Cantilever Beam Stress with Gusset

[edgepflow]

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?

 

[1988ajk]

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.

 

[Studiot]

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 (V_j) and moment (M_j) 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 V_j 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 M_j is similarly made from the moment exerted by the bolt group A (M_A) and the moment exerted by the reaction between the gusset and the cantilever (M_C). 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 (M_B)

 

[edgepflow]

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.