How Do X-Braces Affect Indeterminate Truss Analysis?

[kostoglotov]

Homework Statement

For a larger project we had to redesign a truss to prevent certain members going beyond yield stress.

I've found that due to the nature of the reaction forces and the supports used, the only way to do this is to introduce an X-brace in the bay nearest the supports (as well as some other changes that prevent zero force members from occurring in that bay). It's the only logical thing that will work. Otherwise all of the horizontal reaction force at one of the supports will go into the tension or compression of a single member and that will be beyond the yield stress.

However, when I do the hand calculations for the truss now, when I get to the last bay with the X-brace, it becomes indeterminate. The truss simulator doesn't mind, it simulates it just fine, no singular matrix errors. But I can't figure out how to analyse it. I've tried running with simplifying assumptions about making certain member stresses equal to each other, I've tried cutting the bay through the half way mark and applying method of sections, etc. Everything I've done results in singular matrices.

Here's the system:

imgur link: http://i.imgur.com/5WAHblS.jpg

red arrows are known forces, green unknown. Those little red arrows along the members are member self-weights. Fd is not a reaction force at B, it's part of a distributed load along the top of the truss.

Homework Equations

Sum of moments to zero

Sum of forces to zero

The Attempt at a Solution

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So many. But this is a first year mechanics/statics unit, and we're not supposed to go accounting for displacement of joints or bending moments in our hand calculations.

Am I totally stuffed? I just cannot see how else to get the truss into bounds.

 

[PhanthomJay]

This should not be a first year problem since it is internally indeterminate and involves by hand a tedious process using load and deformation compatability analysis superposition approach. Unless however the x bracing a are slender and the one in compression buckles out, then analyze as a single tension brace which is common. Now if the bracing can take both tension and compression, a simplified approach is to assume each will carry the same load, one on tension and the other in compression. The loading on the members are then about one half the loadings if there was only one brace instead of 2. At least that's how I would do it, you should run the computer software with one brace then 2 and check it out. Be sure to treat the uniform load as point loads at the top joints..

 

[kostoglotov]

This should not be a first year problem since it is internally indeterminate and involves by hand a tedious process using load and deformation compatability analysis superposition approach. Unless however the x bracing a are slender and the one in compression buckles out, then analyze as a single tension brace which is common. Now if the bracing can take both tension and compression, a simplified approach is to assume each will carry the same load, one on tension and the other in compression. The loading on the members are then about one half the loadings if there was only one brace instead of 2. At least that's how I would do it, you should run the computer software with one brace then 2 and check it out. Be sure to treat the uniform load as point loads at the top joints..

I found a way that will get the members to within about 5-7% of what the computer simulates. Basically I assume that there's only three equal stresses, horizontal, vertical, and diagonal, then through some logic, by knowing which members are in tension and which compression, it becomes a simple 3x3 system that gives a good approximation.

The exact method I use isn't really important I don't think. It's part of a much larger project.