Stiffness Analysis Procedure

Recently I happen to read a document on stiffness analysis procedure.

This is the summary of steps to be followed in performing a stiffness analysis :

1. Determine the needed displacement unknowns at the nodes/joints and label them d1, d2, …, dn in sequence where n = the number of displacement unknowns or degrees of freedom.

2. Modify the structure such that it is kinematically determinate or restrained, i.e., the identified displacements in step 1 all equal zero.

3. Calculate the member fixed-end forces in this kinematically restrained state at the nodes/joints of the restrained structure due to the member applied loads. Tables of member-end forces due to member loads for the kinematically restrained members are available later in these notes. The member-end forces are vectorially added at the nodes/joints to produce the equivalent fixed-end structure forces, which are labeled Pfi for i = 1, 2, …, n later in the notes.

4. Introduce a unit displacement at each displacement degree of freedom identified in step 1 one at a time with all others equal to zero and without any loading on the structure, i.e., di = 1 with d1, …, di-1, di+1, …, dn = 0 for i = 1, 2, …, n.
Sketch the displaced structure for each of these cases. Determine the member-end forces introduced as result of each unit displacement for the kinematically restrained structure. These member-end forces define the member-end stiffness coefficients, i.e., forces per unit displacement. The member-end stiffness coefficients are vectorially added at the nodes/joints to produce the structure stiffness coefficients, which are labeled Sij for i = 1, 2, …, n and j = 1, 2, …, n.

5. Eliminate the error introduced in step 3 to permit the displacement at the nodes/joints. This is accomplished by applying the negative of the forces calculated in step 3 and defines the kinematically released structure.

6. Calculate the unknown node/ joint displacements.

7. Calculate the member-end forces.

Can the CAESAR Design engineers in COADE tell me whether the CAESAR uses the above technique in analysing the model ?

Well,yes, in a sense most structural solution software works that way. You are of course describing Castigliano's second therom. Disconnect the piping system from its anchor and diconnect the branches and load it. It will deform. Then calculate the forces and moments needed to reconnect all the disconnected points with the load still applied. But it is better said in this discussion

http://www.eng-tips.com/viewthread.cfm?qid=2614

If you Google "Castigliano's second therom" you will find that many professors of structural design have placed their class notes out there on the Internet.

Have fun, it is an interesting exercise.

Regards, John.

In chapter 9 of "Structural Analysis" by R. C. Hibbeler, it is given:
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"This method, which is referred to as Castigliano’s second theorem, or the method of least work, applies only to structures that have constant temperature, unyielding supports, and linear elastic material response."
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As Piping "structures" are having temperature difference MOST OF THE TIME, so Castigliano's theorem is not applicable to piping.

We just solve F=KX.

I wouldn't say that temperature change would invalidate the Castigliano approach. But the Castigliano's theorem does not address nonlinear response.