How to calculate Section Modulus on Compression Side of Beam??!! 3

[Struct_Dre]

Hello Everyone!

I'm very aware that this may seem like a very stupid question, but I'm stumped so please be kind LOL.

I am designing an aluminum beam for the first time and I need to check the interaction between local buckling and lateral-torsional buckling.

When Fe (flange's elastic buckling stress) is less than Fb (the lateral-torsional buckling stress of the beam) the 2010 Aluminum Manual requires that formula F.2-11 be used to reduce the LTB strength of the beam.

This formula contains Sc.

Sc is the section modulus on the compression side of the neutral axis of the beam.

I have NO CLUE how to find Sc. I assume the formula looks something like Sc=I/y. "I" being the moment of inertia for the entire section and y being the distance from the neutral axis to some point on the compression flange (top flange).

Is this correct?

If so, is y the distance from the neutral axis to the top of the compression flange or is y the distance from the neutral axis to the bottom of the compression flange??

I am extremely confused, have somehow never even heard of Sc in all of my short career, and can't find any examples online. Please help ASAP.

Also, I am designing an Aluminum Association Standard Channel, simply supported with UDL on top flange.

Any help is appreciated!!!

 

[r13]

If not work off principal axes, then torsion needs to be considered, as the load is through the geometry center, which does not coincident with the shear center.

 

[Celt83]

OK, but you can bend an unsymmetric shape about other axes than the principal axis.

yep agreed, but you need to account for the stress gradient created by the nature of the shape being unsymmetric. You can either do this by figuring out the principal axes and associated properties about these axes then transform the applied loading and do M c / I or you can use the general formulas and moments about any axes that you have section properties computed about.

using an L6x4x1/2 long leg vertical with a 1 ft-kip moment about the geometric x-axis such that there is tension on the toe and compression on the heel, just doing M c/I = M/S,bot for the heel would be in the neighborhood of 1450 psi (compression) but the general formula would yield about 3000 psi (compression) so around 2x the stress at the heel. M c/I = M/S,top for the long leg toe is about 2790 psi and the general formula yields about 3200 psi. For design purposes AISC has pretty much shifted to plastic design so different procedure there, where I've seen this cause issues is when working out pile loading with an unsymmetric layout either by design or checking as built conditions the delta in elastic pile force distribution can be significant between just doing M c/I vs using the general distribution formulas.



My Personal Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:

https://github.com/open-struct-engineer

 

[hokie66]

Maybe this is why we don't use many angles as flexural members. And when we do, we are very conservative.

 

[Celt83]

yeah looking at angles correctly can be a cumbersome process the McNulty book dives deep into the topic.

My Personal Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:

https://github.com/open-struct-engineer

 

[r13]

Here is a design manual recommended by AISC. Link

 

[jimstructures]

retired13,

Where did you see that the Single Angle Design manual was recommended or supported by the AISC.

That manual is a self published extension to the AISC Steel Manual. I do not think it is endorsed or recommended by the AISC.

That doesn't mean that I think there is anything incorrect in that manual, I just don't think it is recommended by the AISC.

Jim

 

[r13]

jimstructures,

Maybe my word "recommended" is not appropriate, but it was the sole independent publication referred in Steelwise along with many other AISC publications on the same topic. And for a small cost, I think it is a worthy reading material.

 

[university_professor]

section modulus refers to gross section, not to a part of it.

 

[Celt83]

"The elastic section modulus is defined as S = I / y, where I is the second moment of area (or area moment of inertia, not to be confused with moment of inertia) and y is the distance from the neutral axis to any given fibre."

My Personal Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:

https://github.com/open-struct-engineer

 

[r13]

professor,

I am kind of lost on your comment. Section modulus is derived from the moment of inertia, which is calculated based on the full/gross cross section area, but part of the cross section is in tension, and the remaining is in compression, thus, it is necessary to identify S[sub]t[/sub] and S[sub]c[/sub], unless the shape is symmetrical about the geometric center. Please at least use full sentence when provide insight to something, otherwise people will be misled, or ignore your comment. Sorry, don't mean to be rude.

 

[Agent666]

Retired13, just ignore that user, otherwise known as Johnie134 from a few weeks ago filling the forum with rubbish answers.

 

[r13]

Agent,

Thanks. The worst one liner I've ever seen.