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# Capacity of I-beam as a cantilever2

## Capacity of I-beam as a cantilever

(OP)
In considering the capacity of a cantilever I-beam in bending, I looked at the following standards: AS 4100, BS 5950-1:2000 & SCI publication P360.

Could anyone shed light on the following questions. Assume case of a cantilever segment extending past another beam, with partial torsional restraint. Diagrams are shown in attachment.

Q1:
Comparing AS 4100 to BS 5950-1:2000 and SCI publication P360, the effective length inferred from AS 4100 is close to a value of 2.0L, whereas in BS it’s 5.0L and in P360 it’s also 5.0L (2.0 x 2.5). Have I missed something here?

Q2:
On the assumption that BS and P360 (which is supposed to be derived from BS) are the authority, I can’t seem to get the same capacity when I crunch the numbers (for 310UC118 with an overhang of 5m) ... maybe an error with calculating slenderness.
Please refer to separate Excel workbook.
This may be of help:

Replies continue below

### RE: Capacity of I-beam as a cantilever

Q1: There's a lot of disagreement about the braced length of a cantilever beam. The BS & P360 approach is perhaps the most nuanced of them (and is also shown in the Guide to Stability Design Criteria for Metal Structures (5th) published by SSRC for those practicing with US codes). In many (but not all!) typical building structure applications, common detailing results in the simpler 2*L condition being reasonably correct.

AISC's minimal guidance on the subject is... unfortunate to say the least.

Aside from the theoretical question, the first instruction I'll give to a young engineer with this question is the same instruction I'll give for torsion -- is there a reasonable way to design around it?

I'll leave it to others to troubleshoot the actual calc, since I'm only broadly familiar with AS4100

### RE: Capacity of I-beam as a cantilever

(OP)
Thanks Lomarandil, the comments above assist.

Unfortunately cannot design out the condition in this instance.

Understand that 2L is often correct ... for the case with a cantilever with a fixed base (restrained laterally, torsionally and against rotation on plan), AS 4100 agrees with BS 5950-1/SCI P360. See below from P360.

But the case mentioned initially, for continuous beam with partial torsional restraint, an effective length of 7.5L compared to 2.0L is a big difference.
In AS 4100, the code "PU" infers partial restraint at one end and unrestrained or free at the other end.

And could someone check the numbers in spreadsheet against own work if done before. Converted to PDF in this post, see attached.

### RE: Capacity of I-beam as a cantilever

Great question.

#### Quote (mte12)

Q1:
Comparing AS 4100 to BS 5950-1:2000 and SCI publication P360, the effective length inferred from AS 4100 is close to a value of 2.0L, whereas in BS it’s 5.0L and in P360 it’s also 5.0L (2.0 x 2.5). Have I missed something here?
No you haven't missed anything. I believe BS is conservative and AS4600 is not.

This thread is relevant and delved into LTB fairly deeply though I'm not sure a satisfactory resolution was achieved. It doesn't directly address cantilevers but there was certainly enthusiastic discussion.

I only know AS4100 code application well. But I know enough about it an cantilevers to consider it inadequate and unclear (to me anyway). The code considers doesn't directly address cantilevers. It only captures cantilevers with the implicit assumption that the end flanges are laterally and torsionally unrestrained. Which isn't necessarily true. You can have an 'FF/FF' cantilever members.[/u]

From what I've seen from discussions here the AS4100 code is easier to apply for most circumstances than AISC. But it probably isn't surperior. The BS code seems to be a more thorough implementation of AS4100's approach.

#### Quote (Lomarandil)

typical building structure applications, common detailing results in the simpler 2*L condition being reasonably correct.

#### Quote (mte12)

Understand that 2L is often correct ... for the case with a cantilever with a fixed base

Agreed. But most often correct isn't a great scenario for the 5% of cases. I feel that 2L is too simplistic and potentially dangerous particularly when more and more engineers see codes as a perfect recipe for adequate performance.

As somebody practicing using AS4100 I don't believe it is unconservative for spans supported at both ends. However for cantilevers it seems inadequate and I adopt BS guidance.

### RE: Capacity of I-beam as a cantilever

Posted by StructuralEng101

AS 4100 and BS 5950/P360 differ in their approach to lateral-torsional buckling, which explains the difference in effective lengths. AS 4100 is more conservative. For Q2, check your slenderness calculations—BS and P360 might have different assumptions.

Posted by CivilStruct

The discrepancy likely comes from different assumptions about restraint in the standards. AS 4100 uses a shorter effective length due to different buckling factors. Review how each standard treats slenderness and restraint.

Posted by Enginerd

AS 4100 and BS 5950/P360 treat local buckling and torsion differently. The 5.0L factor in BS/P360 likely accounts for less conservative restraint assumptions. Double-check your calculations for the 310UC118.

### RE: Capacity of I-beam as a cantilever

See AS4100 commentary. Chapter 5 rules are for ideal cantilever support only. Rigid for all rotation directions. Cases C1 and D1 from the AD408 document so AS has similar effective length. Never used them but Appendix H has rules for other cases. BS seems much simpler.

@Human909 Cabtilevers are considered by AS4100. Look at last 3 rows of Table 5.6.1. Also can use general equation for moment distribution (a.m factor) for beams with vertical support at one end but no restraint for buckling.

### RE: Capacity of I-beam as a cantilever

(OP)

Just to be clear, regarding last 2 posts, the case considered is for beam overhang past another member with and without partial rotation restraint (and with load at top ... destabilising). The effective length is 5.0L and 7.5L respectively from BS 5950-1/SCI P360.
AS 4100 will give 2.0L with partial restraint and "no guidance" without partial restraint.

So AS 4100 is unconservative here.

### RE: Capacity of I-beam as a cantilever

"The effective length is 5.0L and 7.5L respectively from BS 5950-1/SCI P360.
AS 4100 will give 2.0L with partial restraint and "no guidance" without partial restraint.

So AS 4100 is unconservative here."

AS gives >2.0 for partial restraint. You're ignoring the kt factor. Say 2.2-2.4 as a guess. BS goes from 2.5 full restraint to 5.0 partial restraint. That's conservative for UC section. If in doubt make it stout stuff. BS picks one number for UCs UBs and plate girders. Don't pretend it's accurate.

The 7.5 case is unrestrained in AS simple method so not unconservative compared to BS.

AS gives Appendix H as something you can still do by hand. But buckling analysis is prob easier these days. AS also covers this.

AS had the same as BS in the.working stress days. Conscious decision to switch.

Edit: Remembered wrong. Top flange factor was only 1.2 in the AS working stress code. Shear centre was same as BS.

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