Plastic Moment Capacity of Composite Shape
Plastic Moment Capacity of Composite Shape
(OP)
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
Thanks






RE: Plastic Moment Capacity of Composite Shape
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
RE: Plastic Moment Capacity of Composite Shape
RE: Plastic Moment Capacity of Composite Shape
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
RE: Plastic Moment Capacity of Composite Shape
Dik
RE: Plastic Moment Capacity of Composite Shape
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.
RE: Plastic Moment Capacity of Composite Shape
RE: Plastic Moment Capacity of Composite Shape
RE: Plastic Moment Capacity of Composite Shape
RE: Plastic Moment Capacity of Composite Shape
RE: Plastic Moment Capacity of Composite Shape
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.
RE: Plastic Moment Capacity of Composite Shape
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.
RE: Plastic Moment Capacity of Composite Shape