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RF-STABLE: importance of the critical load factor, part 2, application in RFEM

In the first part of this series I wrote something to the theoretical foundations. In this part there is now little practical emphasis. But first a little theory.

I had attachments so that small on a critical load factor of 10, the second-order theory to be considered. But what does exactly the number of critical load factor?

This is actually quite simple. If we increase the load to the critical load factor, then the system is unstable. Here is a very simple structural system:

A cantilever column is loaded with a weight (red). The weight is increased ever further. Even if one assumes that the material of the cantilever column always has a linear stress-strain curve, ie, the Hooke's Law holds infinitely long, then the system will eventually become unstable.

occurs on a stability failure. The critical load factor (load factor = branch) states can be increased by what factor the load until the stability failure occurs. Oops! It is here always assumed ideal linear elastic behavior of the structure.

What I said now the Verzeigungslastfaktor? It must be 3 different areas are distinguished:

1. The critical load factor is less than 1 .
2. The critical load factor is 1-10 .
3. The critical load factor is greater than 10 .

In case 1, the situation is clear. The system is already unstable load with ease and thus dimensioned to be weak.

The 2nd Case in practice, the most common case. The structure is under load once stable, but further evidence of stability is required. It must therefore be expected to second-order theory, or it must be buckling out after the replacement staff procedures. In the 3rd

Case, the structural stability is not endangered. There, a simple stress analysis with the internal forces to first-order theory.

If the buckling load factor greater than 1, that is so far no evidence against buckling or stability failure against another.

Two things are to be set.

The bar elements in RFEM can represent no lateral torsional buckling. This is indeed in almost all staff members of other programs. If there is a lateral torsional buckling problem could, therefore, further investigations are then necessary.

The determination of the critical load factor is carried out by solving an eigenvalue problem. In the "normal" calculation is important to note that any non-linearity is taken into account. If allso precipitated rods, precipitating beddings and other non-linearities in the system, then the calculation is at least inaccurate, possibly even incorrect. In this case, helps further the nonlinear analysis of RF-STABLE. More on that in the next part of this series.

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RF-STABLE: importance of the critical load factor, Part 1, Basics

Today I wrote the first time a contribution to a plug-in. The issue is more complex, so I will divide into several parts. The first part deals with some theoretical basis.

Most modules in RSTAB or RFEM're proof modules. The normal operation is that the internal forces with RSTAB or RFEM be identified and passed the qualifications of the components according to relevant standards with modules.

something different is the module RF-STABLE. This is not a normative Detection performed. Why do you need the module then?

At the beginning of structural analysis one is trying to decide whether the forces may be determined under the first-order theory, or whether the deformations have a significant influence on the forces, so the calculation is necessary for second-order theory.

What exactly "first-order theory" and "second-order theory" is, I will take in a later figure does something more closely. Here are just a very brief explanation. In the first-order theory assumes that the stress and strain are linearly related. If, for example, doubled in a single-span beam exposure, then doubled and the deflection. The balance of power can be placed on the undeformed system. Anders II on the theory of procedure. Here, no longer a linear relationship between stress and strain can be assumed. be the equilibrium of forces on the deformed system set up. Here is a very simple example of such a structure:

stress and deformation depend not together anymore linear. The lateral deformation is increased because of the lateral displacement by the vertical force. This cantilever column is a geometrically nonlinear structure or in other words, there is a stability problem.

For the detection of such a structure is no longer enough, a simple stress analysis. It must also be performed on a stability proof. Could be conducted so that the forces are determined on the deformed system, ie, after second-order theory, and then a stress analysis is conducted.

The calculation for second-order theory with modern structural analysis software, today no more no art. If one can expect to first-order theory, then that has some real advantages. Instead of load groups can also use load combinations. on the exact difference between load groups and load combinations I've ever written here etws.

But at what point is a stability proof necessary? It may be that the vertical force is very small compared to the horizontal force. The decisive criterion is the critical load factor. If it is greater than 10, then, the influence of second-order theory are neglected. Is it 10 less, then a stability check is performed.

So, now is clear, what one needs the critical load factor. The second part is about what the exact number and how to calculate with RF-STABLE the critical load factor.

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