Internal Gusset Plate Forces

[sticksandtriangles]

I am reviewing Design Guide 29, vertical bracing connections, and was struggling to understand the derivation of the internal gusset plate forces.

The images from the design guide are shown below.






The force determination on section A-A, I understand and feel comfortable with. I get lost at the force determination on section B-B, Why is there a 1/2 applied on N'? Same thing for the V' determination. More questions to follow on the M' calculation, but let's start with the 1/2 question first.

 

[Deker]

Total shear and axial forces are distributed uniformly across A-A. The moment across A-A is considered to be resisted by an axial couple distributed uniformly across L/2 on each side of B-B. Add these forces that occurs over L/2 to the FBD in Figure 4-7. That should give a a complete FBD that allows you to solve for N’, V’, and M’.

 

[sticksandtriangles]

Ah thank you!

So this is the complete FBD of the gusset, with uniform shear and axial/moment acting along edge A-A?
From here the forces on section cut B-B make more sense.

 

[Deker]

Yes but rather than the flexural stress being distributed in a linear elastic M/S fashion I believe they assume a rectangular plastic stress distribution with a moment arm of L/2.