momentdesignonbeams

Figure 9.1

So the Design of Beams for Moments can be divided into three zones.

From PBF (PM) to Inelastic lateral torsional buckling (ILTB) to Elastic lateral torsional buckling (ELTB).


Now why would this curve behave as it is shown?

What we have on both axis here, is a relationship between the nominal resisting moment of a beam, or its flexural capacity.

On the x-axis we have information regarding the lateral unbraced length of the compression flange on a beam).

You have to notice that this book has information regarding steel design, why would the lateral unbraced length be concerned with the compression flange on this evaluation?

I'm not quite sure.
You'd expect that in most situations those flanges could be encased in concrete.
If we are to check the capacity of flexure on a steel beam, its steel capacity is what is most important to us, the values we get related its length on the compression flange?



Anyway, the result or the function basically goes from flat to less... makes sense that at higher lengths the capacity of flexure is reduced.

I also think the curve is flat for plastic just due to the nature of the reversions that may happen within the member, so value keeps consistent.

As for the LTB It seems to be changing linearly but at a consistent slope, indicating intial signs of elasticity, or break thorugh the plasticity of the member, and lastly the elastic curve shows some smothing that may indicate the variation has grown to a second order rate of change. Could these equations be indication of the behavior change as an increase in order?

I don't know.

But, I know how to design it for what is a lateral unbraced length.

Think of members in terms of their length and cross-section size.

Cross-section values are important along the two axis of analysis, however, the length is just as important.

Longer sections means more slenderness to something, means it can bend along its longitudinal axis, or buckle about it.

The longer or larger that value is, that means that I should lose capacity of holding flexure, and buckle about my axis.

So, in that case, these relationships have been drawned and tabled, and make your life easier to work these days.

More notes on the ranges of behavior for nominal moment capacity.

Remember nominal values (sometimes noted with an n (for nominal), preferrebly should be noted with 0 nor a 1 or often left in blank, as in M) must be factored.

Turn into Mu for ultimate analysis in LRFD and Ma for ASD.