What is unbraced length continuous truss btm chord w/partial comp 3

[swsengineer]

I have a heavy timber truss that has a continuous one piece bottom chord 40'. The first 10' and last 10' are slightly in compression. The center 20' is in tension. I am using the unbraced length of 10' but I'm not sure what the (K) buckling length coefficient should be? If the bottom chord was pin spliced at each of the panel points it would be unstable but since it's continuous it seems to me that a modified unbraced length would be in order. Because the bottom chord is continuous I would think the rotation and translation although aren't free aren't totally restrained either. I was just wondering if any others had dealt with this before and how you handled it. Installing a lateral brace is not wanted, plus the compression is low so I'm not really too concerned with it but I was still curious about how to correctly handle this.

 

[JaredS]

I'm drifting between 0.7 and 2.0 for K.

On one hand the beam is not free to rotate, as there is no pin at the point where tension changes to compression. Also support from the other truss elements prevents it from deflecting wildly.

On the other hand the beam will rotate and deflect at this point due to its own loading.

Because i think the deflection and bending will occur mostly because of loading and not because of buckling I lean towards a case like case b in AISC 13, Table C-C2.2, and use K=0.80 and then I would check for the combined loading.

 

[Lion06]

I would say at best 1.0, but you should really be counting on that bottom chord to brace the compression web members. It's probably not an issue for a wood truss, but still worth investigating.

Unless the bottom chord is actually braced anywhere along it length or the end conditions are anything other than pinned, I would not us anything less than 1.0 for a K factor.

Additionally, I would not use 10' for the unbraced length. That is analogous to using the inflection point (for a beam with reverse curvature) as a brace point. I would use the full 40' and a K of 1.

Jared- It can't buckle in the plane of the truss, but it can still buckle out-of-plane. If the bottom chord is not physically braced out-of-plane at the panel points, you can't assume the diagonals brace it because you are counting on the bottom chord to brace the diagonals.

 

[ronster]

I'm with EIT. K=1 Le=40', You will need a 10" minimum wide bottom chord unless you brace it. Did you check the truss for wind uplift? Most likely you have a loading condition where the entire bottom chord is in compression.

 

[swsengineer]

I lean towards a K somewhere between 1 and 2 or just making sure the bottom chord could handle 1%-2% of the compressive force as horizontal load at these points and making sure the lateral stiffnes of the bottom chord can resist this load within allowables, using the full 40' doesn't seem right. What if you had a 40' tension member pinned at each end but then had a large compressive load 1 or 2' foot from one end causing only the last foot or twp to be in compression. Would you still use 40' as your unbraced length?

 

[Lion06]

sws-

I see your point. What you are talking about is addressed in bending by the Cb factor. I have a really good paper that discusses the Cb factor and analogizes it to columns. I don't know of a similar factor for compression members, however. It is also interesting to note that Cb always equals 1.0 if the maximum moment occurs away from a brace point (which means the location of maximum compression occurs away from a brace point). I see no reason to look at a column differently. If that maximum axial compressive load occurs away from a brace point (which it does), don't take a reduced braced length.

Also, think about it this way. If the bottom chord were to buckle out of plane, what shape would it take? It likely will not take a shape that will have reverse curvature along any of the 40' length. The whole idea behind the K factor is what is the length between inflection points. If you have no inflection points along the member under consideration then K >= 1.0.