Jack Stability / K-Value Question
Jack Stability / K-Value Question
(OP)
See attached sketch.
I frequently encounter conditions similar to the attached sketch. Typically, this detail resembles a leg of shoring frame/ jack etc where the length of the threaded rod is significantly shorter than the tube length and the loads are small (i.e. my concerns are low). However, in theory the portion of length by either the tube or rod is irrelevant relative to the fixity at the nut. For simplicity, lets assume the fixity shown at either end of the sketch (rotation free, translation fixed).
I now am tasked with analyzing a detail, where the axial load is very high and the length of rod is ~40% of the total length of the "column".My cause for concern, in short, is this: What fixity exists at the nut (where the rod threads through the nut and into the tube)?
My opinion: Analyze Tube: via (K=2)(L=L2)/rtube and Threaded Rod via (K=2)(L=L1)/rrod. This conservatively ignores fixity at the nut altogether(i.e.k=2 for each element). Realistically, there is some fixity created at the nut by virtue of the rod threading through the nut which in turn is welded to the tube.
I believe this to be conservative in nature for concentric axial loads in the column.
Opinions/ Comments/ Prior experience?
I frequently encounter conditions similar to the attached sketch. Typically, this detail resembles a leg of shoring frame/ jack etc where the length of the threaded rod is significantly shorter than the tube length and the loads are small (i.e. my concerns are low). However, in theory the portion of length by either the tube or rod is irrelevant relative to the fixity at the nut. For simplicity, lets assume the fixity shown at either end of the sketch (rotation free, translation fixed).
I now am tasked with analyzing a detail, where the axial load is very high and the length of rod is ~40% of the total length of the "column".My cause for concern, in short, is this: What fixity exists at the nut (where the rod threads through the nut and into the tube)?
My opinion: Analyze Tube: via (K=2)(L=L2)/rtube and Threaded Rod via (K=2)(L=L1)/rrod. This conservatively ignores fixity at the nut altogether(i.e.k=2 for each element). Realistically, there is some fixity created at the nut by virtue of the rod threading through the nut which in turn is welded to the tube.
I believe this to be conservative in nature for concentric axial loads in the column.
Opinions/ Comments/ Prior experience?






RE: Jack Stability / K-Value Question
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RE: Jack Stability / K-Value Question
If you were concerned about the nut, you can get coupling nuts that are longer. Or adding a lock nut would add additional stiffness.
RE: Jack Stability / K-Value Question
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RE: Jack Stability / K-Value Question
Does the rod have an acme thread or a regular thread? What are the outside and root rod dia’s.? How high (length of engagement) is the nut, and it’s welded to the tube L2? The two lengths are certainly not irrelevant, and I’m sure you didn’t mean that. But, as a means of getting some sort of a handle on the problem, without any/much load on the full length (L1 + L2) column, apply some lateral load at the nut and see how much you can get the column to deviate ( Δ ) from a stretched wire btwn. the two pin points. Use this as a likely out of alignment Δ and a P/Δ in your column equations. The fits (fit class) are usually kinda loose on these threads to account for dirt, etc. Is there any way, up inside the tube L2 some distance (say .1 or .2[L1]) you could hold the dia. of the rod w.r.t. the inside of the tube; in effect this would then be the back reaction on a canti’ed. rod, and you could start to give it a moment value other than just busting the nut off the end of the tube. Make a 4" long pipe, with a cap pl. on the top, which just fits inside L2 and has an I.D. which just fits the threaded rod. Your threaded rod will fit inside this pipe and push it up as needs be.
RE: Jack Stability / K-Value Question
Also, wasn't obvious from the sketch, but just handling one to see how much slack there was relative to the length would be informative. If there was some known or allowable deflection at the middle, you could design accordingly.
RE: Jack Stability / K-Value Question
I used the Theory of Elastic Stability by Timoshenko. It covers this exact problem. Basically you assume a deflected shape and use the deflections to get the bending moment along the length of the assembly. You can then integrate along the length of the assembly(taking into account the change of section properties)to get the total energy stored.
I can't remember exactly what the deflected shape was that I assumed (book and files are at the office).
If I understand your situation correctly, I would be tempted analyze as if the connection at the nut is fully fixed. You say the tube is welded to the nut, so tube to nut is fully fixed. The nut is threaded onto the rod, my gut feel is that this is fairly close to fixed.
If that connection was pinned then you have 3 pins along the length of the assembly and the buckled shape will be 2 straight lines between the three pins (that is what first came to mind, haven't actually looked into that). Which you can account for in the Timoshenko reference.
I ended up writing a spreadsheet to solve the problem (I had a range of L1's and L2's to deal with). Your answer should fall somewhere between the capacity calculated with just member 1 and just member 2. If you set L1 or L2 to zero you should get the same answer as using simple buckling equations.
RE: Jack Stability / K-Value Question
However, if you really want to find a precise solution, then Caneit has it right. The Timoshenko and Gere book has something called "The Method of successive Approximations" that is used for stepped columns like this. There is a useful example (C3.2) of this method in appendix C of the AISC design guide on tapered members (DG-25).
If you are like me you think it is fun coming up with exact hand calcs for weird cases like this. If so, then that example is probably a good place to start .
RE: Jack Stability / K-Value Question
RE: Jack Stability / K-Value Question
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RE: Jack Stability / K-Value Question
RE: Jack Stability / K-Value Question
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RE: Jack Stability / K-Value Question
If you are outside of the range of the tabulated results in Roark's, I recommend you turn to our buddy Mr. Timoshenko and his seminal text, Theory of Elastic Stability.