Breyer Knee Brace Connection vs Risa Frame Analysis 1

[smokiibear]

Looking at Breyer's 6th edition of "Design of Wood Structures," and specifically at the knee brace design in chapter 12 for lateral resistance. Simple statics, simple solution for finding axial load in knee brace.

Modeling the same concept in Risa so far has yielded very different results, with much higher axial loads in the brace. I know it is caused by how we are setting up our model and loads, but I don't understand how to reconcile the difference. I've set up two columns, 1 beam, and 2 braces. The boundary conditions at grade have reactions in x and y, and free for rotation around z axis. All other member ends are free (transferring no moment). Lateral point loads are input at the top of the columns.

As mentioned, the axial loads in the braces are very different with the two procedures. Breyer takes the total lateral load and divides it by the number of resisting columns, solving for the base shear at each column. Then taking a free body for one column and brace element, the axial load of the brace and resultant lateral load at the top of the column are resolved. This method naturally results in a smaller lateral load at the top of the column. Solved statically, the brace axial loads are small.

Can someone speak to what I'm missing in relating the two methods?

Thanks.

 

[JoshPlumSE]

This is the type of problem that I always enjoy. I built the same model in RISA and came up with different results than Breyer example 12.8. Though it wasn't only different by about 10%

The basic difference is that the lateral shears do not distribute equally between columns. I can see the logic for doing so in a hand calculation. But, there is some frame action in the structure that they just aren't accounting for. If I assume an infinitely rigid beam, then I get the answer in the example. See the two different ways of modeling the example in the attached file.

 

[JoshPlumSE]

Sorry, that attachment probably won't work. Try this one instead

 

[smokiibear]

Blush. We ran the same analysis, and I did get the same results as you. While doing some comparisons in my head, I skipped the statics step and got into trouble. Thanks for sending the file over. Nice to know I really wasn't off.