(Again, credit goes to Dale and other fellow engineers who shared the concept of the unchartered territory of twisting moments and in-plane shear in shell elements that sparked my curiosity and inspired this writeup.)
Question:
In SAFE, is it ok to use the bending moments for design from a) the moment contours M11 and M22, and b) the bending moments from the strip forces?
Answer:
I’d give it a resounding NO in a capital and bold font style. Why? Because the bending moments from the moment contours and the strip forces do not account for the twisting moment, namely the M12 or the Mxy as some may call it. This twisting moment is what Wood and Armer added to the normal bending moments.
To illustrate, an infinitesimal element below is subjected into out-of-plane bending moments which are the m11 and m22. Also in the figure is m12 which is the twisting moment that is included in the computation of the final bending moment to be used for design.
Ok, so before you get drowsy and close this page, let me now illustrate the difference in magnitudes of using the moment contour, the strip moment, and the strip moment used for design:
The example below is an edge middle strip of 6.0m width. Let’s try to compare the bending moments taken from a) moment contour or M22; b) strip moment that can be viewed when showing the strip forces; and c) design moment that SAFE used to generate the required reinforcement. The general idea is, wherever we get the bending moment, they should be the same (it will make no sense if we get different results, right?) but let’s see if that’s really the case.
In the moment contour above, we’re getting an average of +/- 100 kN-m/m of bending moment.
In the strip moment, we got 643.251 kN-m. Dividing it by 6.0m we get a bending moment of 107.21 kN-m/m
Last but not the least is the design moment used by SAFE. In the snapshot, the bending moment at the bottom is around 713.416 kN-m so dividing it by 6, we get 118.90 kN-m/m of bending moment.
Now there’s a difference. Not much difference you say? It’s because the sample model has a simple and regular framing. Compare it to a more complex floor layout and you’ll see a stark difference (go figure for yourself!).
So what happened to the design moment and why is it different from the first two means of getting that flexure? Blame it on the Wood-Armer equations for combining the torsional moments to the moments in the same orientation as the global X and Y axes.
Follow Up Question:
Is this twisting moment the resultant of the M11 and M22? What does this torsional moment look like anyway?
First, no the twisting moment or the M12 is not the resultant of M11 and M22. Second, continue reading below for you to know on how we interpret it. Again, credit goes to my fellows for sharing it so that I can share it with you too.
Let’s get familiar with these principal moments, shall we?
What we saw above are the principal moments and their respective directions (Mmax is the longer arrow and the shorter one perpendicular to Mmax is the Mmin). And take note that the principal moments are angled, such that they don’t necessarily coincide with the global X and Y axes. But what are these principal moments anyway? We need to face again our archnemesis way back strength of material days.
The circumference represents the out of plane bending moments at different angles. This site offers a nice animation of the envelope of normal and twisting moments on a finite element at different angles. Going back to the above figure, Mmax and Mmin are the principal moments which happen when the twisting moment M12 is zero. Conversely, the maximum twisting moment occurs at point C, which is the average of the Mmax and Mmin. Note that M11, M22, and M12 do not, and will never simultaneously reach their maximum values.
In a way, the effect of the twisting moment closely resembles that of the bending moment on the familiar orthogonal axes of a slab. That, perhaps is the same reason why Wood and Armer proposed to combine the normal bending and the twisting moments to produce a design moment that is larger than the bending moment normal to an axis that does not coincide with its principal moments.
Since most FEA softwares already include the twisting moment to derive the design flexural reinforcement, I believe that aside from investigating the behavior of a floor plate, in SAFE:
- it’s no use looking at the moment contours and the strip forces per se and using them to derive the design reinforcement;
- the m12 moment diagram in itself means nothing aside from the aforementioned behavior evaluation;
- the strip bending moment is only but a good estimate of the probable ultimate bending moment that can be used for design;
- you have to rely on the design strips in doing the averaging and inclusion of the twisting moments for you
I’m not closing my mind though for other ideas, possibilities, and mathematical concepts that I don’t know yet regarding my four deductions above. We’re in a scientific community anyway, so unless proven wrong you might as well agree with me.
You don’t? I hope you’ll share your take on this in the comment section below. Thanks in advance!
The post Understanding M12 (Out-of-Plane Twisting Moments) In Shell Analysis Outputs appeared first on Civil Engineering Community.
source https://www.civilax.com/understanding-m12-out-of-plane-twisting-moments-in-shell-analysis-outputs/
