Designing a single angle 2

To compute your yielding moment, you use a section modulus Sx

To compute your plastic moment, you use your plastic modulus Zx

Unbraced lengths do not affect which modulus you use. However, your unbraced length will affect your critical stress (Fcr) in your LTB calculation. You need to see if LTB applies, if so, then you will be asked to compare your plastic moment to your nominal moment (which would be your LTB moment if it controls).

Why isn't the engineer who originally specified the angle not being asked this question via an RFI?

My supervisor is the EOR, the question came on a shop drawing, and that was extraneous information.

I know that the longer lintel span case will likely require LTB design because the L[sub]p[/sub] is less than L[sub]b[/sub] but the LTB design hinges on computing M[sub]y[/sub] correctly. If I understand you correctly (andriver), you are saying that the plastic moment only applies in LTB design and I should use F[sub]y[/sub]*S[sub]x[/sub] when computing the yield moment and F[sub]y[/sub]*Z[sub]x[/sub] in LTB design?

conradlovejoy - I have run across this situation before and feel your pain. I can't speak for the 14th ed, but the 13th ed definitely leaves some things to be desired for single angles. I believe there is an example on the CD that accompanies the manual (or perhaps an AISC design guide), I suggest you take a look.

No that is not what I am trying to say. Also, I probably spoke to soon and should have at least flipped open my AISC book.

Your plastic modulus is only used to compute your plastic moment, however, looking at AISC F10, you are not required to compute your plastic moment. So you can forget all bout the plastic section modulus. This isn't always the case, as you can see in section F11 you are asked to compare your nominal moment to your plastic moment. My mistake.

For angles, you would compute My which is your yielding moment. This is just Fy*Sx (section modulus). EDIT ACTUALLY AISC Says My Shall be 0.80*Fy*Sx

You also need to check LTB. You have two cases Me <= My or Me > My. If Me <= My, use equation F10-2 to compute your nominal moment. If Me > My, compute EQ F10-3. If EQ F10-3 <= 1.5My, then EQ F10-3 is your nominal moment. If If EQ F10-3 > 1.5My, then 1.5My is your nominal moment. Hope this helps.

I guess my confusion is why is the plastic modulus used to find the nominal yield strength of a w-shape beam in flexure if that is not the case for other steel sections. I am unsure how the member geometry effects when to use plastic moment design (mostly because the paragraph in F10 states that the yielding limit state is a plastic moment...)

When I was fresh out of school, I nearly lost my mind trying to properly design brick angles. They are complicated:

1) They are subject to torsion.
2) The torsion adds to brick deflection.
3) How the torsion is resisted at the bearing condition is complex
4) Design for displacement, LTB, Zx/Sx, shear etc...
5) Accounting for the fact that the lintel just kinda formwork until the mortar sets up.
6) Potential out of plane loads if there's a control joint one or both sides of the window.
....

A couple of decades on, I just do this:

1) Make it stiff. L/600 ignoring the twist.
2) Make it strong. Sx, not Zx. 36 ksi.
3) Make it practical. 5/16" max leg stiffness.

I don't even bother with LTB. So far, so good.



I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

FoxSE, I am using the 13th edition as well since it is what I had in school. I just recently got into the structural designing gig, unfortunately so I feel woefully behind where I should be based on how long I have been out of school.

Be careful as the the neutral axis will be inclined and moments in the other plane (about weak axis) will appear, due to the eccentric feature of single angle sections.

Jason McKee
proud R&D Manager of
Cross Section Analysis & Design
Software for the structural design of cross sections
Moment Curvature Analysis
Reifnorcement Design etc.

Thanks KootK, The deflection was calculated and not a problem using L/600. The angle is 3/8 and very likely plenty for the scenario, but for my own sanity I was trying to run the numbers and found out I still have a lot of questions about appropriation.

Conrad,

Agreed, that is confusing. Maybe someone with more years under their belt can chime in.

In response to FOX suggestion that you look up the AISC example problems, I have attached to this post the single angle flexure example provided by AISC

Jason, will 6ft of brick veneer above the angle cause enough deformation to consider what you're referencing?

OP said:

I guess my confusion is why is the plastic modulus used to find the nominal yield strength of a w-shape beam in flexure if that is not the case for other steel sections.

Click to expand...

Sometimes, your individual plate elements will buckle at a compression stress lower than M/Zx. Or even M/Sx for that matter. If that's the case, they you cannot mobilize the higher levels of compressive stress implied by Zx (or Sx). We usually use plate width to thickness ratios to assess the potential for local buckling.

If you really want to chase down the single angle stuff in detail, google "single + angle + Trahair". It's mostly Trahair's research informing our design equations these days.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

If you have to use LTB would recommend picking up a copy of the Single Angle Design Manual. We attended a webinar by the author a while back and have found the examples helpful.

Link

Believe the author also has some spreadsheets developed for it that he'll share for a fee if you contact him. Obviously vet yourself before using.

KootK said:

A couple of decades on, I just do this:

1) Make it stiff. L/600 ignoring the twist.
2) Make it strong. Sx, not Zx. 36 ksi.
3) Make it practical. 5/16" max leg stiffness.

I don't even bother with LTB. So far, so good.

Click to expand...

That is basically my approach except I usually go much stiffer if it is a retrofit as the masonry assembly does not have as much give once it is set-up. I also use 3/8" leg angles when appropriate.

Hershey said:

If you have to use LTB would recommend picking up a copy of the Single Angle Design Manual.

Click to expand...

Ordered! Thanks for the recommendation. I'll report back in June when the darn hard copy arrives this side of the border...



I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

Per AISC 360-10 (or AISC 360-05), the yield moment (M[sub]y[/sub]) is equal to F[sub]y[/sub]S. For the special case of an equal-leg angle with bending moment about a geometric axis with no lateral-torsional restraint within the span, the yield moment is equal to 0.80F[sub]y[/sub]S.

If the angle lintel in question is unequal-legged and has no lateral-torsional restraint within the span, AISC Chapter F10 requires the moment be broken into components about the principal axes. The strength about the major principal axis is determined from equation (F10-5) and equations (F10-2) or (F10-3), depending on whether M[sub]e[/sub] ≤ M[sub]y[/sub] or M[sub]e[/sub] > M[sub]y[/sub]. The strength about the minor principal axis is limited to 1.5My since lateral-torsional buckling does not apply to that axis. You then check the combined bending stresses using the interaction equations from Chapter H.

Once you understand the bending behavior of single angles (not a simple task, as witnessed by KootK), and are ready to make a profit, I recommend getting a copy of "Safe Load for Laterally Unsupported Angles" by Leigh, Thomas, and Lay. This paper was published (re-printed, really) in the first quarter, 1984 edition of AISC Engineering Journal. The article is available free of charge to AISC members ( The paper is based on the Australian steel code of that time but provides span tables that will provide a good starting point for selecting an angle lintel or as a check on an angle lintel you have otherwise designed. For more general background information on the bending of single angle members, another Engineering Journal paper ("Design Aspects of Single-Angle Members" by Pierre DuMonteil) may be helpful. This paper was published in the fourth quarter, 2009 edition. For a real quick read on background material, I recommend the Chapter F10 Commentary.

I assume this is a loose lintel over a window opening. What are you using for loadings? A triangular mass of brick with a base of the window opening and isosceles legs above? The brick beyond will arch over the opening. Usually, the load is too small to get into a highly theoretical analyses. Make some conservative assumptions noted above and move on. I use between 5/16" to 3/8" thicknesses for loose lintels. You really can't use thicker angles without noticeably affecting the mortar joints. If you are supporting CMU, you can use double angles and balance one against the other.