Lateral Bracing Help

[Const_Eng]

I'm not sure if it's because it's late in the day, but I'm having trouble deriving the stiffness equations in the lateral bracing DESIGN EXAMPLES of Yura, Fundamentals of Beam Bracing. Can anyone help me out with an explantion? Every time I try to derive this I end up cancelling out the cos(theta) term, instead of ending up with the cos2(theta) term seen in the solution.

Part 2 of my question is: why is the stiffness calculated differently between Example 1 and Example 2? Example 1 multiplies by cos2(theta), whereas Example 2 effectively multiplies by cos3(theta).

Yura (Design Examples towards end of document):

http://www.scribd.com/doc/63965314/Fundamentals-of-Beam-Bracing-1

 

[McEngr]

I'm not sure if I can comment on your link, but I always use appendix 6 of the AISC. Thoughts?

 

[Const_Eng]

The specific equation from DESIGN EXAMPLE 1 I'm trying to derive is: k=cos^2(theta)(AE/L). I can't get the cos^2(theta) term, it always cancels when I try to derive. I understand the requirements of AISC App 6, and it seems it should be a simple statics problem. Thanks!

 

[kevo_55]

^^What you are looking to derive is effectively the rigidity of the brace itself acting at an angle.

The overall topic is actually construction engineering, but the same will work for actual structural engineering.

Typically, I've seen this function derived by using the method of virtual work for braced frames.

You can derive this equation yourself but you'll never be asked how to do this on the PE/SE exam. You'll just be expected to know this when calculating the rigidity of each LFRS in the direction of the force for the SE exam to verify your center of rigidity and torsional component of your base shear force.

I have no idea what would be expected application-wise on the construction PM exam for the PE (civil).