Steel bracing - stiffness calc for distributing lateral load into braces

[krdal12]

Hi everyone, it's my first post here.

I'm a senior structural engineering student and I'm designing the LLRS for a steel-frame building in my senior project. Before, I had a simple rectangular shape for my building (plan view) and braces placed in a doubly symmetric way. To determine the amount of shear force each LLRS element experienced, I used the equation k = (EA/L)cos(theta) to determine the stiffness of a simple brace (from a past steel design course). But I found out that one brace in the bay of a frame isn't enough and I need to use a cross brace. But of course, this changes the stiffness of my LLRS element. I can't find a new equation for stiffness (k) that's suitable for a cross-brace. I tried using SAP2000 to see if I could calculate the stiffness outright by modeling the section, applying a unit load and dividing it by the lateral displacement, but the stiffness I got from that is less than half of what I calculated using k = (EA/L)cos(theta) and I'm getting frustrated. I wasn't expecting to have to modify my design. My senior project conference poster is due in just over 24 hours and I want to have a square HSS section chosen for it. Would someone be able to help me?

Thanks in advance!

 

[Celt83]

EA/L cos theta is the axial stiffness of just the brace itself not the lateral stiffness of the frame.

Use the relationship F=kD to get the frame stiffness from SAP, ie apply a horizontal 10kN load and take the resulting lateral deflection and do F/D = k.

I'm making a thing:

http://www.thestructuraltoolbox.com

(It's no Kootware and it will probably break but it's alive!)