Yield Moment (My) 2

[StructuralAddict]

In built-up plate girders, if the web is of grade 36 ksi and the flanges are of grade 50 ksi, then what how would the yield moment (My) be calculated? Is it My = (36ksi)x(Section Modulu to bottom of flange) or is it My = (50ksi)x(Section Modulus to top of flange)?

 

[ProgrammingPE]

Since you have two different yield stresses, either the flange or web may yield first depending on the exact dimensions. In order to figure out the Yield Moment, My, you need to determine the moment that yields the flange, as well as the moment that yields the web, and then use the smaller value.

Stress at any height due to moment:

fb = M * y / I​

Yield moment with one yield stress:

My = Fy * (I / y) = Fy * S​

Yield moment with different web and flange yield stresses:

My,flange = Fy,flange * I / c
My,web = Fy,web * I / (c - tf)
My = MIN(My,flange, My,web)​

I - Second moment of area
y - Distance from the Neutral Axis to any given fiber
c - Distance from the Neutral Axis to the most extreme Fiber
tf - Flange thickness

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[HTURKAK]

By visual inspection , one can say the web ( grade 36 ksi ) will yield before flanges ( grade 50 ksi )

In Eurocode BS EN 1993-1-5 (Part 1-5: Plated structural elements ) , this is called HYBRID GIRDER . Hybrid girders may have flange material with yield strength fyf up to 2.0*fyw if ,
- the increase of flange stresses caused by yielding of the web is taken into account by limiting the stresses
in the web to fyw
- fyf is used in determining the effective area of the web.

( The two conditions copy and paste from the code ).



Use it up, wear it out;
Make it do, or do without.

NEW ENGLAND MAXIM

 

[271828]

If you're in AISC Land, you'll need to back up to some older Specifications when so-called hybrid plate girders were used. The last two or three Specifications have equations derived based on equal web and flange yield stresses.

Conceptually, it depends on what you're using My for. If you're using it to decide between inelastic buckling and elastic buckling, then you might need to use the flange regardless of whether My is larger for it or the web. That's because residual stresses are max in compression at the flange tips.

 

[dik]

Is failure at web reaching fy=36 or the flange edge fy=50. Also let flange edge reach fy=50 and calculate the depth of fy=36 from the web down (web yielding)
Easier calculating Zx (plastic section) if Class 1 or Class 2 section.

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

 

[JAE]

By visual inspection , one can say the web ( grade 36 ksi ) will yield before flanges ( grade 50 ksi )

No not always.

If you have very thick flanges relative to the depth it is possible (as ProgrammingPE suggests) that the web flange could yield first, despite its Fy=50.

A 12" deep beam with 2" flanges (unlikely of course) would yield the 50 ksi flanges before the 36ksi web.

 

[human909]

Why are you trying to calculated the yield moment of the web? Personally I'd be more concerned about the plastic section moment than of the member than worrying about a tiny bit of yield of the web that could occur as the member experiences strain during loading.

The strength and serviceability will be controlled by the stress/strain in the flange and not the web.

Some controlled yielding is not something to be feared in our structures. In fact it is perfectly normal part of our design even in serviceability conditions. (Eg; most plies in bolt bearing)

 

[dik]

With the plastic section modulus, the web becomes part of the design... same with elastic design. Depending on the element proportions, the web may contribute.

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

 

[human909]

Of course the web contributes, but the lower yield strength shouldn't be an issue. That my point was that the lower yield strength of the web would barely be a factor if you allowed some yielding with the plastic section moment.

With the elastic section moment you will likely be really limiting your capacity and not suitably utilising the yield limit of the flange.