Dear Quang

When we are talking about rotation, we should clarify what kind of rotation we mean. The rotation of plastic hinges, the cord rotation of beam, etc. here are some essential points that you should be aware of:

1- The total rotation of the system is the sum of rotations of beams, column, and the panel zone.

2- The rotation of plastic hinges are hard to calculate because of the real-time changes in the length of plastic hinges.

3- It is recommended that the tests on the composite systems perform one-sided (one beam connect to one column) because the beams at two face of the column act differently since one resists positive and the other resists the negative moments and decoupling the composite action in this situation is a big challenge.

4- It is hard to satisfy the weak beam-strong column criteria when using two beams and one column test setup. Not fulfilling this criterion may lead to the propagation of the plasticity in the column instead of the beams that will interrupt the transfer and distribution of column moment among the beams.

I recommend you to use moment-drift instead of moment-rotation which is more applicable and practical and also use the conventional AISC 341 method of qualification of connections.

good luck

Dear Quang

The technique has changed and many details are observed today, which were not in the past because the possibilities to measure, to analyze and to build some m-theta curve were different.

In a simple and old way of test, which use the T experimental configuration, the length from the supported extreme to the connected part is minimum, to ensure that answers are reasoanble. I would calculate:

1) the moment is already the moment of a central loaded beam M= PL/4, being P the load applied by the hammer and L the distance between supports, which in fact occur on both sides, discounted the efect of the distance from column centroid to the beam line surface. Another problem, since in your case the column is circular. Then, consider the externa diameter d of the tube, I would use the moment M= P(L-d)/4 simply; and,

2) the deflection is caused by deformation of the connection, not from the excessive flexure of steel-beam and th eir components (in this case, concrete part). Therefore, it is imaginned that the rotation on the connection is the theta= arctg [2.dy/(L-d)] taking the difference between the angle of rotation caused by the beam elastic bending (which tends to be very low too), with the length (L-d)/2.

However, I agree withn Safael that this is not a very conservative measure, because it captures the answer without knowing what happening inside the filled tube, the plasticity effect (if any). Also as there's no perfect beam, probably you will find different reactions for the left and right side supports on the test and, again, which will be the answer considered?

Moreover, I agree that a minimum not simmetric moment or deformation (rotation) will appear due to this left-right minimum differences but which, when plasticity appears, may again maskarade the observed work.

Too complicated is guarantee the influence (or to measure) the separation between concrete slab and steel surface, during the test (if any) either. Or to guarantee that concrete is in fact working together with steel.

Unfortunately, I have not done any test in my life, but read a lot of papers on it, though still confess my ignorance. I tried to give a simple lines which I wonder that you already have in mind. Why did I answered? Because I love this subject and still interested about other answers. Good luck.

I would like to add a comment: if the plasticity appears in the beam next to the weld, (some steel part yielding or some local buckling in the compression side) maybe the corresponding deformations must be considered from the "connection". Thus, I suggest, it must included on the M-theta curve.

However, if the plasticity appears in the tube, like some visible ovalization, some corrugation or localized damage; it becomes a questionable decision to allow such behavior be include in the curve. This is because when you are using a curve (one already existent), you suppose that only the connection is involved and not the called "panel zone" as way to speak. Obviously, there's no painel zone in a tube, but you have a medium (steel tube filled with concrete) which behavior changes also, but that is not the connection. For this reason, you must tell for others that the M-theta curve includes this effect.

Otherwise, use a very thick tube in the experiment (like a "undeformed" body) where all the measured displacements are due to the beam flexibility and the connection. In such case, the M-theta curve involves only the connection.

It will be good if is possible to keep the left and right supports reaction equal. This can be done in the start, after a tiny calibrating force is applied (e.g. 3% to 5% of the prescribed load)by a little horizontal adjustment of the position of one support relative to the other. Nevertheless, depending on the column (tube) unequal behavior during the yielding stress stage till the collapse, some side can deform more than the other, hence some difference in the value of reaction can appear.

Maybe, you can improve the answers, if the welding process of the steel beams to the tube be done simultaneously, in both sides, at the same levels, using two workers for it. The idea is that the welding contraction caused by the cooling, after the weld is done, is of the same amount at both sides, to keep some symmetry as result of the welding process. You could say that it is uncommon that when doing these weld in the field, the constructor use this scheme. I agree, but the intention is to provide a little difference in both side instead of very different values, which make uneasy to decide which to use, which is more close to the real behavior. I mean, when the answers converge (little difference), you can believe in the findings, while when they get apart, you don't know more what you must consider.

But this is only my oppinion. Surely, others can think different. And I hope for it.

PS: I made a little mistake in the previous answer, where the equation term " /2" is now "/4" (of course). I changed the L definition and forget to correct the equation. I edited it now.

You may use Static Riks option in Abaqus