Plastic Moment Capacity of Composite Shape

[StructuralEngGuy]

Does anyone know how to calculate the plastic moment capacity of a composite shape with varying Fy? For example, a wide flange beam (Fy=50ksi) with channels welded to the top and bottom flanges (Fy=36ksi)? I did it by summing the moment capacity of the wide flange beam and the moment capacity of the two channels seperately. Does that seem right? Any help would be appreciated.

Thanks

 

[BAretired]

No, that is not correct. I believe that, for composite sections with varying Fy, you should be using the lower yield point for all of the steel.

You need to calculate the plastic modulus of the entire section, wide flange plus two channels, then determine the plastic moment, assuming all of the parts have a yield point of 36 ksi. It is a bit conservative, but it is the way that most codes require you to consider built-up members.

BA

 

[hokie66]

I don't know what codes say about it, but I would have agreed with the OP's way of doing it. The channels will go plastic first, but will still carry the same load until the beam reaches its own yield. So in accordance with the philosophy of plastic design, the moment capacity is dependent on the yield of the entire section.

 

[dik]

I'm not sure why you would you would undertake this unless it's for remediation or renovation. YOu are venturing outside of normal practice.

With plastic design, the lower strength section would yield, and deform until the higher strength section would yield. It is appropriate to consider both yield values as long as the materials are capable of undergoing the deformation.

You have to check b/t ratios for local stability of the added sections. You also have to check for overall stability; this is not normally a problem because there is usually sufficient lateral bracing, but I don't know the application.

The resulting section should be reasonably symmetric to prevent second order effects.

The new sections have to be welded with sufficient weld material to attach the members.

Lastly, deflections have to be determined and because of the plastic action and different materials this is the topic of a new discussion <G>. The deflection curve may have four or more regimes (a typical rolled section may have three or four). Consult a good book on plastic design for calculation of this.

Good luck...

Dik

 

[dik]

I should have added with the weld note that the normal A'ybar over I b isn't applicable.

Dik

 

[Lion06]

If I'm understanding your situation correctly, you have a WF wiht a channel on the top and a channel on the bottom, not a WF with a channel on each side.

In the former case, the bending moment of the channel is not revelvant. the moment capacity of the two channels as a ficitious section would be relevant. I would the Mp of the WF with the Mp of the channels using the section properties based on there location. The only deformation the channels will need to take is axial, and it won't be significantly more than it takes to make them plastic.

 

[ishvaaag]

As long connection at the shear interface (web or bolts) stand sound till the limit states and plane sections remain plane along bending you can study the stress-strain progress in some spreadsheet or worksheet. At some point we can surmise -the stress-strain diagrams can tell- the WF flanges and the channels' sections will be yielding, and upon further progress to complete plastification of the section, plastic moment capacity most surely can be evaluated for such state; but this is Mp, not the true Mn for which any other considerations relevant must be taken unto account as dik makes clear.

 

[miecz]

If you were designing to AASHTO, Article 6.10.1.3 allows the use of a hybrid section with the web yield strength higher than the flanges. In this case, the yield strength of the web can not be taken greater than 120% of the yield strength of the lower strength flange. I can't find any provision in AISC's 13th Edition. In fact, I have a hard time finding anything in the 13th Edition.

 

[dik]

Just a caution about plain sections remaining plain... this may not have a correlation with the stresses or forces involved, once yielding occurs... forgot to add that the moment rotation curve is not likely linear with the intended fabrication.

 

[miecz]

I think you could avoid a lot of complexity in the deflection calculation by keeping the flanges below yield under service loads.

 

[271828]

LOL, why are you guys making this so complicated?! hokie66 is correct.

It's as simple as taking Mp of the W-shape using Fy = 50 ksi and adding Mp that one gets from the channels spaced the correct distance away from the centerline of the W-shap. The contribution of the channels would be

Mpchannels = 2*Achannel*Fy*(d/2+twchannel-xbarchannel)

with Fy = 36 ksi and d for the w-shape.

 

[miecz]

271828-

I'm not sure it's so easy. This built up section is similar to a hybrid girder. According to Article 11.6 of Salmon and Johnson (5th Ed.), AISC recommendations for hybrid girders were based on research by a joint ASCE-AASHTO Commetee. Rather than the rational approach you propose, they came up with a "Strength reduction formula" that was published in AISC's 3rd Edition, but has been removed from the 13th. S&J concludes that the 13th edition does not consider hybrid girders to be a viable alternative.

 

[271828]

Right, but he just asked for "plastic moment capacity."