Flat bars and plates

[Vector1962]

I've followed the procedure contained in AISC specification F11 to determine the Mn. I used the AISC design guide examples, example F.12 and AISC spec section F11. The procedure seems pretty straight forward, I have it in Mathcad. I also was able to reproduce the calculations that produce table 3-18a (all within a couple psf); also, in Mathcad. Comparing the results of the 2 procedures, they yield vastly different results. Shouldn't the procedures produce reasonably similar results?

 

[JAE]

Which AISC specification?
Which Design Guide?

F11 is for plates and bars (i.e. individual members) in flexure.
Table 3-18a is for checkered plate.
Not sure if what you are designing here are the same things.

Perhaps some more detail?

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[dik]

JAE: even less clear for those not totally familiar with AISC requirements.

Dik

 

[JoshPlumSE]

F11 being the section for rectangular bars and rounds. This section will take you all the way up to Mp = 1.5*My for a rectangular plate
F12 being the section for unsymmetric shapes. This section limits you to My. So, for a fully supported plate you've already got a 50% difference.

Why is F12 so much lower? My belief is that it's merely an acknowledgement that we don't know that much about how a totally unsymmetric shape is going to behave.

 

[Vector1962]

AISC 13th edition. I've been using A36, Fy36, Fu58, E29000 for both procedures. I think they are correct as I can reproduce Table 3-18b pretty close. The design guide is "Steel Design Examples", in pdf format.

 

[racookpe1978]

Look at the boundary assumptions for the two cases: You might find differences.

 

[Hokie93]

What two procedures are you referencing? The plates in Table 3-18b are in weak-axis bending. Example F.12 from the AISC Design Examples (version 14.2) concerns strong-axis bending of a plate. Both weak- and strong-axis plate bending are covered in AISC 360-10 Section F11 but, depending on the unbraced length for the strong-axis case, the results would be significantly different.

 

[dik]

Josh F11 is for rectangular shapes and the 1.5 represents the shape factor bd2/4 vs bd2/6
I don't know about F12.

Dik

 

[JoshPlumSE]

Yeah, I misunderstood his (somewhat poorly worded) question. I thought he was using provisions from section F11 and comparing them to what he'd get using the provisions from F12.

 

[MotorCity]

Mathcad? Have you tried f = M/s?

 

[Vector1962]

Suppose i have a span of 1.5' and 3/4" thick bar, 12" wide. according to table 3-18b the plate has 7980 psf allowable. Simple enough, as i note above, can reproduce this table. Following the procedure of F11 (which by the way states it's applicable to bending either any geometric axis) the resulting allowable calculates to 10,780 psf. I'll restate the question, less poorly, Shouldn't the procedures produce reasonably similar results? lastly, i appreciate the responses thus far, thanks so much. I would note however, haven't seen anything that explains why the discrepancy.
Oh.. "Mathcad" is a software package that does math.

 

[Hokie93]

The difference is that the plate bending stress is limited to 24 ksi (ASD) in Table 3-18b. This is covered in the table notes on page 3-12 of the 14th edition AISC Steel Construction Manual. The equivalent "allowable bending stress" from Section F11 is 0.90F_y, or 32.4 ksi for ASTM A36 plate.

 

[Vector1962]

@Hokie93, Excellent, thanks so much. I have the 13th edition and yes, 24ksi LRFD (16ksi ASD which I used). In the 13th edition, I don't see the 0.9Fy provision you reference. However, 0.9Fy is more than the double the 16ksi per the table notes you reference. The more conservative approach are the table 3-18 values and will use those. Please note, This was not an academic exercise as we're planning to support roughly $20M worth the equipment on the selected bar grid and I need/(would like) to understand every nuance of the associated calculation. I think since I can recreate the table I'll proceed with that (plastic moment makes sense). Nobody will care, design by AISC table 3-18 or F11 if the support system is no good. Best to understand the engineering behind both. I wonder if F11 shouldn't make reference to table 3-18? Actually, I wish there was some discussion available as to why the F11 rectangular design spec design procedure doesn't directly result in the Table 3-18 values; seems like it should. At any rate, thanks eng-tips for the tips.

 

[Hokie93]

The 0.90F_y "allowable bending stress" is derived from Section F11 as follows.

M_n = M_p = F_yZ ≤ 1.6M_y
The shape factor (Z/S) for a rectangular cross section is equal to 1.5.
The factor of safety (Ω) is equal to 1.67.

M_n/Ω = 1.5M_y/1.67 = 0.90M_y = 0.90F_yS

M_n/Ω = F_bS

Therefore the "allowable bending stress" (F_b) is equal to 0.90F_y.

I am not certain as to why the allowable bending stress in Table 3-18b is limited to 16 ksi (ASD) but I suspect it is a combination of:
1.) Historical precedent (the 16 ksi value was used in the 9th edition AISC Steel Construction Manual) and apparently good performance based on the historical precedent.
2.) Table 3-18b references ASTM A786 and that standard does not directly specify a minimum material yield strength. Perhaps AISC is allowing for the possibility of "low" strength material being specified.
3.) Checkered plate floor is often used in applications where it will be 'abused' in service. Limiting the bending stress to 16 ksi provides an additional factor of safety.
4.) Table 3-18b covers only uniformly distributed loads. Limiting the bending stress to 16 ksi provides some excess capacity for unexpected concentrated loads.

There is no requirement to use the capacities provided in Table 3-18b; you are required to follow the AISC Specification (provided your governing building code references the AISC Specification). Provided that you are satisfied the in-service conditions don't necessitate a greater factor of safety and you have limited deflection to a reasonable value, there is no reason you cannot design the floor plate to the AISC Specification requirements.

 

[Vector1962]

Excellent. Thanks again.