Elastic and Inelastic Design & Analysis 3

[Mark1921]

Hello!

Can anybody confirm if my understanding of RC and steel's elastic/inelastic analysis and design are correct. I never found a straightforward answer from Google so maybe these are wrong. Can someone please help me, i'm trying to learn the basics.

REINFORCED CONCRETE:
Elastic Analysis - Moment Distribution Method
Elastic Design - Working Strength Design
Inelastic Analysis - ?
Inelastic Design - Ultimate Strength Design (Am I right on this?, I figured it's inelastic design since the stress is non linear (BELOW)

STEEL:
Elastic Analysis - Stiffness Method (Matrix), Method of Joints/Sections
Elastic Design - Allowable Stress Design
Inelastic Analysis - ?
Inelastic Design - Load and Resistance Factor Design

Additional: Are inelastic and nonlinear analysis just the same?

Thank you!

 

[Teguci]

A few notes:
- With strength design, designing spanning members to stay in the elastic range is not typical except for brittle materials like glass. Engineers use reinforced concrete and steel because those materials can exceed their elastic range and perform well into the plastic (inelastic) range without failure.
- For non-redundant axial members,(columns, walls, braces) the design state must be in the elastic range or the structure will fail. Even so, the analysis is on the yielding state of that column.
- ASD and LRFD will lead an engineer to choose the same or close to the same size structural elements (ie different approach with the "same" answer). Both ASD and LRFD consider the plastic limit state when assigning a capacity for a structural element.
- The cracking of concrete, which is necessary well before the tension reinforcement reaches it's yielding stress, is a plastic deformation. To provide an elastic analysis of concrete I'd be looking at the rupture strength of the concrete and the I-gross of the section. Really only do that for precast members.

 

[Mark1921]

Wait. ASD is plastic design?

 

[Guastavino]

There may be some nuance I'm unaware of but I consider inelastic and non-linear analysis to be the same.

As for other questions, LRFD is NOT inelastic design. LRFD has some "inelastic" concepts such as Zx plastic modulus for steel, but inelastic design is well beyond that of traditional LRFD. Frankly, I don't know anyone who does inelastic design for routine structures. Most of the building code is based on elastic design/analysis with cosmic fudge factors like Cd and R to account for inelastic behavior. Inelastic design is for PHDs, elastic design is for consulting engineers.

 

[Mark1921]

Ok. But how about ultimate strength design in Reinforced Concrete? The stress goes beyond the elastic, but it considered inelastic design? Why?

 

[KootK]

But how about ultimate strength design in Reinforced Concrete? The stress goes beyond the elastic, but it considered inelastic design? Why?

You kind of answered your own question here. It's inelastic design because it considers stress and strain beyond the elastic range.

My take:

1) Separate structure analysis methods from member design methods in your mind. We mix and match. For example, we often analyze structures elastically and then design the members within those structures by plastic methods.

2) Under modern member design methods, you generally have:

2a) Concrete and masonry designed using plastic methodologies.

2b) Ductile metals such as steel and aluminum designed using plastic methodologies.

2c) Non-Ductile materials such as wood and glass designed using elastic methodologies simply because their potential for brittle fracture prevents them from developing plastic capacities.

3) Under structure analysis methods, there are a nearly infinite number of options.

3a) Most commonly, we perform a linear elastic analysis, regardless of member design strategy.

3b) Nowadays, we often run elastic P-delta analyses to check stability. This method is a common example of an analysis that is both elastic and non-linear.

3c) In some circumstances a pushover type analysis is performed where member plastification is considered. This would be an example of an analysis that is both plastic and non-linear

This is a first rate, free text book that does an excellent job of covering the analysis side of the coin: Link


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.

 

[Mark1921]

From the responses above, I conclude the ff:

In structural analysis, we have:
(1) linear elastic (MDM, Stiffness Method)
(2) non-linear elastic (P-delta)
(3) non-linear plastic (Push-over)

In member design:
RC:
Elastic: WSD
Plastic: Ultimate Strength Design

Steel:
Elastic: ASD/ LRFD
Plastic: ?

Is this right? Do we Plastic Design for Steel? Thank you for the patience guys.

 

[MacGruber22]

Steel:
Elastic: ASD/ LRFD
Plastic: ?

That is kind of odd how you are trying to define the capacity philosophy. Sometimes, when designing to the LRFD load level, the steel sections are such that you can only utilize the elastic capacity due to buckling that will occur before reach the elastic limit. You can only use the plastic capacity of sections that are compact enough to do so. This restriction goes up for seismic design.

Don't forget about ASD in the context of old steel working stresses. The letters remained the same but the acronym changed to a different definition (at least in the American steel design realm).

Also, to reinforce KootK, buckling analysis involves non-linear systems of equations, but buckling can occur during the range of elastic stress or inelastic/non-linear stresses.

"It is imperative Cunth doesn't get his hands on those codes."

 

[Mark1921]

I'm talking about the range that the steel/concrete member can carry if designed on ASD/LRFD or USD, that's why I keep on defining them. I also kept reading terms like "Plastic Design" and "Elastic Design." Does "Plastic Design" means designing a member based on plastic analysis, and "Elastic Design" for elastic analysis?

Thank you for the responses.

 

[MacGruber22]

Mark, ultimately it will take you a few years of research and learning at work to develop a good understanding of the topic. Nevertheless, I will try to provide some more.

Using plastic design techniques does not necessitate using a plastic analysis, but plastic analysis requires satisfying plastic design criteria. Here is why: current practical structural engineering procedure (within the codes) involve elastic analysis for both steel and concrete, along with some modifiers for stiffness (cracked concrete moment of inertia for example) to capture a more reasonable stiffness that will occur at ultimate capacities. This allows fairly quick and simple analysis methods, because engineers have to be very efficient and only as precise as needed. The codes have developed capacity equations which allow for plastic capacity when certain criteria have been satisfied.

True plastic analysis is very very rare - it is an attempt to bypass the code simplifications (mentioned above) to try to predict the redistribution of loads throughout at structure by modeling the materials' inelastic curve, and to get as much additional capacity out of sections as rationally possible. Plastic analysis models can vary in their precision too. They can be performed assuming elastic-perfectly plastic behavior (strait line elastic up to a flat/constant plastic line) or a more "precise" relationship between stress and strain over plastic behavior. Plastic analysis is generally not compatible with the model design code provisions, therefore it should be used only by experienced engineers in special situations. Plastic analysis is only performed at factored loads, because you don't want a structure to yield at those nominal (average) loads.

To me, a statistical mindset is the way to go when thinking of how you use the analysis with the design and why. You can choice to analyze your structure at nominal ("average") or factored (95% percentile +/-) loads. Most material codes allow you to choose how you want to proceed. There are nuanced reasons to prefer one over the other. Nominal loads are compared to a lower percentile of member/material capacity because their uncertainty is higher. Factored loads are compared to near the lower limit of ultimate capacities, because their statistical certainties are similar.

Hopefully, for others here, I didn't grossly violate generalizations...


"It is imperative Cunth doesn't get his hands on those codes."

 

[Mark1921]

So basically, the codes AISC & ACI which contains ASD/LRFD & WSD/USD are all elastic design with plastic methodologies to allow for plastic capacity, is that right?

I have so much to learn, but thank you for the input!

 

[MacGruber22]

Mark - Not a big fan of general statements, but I would tweak your statement a bit by:
1. Changing "elastic design" to elastic analysis, as in when you run you model in STAAD, RISA, etc. it uses the linear elastic properties (or some variant) of the sections.
2. WSD for ACI died out as an alternate capacity method awhile ago. There may have been some consideration of post-elastic stuff peppered in the old WSD code, but the main philosophy did not consider plastic section capacity.

I am surprised you even brought up working stress design for concrete. I would have thought the universities burned all of those books years ago.

"It is imperative Cunth doesn't get his hands on those codes."