Elastic Structural Analysis followed by plastic member capacity design

[CivilSigma]

Something has been bothering me about principles of steel structure analysis and design...


In the design of beams for example, if I am intending to use a section's plastic capacity (Mrp), can I compare that to the Mfy obtained from elastic analysis? Or do I need to perform plastic analysis of the beam to obtain Mfp and compare that to the sections Mrp?

I have always performed elastic analysis, and sized appropriate members based on plastic section capacity.
Is this conservative? or do I have a fundamental misunderstanding?

 

[dik]

For Class 1 and 2 sections you can use the design moment calculated using the plastic section modulus. This reflect the section being more 'stocky' and not susceptable to local elastic buckling. Plastic design is something else. For plastic design you are looking at the collapse mechanism and taking advantage of residual strength. The failure load of a structure may go beyond that that causes elastic failure. For example a steel beam with fixed ends and a uniform load fails elastically at wl^2/12 when the end moments reach their elastic moment capacity. The code allows you to use the resisting moment determined using the plastic section... this gives you an increase of about 10% or 15%. Failure due to a UDL occurs when the end moments become plastic, and the mid span moment becomes plastic. This occurs at wl^2/16 for the end moments and midspan moment, for an increase of 33%. Actual failure does not occur until a plastic moment develops at midspan. Clear like mud?

There are a couple of other issues that you have to be aware of... plastic design does not address instabilities. In addition, there are stress issues related to residual stresses from previous loading. This is referred to as 'shakedown' analysis. It's not always 'just a walk in the park'.

Plastic design is less conservative. It is not generally used and it is generally much less costly. Members tend to be smaller and there are fewer pieces to handle.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[271828]

For statically determinate structures, one plastic hinge is sufficient to cause a failure mechanism. Thus, comparison of the maximum bending moment from an elastic analysis to the plastic flexural strength is consistent.

For statically indeterminate, one plastic hinge won't cause a collapse mechanism, so comparison of the maximum bending moment from an elastic analysis to the plastic flexural strength is conservative.

In the AISC Specification, Appendix 1.3 supports what used to be called Plastic Analysis and Design. With this method, the load that will cause collapse is compared to the applied load from LRFD load combinations. It's a more consistent approach for strength evaluation. However, in every continuous beam example I've designed with this approach, the resulting beam is only one or at most two sizes smaller than what one would get from the elastic approach described above. One could probably go down another beam size or two if not for the requirement to typically use a 10% reduction, that is, 0.9Mp. The 0.9 isn't the resistance factor. Also, the lateral-torsional buckling bracing requirements are a lot more complicated and usually more stringent than those used for the elastic approach.

With modern tools, it's much easier to compare the elastic analysis results to phiMp. There's a good chance deflection will control anyway. Also, to check deflection, you need an elastic model, so checking strength using plastic analysis ends up being a lot more work.

 

[dik]

Thanks... I should have noted the structure cannot consist of simple spans, and requires continuity.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[dik]

Not my experience... with plastic design, the deflection will be about 1/3 the elastic simple span , the elastic moment deflection. LTB is generally less of an issue because you are using stockier sections (Class 1)

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[271828]

...with plastic design, the deflection will be about 1/3, the elastic moment deflection. ...

Not sure I understand. How do you compute the deflection when using plastic design and when using an elastic analysis? I would expect the deflection calculations to be the same either way because deflections are computed at lower load levels.

 

[dik]

I design the beam as a fixed end condition (or fixed and pinned), but with modified end moments to reflect the larger M/EI component. Generally at service loads the beam is elastic... so, it's easy. Because of the continuity, deflection is not normally an issue. The calculated deflections for a plastically designed beam will be approximately 1/3 that if the same beam and loading were simply supported.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[271828]

OK. Understood.

I was typing about designing the same continuous beam with plastic design vs using the elastic analysis method described by the OP.

 

[dik]

The design has two distinct components. Using elastic design with a resistance determined using the plastic section, and the plastic design using both the mechanism of failure coupled with the resistance determined from the plastic section. One gives you an increase of about 10-15% (based on the shape factor) and the other gives you an increase of about 30%, based on the mechanism of failure. With fewer pieces to handle, it's generally a win-win.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[dik]

I think I'm going to summarise this and put it into a 'canned' reply; the question about plastic design comes up occasionally and it would be nice to have a consistent reply...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik