not fully detailed.

Who May Find This Useful

Engineers and students interested in structural analysis, particularly those dealing with cantilever beams and gusset supports, may find the discussion relevant.

edgepflow
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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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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.
 
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)
 

Attachments

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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.
 

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