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# LRFD Approach to HSS Tubing

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## LRFD Approach to HSS Tubing

(OP)
I need a steel guy (or gal) for this one.
Re: AISC LRFD Manual, 3rd Ed. Chapter 16.2, Hollow steel structural sections.

My problem is in dealing with Sect. 5.1 for a round HSS tube used in flexure. Table 2.2-1 shows the maximum limiting D/t ratios for local buckling under several usages. Now, for a 65ksi material with Lambda-r varying in the range of 138 to 200 for a hollow circular section, the limiting Mn/S is shown by equation (5.1-2).

If I run a spreadsheet on varying D/t values in the range of 138 to 184, the resulting Fb varies from 69.4 ksi to 52.0 ksi. For comparison, if I look at ASCE's Manual 72 (for tapered steel transmission poles), the limiting Fb values for that same D/t range are 58.5 to 55.3 ksi, respectively.

I can understand why Manual 72 would tend to be a little more conservative because of how the tubes might be fabricated and seam-welded, but my question is this: Why would AISC have an equation that produces a permissible stress of 69.4 ksi when the yield strength of the material used is only 65 ksi?

### RE: LRFD Approach to HSS Tubing

You are thinking in terms of ASD by looking at stress compared to Fy.  It is true that equation 5.1-2 gives the nominal moment as:

(some factor >1) times Fy times S

But the commentary for 5.1 offers some insight into the situation.  The section actually develops some, or all of its PLASTIC moment strength, thus, the limit state for your range of D/t between p and r does exceed Fy when combined with S....but you have a condition where your stress is somewhere between elastic and fully plastic.

If you notice, equation 5.1-1 uses Z while the other two use S.  This is because the behavior in 5.1-1 is FULLY plastic while the other two are only partially plastic.

### RE: LRFD Approach to HSS Tubing

(OP)

JAE:

Thanks for the comeback.

Yes, I did notice the use of the plastic modulus Z where D/t is less than Lambda-P. But, I wasn't dealing with the range between P (D/t=138) and R (D/t=32), but rather for a range above P (but less than 0.448E/Fy, which is 200).

What I gather from what you are saying is that even as we transition from D/t's below 138 to values above 138, we are still sort of floating in a nebulous area where the material is trying to determine if it wants to be plastic or elastic.

Evidently, according to the way that 5.1-2 works out, tests have shown that the behavior is somewhere in between.  So, in order to obtain Mn in that region, one would still use the regular section modulus S, but would be allowed to multiply it by an Fyb larger than Fy in order to simulate the partial plasicity of the material.

According to the Commentary, then, it seems that we would be in a range where the shape factor Z/S would equal about 1.07 (69.4 ksi/65 ksi).  And, this would steadily diminish as D/t approached 148, at which time we would be limited to Fy again.  Of course, for values from 148 to 200, the allowable stress would gradually diminish below Fy until it actually went down to 48 ksi (where D/t=200).

Am I on the right track here?

### RE: LRFD Approach to HSS Tubing

Polecat - yes...you said it all great...especially your paragraph 3 "Evidently...".

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