## Robot Structural Analysis

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# Errors in Canadian steel code design - axial tension and bending

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I came across two scenarios resulting in incorrect results, both related to axial tension.

#1

In the first scenario Cf=3.57 so the section is under compression, therefore the equation marked in the picture below does not apply as it applies only to tension.

#2

In the second scenario there are two identical beams with the exact same bi-axial bending and small compression in the first one and small tension in the second one.

Now, the first results below (for the case of compression) are correct. The second results (for tension) one would expect to be almost the same, because the axial force is insignificant. However, the utilization ratios are smaller in the latter results. That is because the second equation is mechanically copied from the code without appropriate interpretation. The code is somewhat imprecise here, but it is rather obvious that weak-axis bending cannot be ignored in equation 13.9.2(a) and should be added to this equation, resulting in: Mfy/Mre + __Mfz/Mrz__ + Tf*Zy/(Mre*A). Otherwise, the case of lateral-torsional buckling and weal-axis bending is ignored.

The third equation is wrong even when mechanically copying the code. The code specifically says "where Mr is as specified in Clause 13.6", that is for laterally unsupported member. This is because tension only helps to reduce the effect of lateral torsional buckling and in no way helps with weak-axis bending.

This is a serious error that may result in significantly under-designed members.

# Re: Errors in Canadian steel code design - axial tension and bending

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Patrick,

Thank you for sending these remarks. I will investigate this issue but I may not be able to answer immediately. I expect that I will need a bit of time to check that.

**Artur Kosakowski**

# Re: Errors in Canadian steel code design - axial tension and bending

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#1

In the first scenario Cf=3.57 so the section is under compression, therefore the equation marked in the picture below does not apply as it applies only to tension.

I think you are right. After looking at this issue I assume this is the wrong display of the verification formula when you disable buckling in the bar type. If that is enabled (which I believe should be in case you want to consider compression having LTB enabled at the same time) the result dialog looks like this:

#2

The second results (for tension) one would expect to be almost the same, because the axial force is insignificant. However, the utilization ratios are smaller in the latter results. That is because the second equation is mechanically copied from the code without appropriate interpretation. The code is somewhat imprecise here, but it is rather obvious that weak-axis bending cannot be ignored in equation 13.9.2(a) and should be added to this equation, resulting in: Mfy/Mre +Mfz/Mrz+ Tf*Zy/(Mre*A). Otherwise, the case of lateral-torsional buckling and weal-axis bending is ignored.

Again I think your point may well be right however looking at the Canadian code itself I have some doubts. As far as I can see (I'm sorry if I'm wrong but this is not the code I'm really familiar with) the part that describes compression + bi-biaxial bending clearly shows these 3 components in the corresponding verification formula. Why for tension and bi-axial bending only two (axial force and one bending moment) are listed in the verification formula in the code? Any reason for this? Why these two formulas (tension vs. compression) as shown in the code have got different look?

Could you give me some references that describe the verification of tension + bi-axial bending which I could look at please?

The third equation is wrong even when mechanically copying the code. The code specifically says "where Mr is as specified in Clause 13.6", that is for laterally unsupported member. This is because tension only helps to reduce the effect of lateral torsional buckling and in no way helps with weak-axis bending.

Indeed assuming that the other bending moment should be included in the second verification there is no need for the 3rd one but assuming that the code deliberately says that only one bending moment should be used it may have sense.

**Artur Kosakowski**

# Re: Errors in Canadian steel code design - axial tension and bending

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#1

It looks like there is one more thing wrong here. **Cf/Cr** is missing in the first equation.

#2

"Why for tension and bi-axial bending only two (axial force and one bending moment) are listed in the verification formula in the code? Any reason for this? Why these two formulas (tension vs. compression) as shown in the code have got different look?"

That is why I said that the code is somewhat unclear, but I gave you a good explanation why weak-axis bending cannot be excluded. Also, note that the equations in clause 13.9 use Mf (without specifying the direction) rather than Mfx or Mfy. Also, following your logic, why would the first equation include both direction? Clause 13.9.1 also does not include specifically Mfx and Mfy.

"Could you give me some references that describe the verification of tension + bi-axial bending which I could look at please?"

I do not have any such references handy, so you guys have to do your own homework if you want to confirm that.

"*The third equation is wrong even when mechanically copying the code. The code specifically says "where Mr is as specified in Clause 13.6", that is for laterally unsupported member. This is because tension only helps to reduce the effect of lateral torsional buckling and in no way helps with weak-axis bending.*

Indeed assuming that the other bending moment should be included in the second verification there is no need for the 3rd one but assuming that the code deliberately says that only one bending moment should be used it may have sense."

No, it does not make any sense at all, even if you want to check just one direction. Again, tension does not help with weak-axis bending, because there is no LTB for weak-axis bending.

# Re: Errors in Canadian steel code design - axial tension and bending

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Patrick,

The following changes are introduced in the SP4 for Robot 2013:

The verification formula 13.9.2a displayed in the 2nd row should also include bending moment is Z direction (axial force + My + Mz)

The verification from the 3 row should not be done.

Please check for the availability of this update at the beginning of the next week.

**Artur Kosakowski**