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Question regarding Ultimate Limit State Design
11

Question regarding Ultimate Limit State Design

Question regarding Ultimate Limit State Design

(OP)
I was doing some additional background reading on ULS design, and found the following quote on wikipedia:

Quote (Wikipedia)

The ULS condition is computationally checked at a certain point along the behavior function of the structural scheme, located at the upper part of its elastic zone at approximately 15% lower than the elastic limit. That means that the ULS is a purely elastic condition, located on the behavior function far below the real Ultimate point, which is located deep within the plastic zone.

I can't find a reference for the approximation of 15%. We perform sectional analysis of members based on the plastic condition, and these loads are based on partial factors of safety to materials and loads. But I can't find anywhere that provides details about it remaining elastic.


RE: Question regarding Ultimate Limit State Design

The steel yield "stress vs strain" curve below answers your question. Note that point B is the true yield stress. The yield stress we use for design is point A, which is at the end of linear range. At true yield, the member won't be fully restored to it's original shape after the load is removed.

RE: Question regarding Ultimate Limit State Design

If that was intended to be a general definition, it is ridiculously over specific.

The wording is also unnecessarily obscure.

The ULS capacity is an approximation of the applied action that will cause section failure, factored down either by a single factor, or by partial factors applied to different materials. How the stress and strain conditions relate to the actual behaviour of the material depends on the material and the design code.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Question regarding Ultimate Limit State Design

The ULS condition is computationally checked at a certain point along the behavior function of the structural scheme, located at the upper part of its elastic zone at approximately 15% lower than the elastic limit. That means that the ULS is a purely elastic condition, located on the behavior function far below the real Ultimate point, which is located deep within the plastic zone.

What are the base for Fy and E in ULS - same as ASD, within linear elastic range.

RE: Question regarding Ultimate Limit State Design

On reflection, I think the Wikipedia statement is just wrong, as well as being over-specific and unnecessarily obscure.

The definition of the ULS for bending is strain based, with a strain well in excess of the elastic limit. In the great majority of cases sections will remain elastic under the maximum load, because the design load is factored up and the design strength is factored down, but in the rare cases where the ULS is actually approached or reached, because the section is over-loaded and under-strength, it will be in the plastic strain range, which it should be able to accommodate without total failure.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Question regarding Ultimate Limit State Design

I agree ULS is often beyond the pure elastic limit. Eg it is common to use plastic modulus and effective section modulus to calculate ULS which by definition assumes the section is past the pure elastic limit.

As for the 15% margin, it depends upon the material. I agree this figure is far too specific

RE: Question regarding Ultimate Limit State Design

Agreed with the above 2 posts.. I've read the statement more than 5 times and i still don't get what the statement is actually trying to convey. Or may be i should say that i get what it's trying to state but I don't agree with 90% of the definition.

Ultimate limit states are defined for designing purpose which state the maximum load/stress or strain a material can bear, before it starts to deform plastically (in case of ductile material) or fail (in case of brittle material) theoretically.

In actual failure may occur after alot more load or alot more deformation than the defined ultimate limit states.

Euphoria is when you learn something new.

RE: Question regarding Ultimate Limit State Design

2
Bottom line - don't attempt to use wikipedia as a technical resource.

Rod Smith, P.E., The artist formerly known as HotRod10

RE: Question regarding Ultimate Limit State Design

Note that we design the material to be "at yield" condition, not "have yield", doesn't it means the material remains in the elastic range? The OP's quote simply points out that the word "ultimate" in ULS leads to the misconception that it is associated with the ultimate stage in the plastic region, which is further down the property curve from the yield point (To be in the plastic range, the stress must be greater than Fy, even slightly). I guess the 15% lower is meant, that even in the ULS design, the stress in the material remains below the yield, again, in the elastic range.

RE: Question regarding Ultimate Limit State Design

A graph is better than thousand words.

RE: Question regarding Ultimate Limit State Design

One of us should delete or modify it.

RE: Question regarding Ultimate Limit State Design

Quote:

Bottom line - don't attempt to use wikipedia as a technical resource.

I disagree, Wikipedia is a valuable technical resource, you should just not rely on anything you read there without confirmation from an independent reliable source, but that applies to any technical resource.

retired13 - a graph with a few words of explanation might be worth a thousand words, but I'm not sure what your added red squiggly lines represent.

I think your previous post is a good interpretation of what the Wikipedia article is saying, but the Wikipedia article is wrong. To take reinforced concrete as an example, because the strain limits are explicitly stated, at the Ultimate Limit State the concrete will have a maximum strain about 5 times greater than the elastic limit and about 3 times the strain at which it goes plastic. The tension steel in an under-reinforced section will be in a similar state. Most concrete sections will never reach anything like this state because of the design load factors and strength reduction factors, but the whole basis of designing for the ULS is that if a section does reach this state it should allow sufficient plastic strain before failure for the load to be distributed elsewhere. It is not a requirement of ULS design that all real structural members remain in the elastic range under all actual load conditions.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Question regarding Ultimate Limit State Design

Quote:

One of us should delete or modify it.

Good luck with that.

If anyone knows someone with an established academic reputation in structural design it might be worth getting them to have a look at it.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Question regarding Ultimate Limit State Design

Quote (IDS)

I disagree, Wikipedia is a valuable technical resource,

Maybe it's ok for materials and product references, but as demonstrated in this case, it's not a reliable resource for design or analysis.

Quote:

...you should just not rely on anything you read there without confirmation from an independent reliable source,

If you have to take that extra step, why not just refer to a reliable source from the outset?

Quote:

...but that applies to any technical resource.

I disagree. There are plenty of reliable technical resources that don't require a secondary source.

Rod Smith, P.E., The artist formerly known as HotRod10

RE: Question regarding Ultimate Limit State Design

Quote:

If you have to take that extra step, why not just refer to a reliable source from the outset?

The same reason you should check calculations, even if they come from a reliable source.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Question regarding Ultimate Limit State Design

Reliable sources, e.g. published articles, research studies, design guides, etc. from recognized entities, such as PCI, AISC, TRB, PTI, and ACI, can confidently be assumed to have been checked by at least several experts in the field. I would not, and do not, have any hesitation about using them without independent verification. I don't put wikipedia on anything close to the same level. For anything related to engineering analysis or design, I won't bother to look at wikipedia, since I'd want an authoritative source for my information, anyway, so I would consider it a waste of my time.

Rod Smith, P.E., The artist formerly known as HotRod10

RE: Question regarding Ultimate Limit State Design

I deleted the offending sentences. The whole section deserves a rewrite.

RE: Question regarding Ultimate Limit State Design

I agree. Wikipedia is a fantastic source of information, in fact it is largely clearer and more accurate than the average post from eng-tips.com.

However that doesn't mean that you should you as a professional engineer use it as an authoritative source. Beside EVEN "authoritative" sources have had and STILL have their own issues. Generally these are edge case scenarios but still highlights how even 'authoritative' sources get it wrong or in some circumstances.

Exercising you intelligent judgment is rather than simply following a recipe is what make you an ENGINEER and not a sheep. (The phrasing and the blog is not mine, but another eng-tips contributor)

RE: Question regarding Ultimate Limit State Design

Quote (IDS)

at the Ultimate Limit State the concrete will have a maximum strain about 5 times greater than the elastic limit and about 3 times the strain at which it goes plastic.

Very difficult to connect concrete with "plastic". I know the magic number is 0.003 (ultimate strain), after reaching that point, if not crushing outright, the stress will decrease rapidly. So what is the benefit of allowing larger strain rate?

Please do not give up on fundamental to make an argument that will not stand test.

RE: Question regarding Ultimate Limit State Design

Quote:

So what is the benefit of allowing larger strain rate?

I didn't say there was a benefit in allowing a larger strain.

I said that at the ULS strain the concrete was already well past the elastic strain, as is shown in the graph you posted.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Question regarding Ultimate Limit State Design

On a side note this is the weirdest steel stress strain curve I've ever seen, i'd even say incorrect if it's meant to represent a real stress/strain curve for a structural steel

.... did it come from the same wiki page?




I'd like to think any engineering student could come up with a better explanation of the ULS than the OP's wiki explanation. I've been trying the structural engineering thing for several decades and have absolutely no idea what they are actually trying to say.....

RE: Question regarding Ultimate Limit State Design

(OP)


I actually always kind of viewed ULS design to be somewhere within a range of the idealized bi-linear stress strain curve, as opposed to the point just beyond yield. The point just beyond yield I imagined would be a kind of elasto-plastic range where the flanges would have surpassed the yield point, but the web section would be partly elastic still. Our sectional analysis of beams is based on a full plastic capacity section, which in my eyes would be somewhere further along the curve. Please can somebody correct me if they disagree?

Ultimately, I made this post because I thought it is very difficult to quantify exactly where we stand in terms of parts of our structure remaining in the elastic range and parts in the plastic range (but below ultimate state). In some cases members will remain elastic, but in some I believe it's possible that they enter marginally into the plastic range, but do not reach their ultimate plastic (collapse) state. The direct quote of 'upper 15%' made me question if there was a rational analysis behind this number.

RE: Question regarding Ultimate Limit State Design

I think there is some confusion with the word "ultimate".

"Ultimate" in the context of ULS is not the same as "Ultimate" in terms the ultimate strength of a material.

The ULS condition can occur while the material in question is in any range of stress conditions. The ULS condition can represent a steel beam which has its entire cross section fully plastic, it can represent a steel beam that has just yielded at its extreme fiber if it is not able to develop its full plastic capacity, or it can represent a stability failure where the cross section is no where near its yield limit. In a steel connections, the ULS condition could represent the actual ultimate strength of the material (fracture).

RE: Question regarding Ultimate Limit State Design

(OP)

Quote (CANPRO)

I think there is some confusion with the word "ultimate".

"Ultimate" in the context of ULS is not the same as "Ultimate" in terms the ultimate strength of a material.

The ULS condition can occur while the material in question is in any range of stress conditions. The ULS condition can represent a steel beam which has its entire cross section fully plastic, it can represent a steel beam that has just yielded at its extreme fiber if it is not able to develop its full plastic capacity, or it can represent a stability failure where the cross section is no where near its yield limit. In a steel connections, the ULS condition could represent the actual ultimate strength of the material (fracture).

That's the essence of my edits to the graph I think? My understanding is that under ULS the section could be in any range really from yield point to failure. Otherwise I consider it as elastic.

RE: Question regarding Ultimate Limit State Design

Quote:

...under ULS the section could be in any range really from yield point to failure. Otherwise I consider it as elastic.

I think CANPRO's description is more accurate. The ultimate limit state can be reached well below yield, if there is a buckling failure. My understanding is, that is the essence of limit state design - capacity is calculated based on the limiting (lowest) failure condition. The 'ultimate' part indicates that it's calculated based on the expected failure level, without a factor of safety applied to the capacity, i.e. no resistance factors, distinguishing it from LRFD. It's essentially the same as what we call Load Factor Design (LFD) in the bridge design world.

Rod Smith, P.E., The artist formerly known as HotRod10

RE: Question regarding Ultimate Limit State Design

Some design checks are based on the ultimate tensile strength also, for example welds, bolts, net section tension checks in steel, etc.

RE: Question regarding Ultimate Limit State Design

I'd agree, Agent666 - whatever constitutes failure for the component under consideration, whether it be a serviceability limit or a strength limit.

Rod Smith, P.E., The artist formerly known as HotRod10

RE: Question regarding Ultimate Limit State Design

fracture point,

If your sketch holding true, then you will have a limiting steel stress (FLS) higher than Fy in all controlling strength criteria (equations) in the code, and your calculated member stress (FS) will be allowed to be higher than Fy, since FLS > FS > Fy, so the member is in the plastic range and deform plasticly. Do I get you right? If so, please read the definition of "plastic deformation" below, and judge yourself. You can also google the words "plastic deformation" to find results to compare the correctness of this definition.

Quote (Merriam-Webster.com)

Definition of plastic deformation
: a permanent deformation or change in shape of a solid body without fracture under the action of a sustained force.

RE: Question regarding Ultimate Limit State Design

Agent666 & Rod,

I'm not familiar with welding but follows the code. Below is the only thing I think somehow explains the brittle characteristics of welding medium. In another words, I don't believe welding metal posses plastic property/behavior. The "welding forum" should be able to provide broader/concise explanations.

Quote:

When molten metal is exposed to air, it absorbs oxygen and nitrogen, and becomes brittle or is otherwise adversely affected.

RE: Question regarding Ultimate Limit State Design

Here is a definition of ULS from UK website.

Quote:

Ultimate limit state (ULS)
The ultimate limit state is the design for the safety of a structure and its users by limiting the stress that materials experience. In order to comply with engineering demands for strength and stability under design loads, ULS must be fulfilled as an established condition.

The ULS is a purely elastic condition, usually located at the upper part of its elastic zone (approximately 15% lower than the elastic limit). This is in contrast to the ultimate state (US) which involves excessive deformations approaching structural collapse, and is located deeply within the plastic zone.

If all factored bending, shear and tensile or compressive stresses are below the calculated resistances then a structure will satisfy the ULS criterion. Safety and reliability can be assumed as long as this criterion is fulfilled, since the structure will behave in the same way under repetitive loadings.

BS EN 1990 Eurocode – 'Basis of structural design' describes four ultimate limit states:
EQU: Loss of static equilibrium of the structure.
STR: Internal failure or excessive deformation of the structure.
GEO: Failure or excessive deformation of the ground.
FAT: Fatigue failure of the structure.

RE: Question regarding Ultimate Limit State Design

(OP)

Quote (retired13)

fracture point,

If your sketch holding true, then you will have a limiting steel stress (FLS) higher than Fy in all controlling strength criteria (equations) in the code, and your calculated member stress (FS) will be allowed to be higher than Fy, since FLS > FS > Fy, so the member is in the plastic range and deform plasticly. Do I get you right? If so, please read the definition of "plastic deformation" below, and judge yourself. You can also google the words "plastic deformation" to find results to compare the correctness of this definition.

I don't quite follow - any chance you can try explain again for me please? We use a bi-linear idealization of the stress-strain curve, discounting any contributions from strain hardening. That's what I marked on the graph.

Quote (retired13)

Here is a definition of ULS from UK website.

Quote:
Ultimate limit state (ULS)
The ultimate limit state is the design for the safety of a structure and its users by limiting the stress that materials experience. In order to comply with engineering demands for strength and stability under design loads, ULS must be fulfilled as an established condition.

The ULS is a purely elastic condition, usually located at the upper part of its elastic zone (approximately 15% lower than the elastic limit). This is in contrast to the ultimate state (US) which involves excessive deformations approaching structural collapse, and is located deeply within the plastic zone.

If all factored bending, shear and tensile or compressive stresses are below the calculated resistances then a structure will satisfy the ULS criterion. Safety and reliability can be assumed as long as this criterion is fulfilled, since the structure will behave in the same way under repetitive loadings.

BS EN 1990 Eurocode – 'Basis of structural design' describes four ultimate limit states:
EQU: Loss of static equilibrium of the structure.
STR: Internal failure or excessive deformation of the structure.
GEO: Failure or excessive deformation of the ground.
FAT: Fatigue failure of the structure.

This is pulling that value of 15% again. Where does this come from? How are we able to quantify ULS design to be within 15% of the plastic limit?

Quote (CANPRO)

I think there is some confusion with the word "ultimate".

"Ultimate" in the context of ULS is not the same as "Ultimate" in terms the ultimate strength of a material.

The ULS condition can occur while the material in question is in any range of stress conditions. The ULS condition can represent a steel beam which has its entire cross section fully plastic, it can represent a steel beam that has just yielded at its extreme fiber if it is not able to develop its full plastic capacity, or it can represent a stability failure where the cross section is no where near its yield limit. In a steel connections, the ULS condition could represent the actual ultimate strength of the material (fracture).

I like this definition!

RE: Question regarding Ultimate Limit State Design

What "UK website" did you quote that from, retired13?

Rod Smith, P.E., The artist formerly known as HotRod10

RE: Question regarding Ultimate Limit State Design

If the code allows plastic deformation/behavior, the Fult will replace wherever the Fy is in use.

My advice, don't be distracted by the arbitrarily assigned 15%, it can be 20% for shear, 10% for flexural, though I think you can find a way to compare the code permissible stress to the yield stress, and get pretty close result. Anyway, the percentage shouldn't be the focus, the concept should.

RE: Question regarding Ultimate Limit State Design

Rob,

Source and paper linked. Link

RE: Question regarding Ultimate Limit State Design

Upon further reading, it's seems I need to modify my comments somewhat. Most of what I read indicates that "Ultimate Limit State" (ULS) design is the 'strength' subset of "Limit States Design" (LSD), which includes the "Serviceability Limit State" (SLS) for some design philosophies, such as LRFD, and not for others, such as Ultimate Strength Design (USD) and Load Factor Design (LFD), previously used by AASHTO. LSD then, encompasses pretty much all of the commonly used design approaches except "Working Stress" (AKA "Allowable Stress") design.

Rod Smith, P.E., The artist formerly known as HotRod10

RE: Question regarding Ultimate Limit State Design

Rod,

I think USD is under the umbrella of ULS, I read an article somewhere, in the title it says "ULS design of reinforced concrete AS, ACI and European codes". Link

RE: Question regarding Ultimate Limit State Design

retired13 - the description of ULS in your link is suspiciously similar to the Wikipedia version, including the 15% number. I suspect they just copy and pasted from an earlier Wikipedia version, or maybe vice versa.

I'll have a look for a definition I like more for further discussion.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Question regarding Ultimate Limit State Design

From: http://www.seismicresilience.org.nz/topics/resilie...

"Ultimate limit state (ULS)

Design for the ULS represents a defined process that is aimed at ensuring the probability of collapse of a building (and therefore the risk to human life) is at an acceptable level. The ULS process is therefore primarily associated with consideration of large (severe), relatively rare events.

In AS/NZS 1170, compliance for the ULS for typical buildings (those with a design life of 50 years) is confirmed using a single level of load based on between a 1-in-100 and 1-in-2500-year event. This is dependent on the assigned IL and the particular environmental effect under consideration. For example, the design seismic load used for ULS checks for a typical IL2 building is based on the defined 1-in-500-year earthquake shaking. These loads are consistent with those used internationally, which is the reason they have been adopted in New Zealand. The ULS design criteria, when checked using the defined load, are set to provide the required level of confidence that the life safety objective has been met across all rare events."

This is from a New Zealand web site, but Part 1 of the referenced code is a joint Australia/New Zealand document. For specifics of earthquake design there are separate parts for Australia and New Zealand, but the general principles in Part 1 apply to both.

See the link for more background and definition of Serviceability Limit State.

Personally I think we should have three specified limit states (serviceability, strength and collapse), but that's another discussion.


Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Question regarding Ultimate Limit State Design

Yes, our codes (NZ/AU) simply work on the principle of if we follow these detailing and design requirements, our structures will at MCE (Maximum credible Earthquake 1:2500 event) level will maintain a sufficiently low probability of collapse. In NZ we have some considerations we need to satisfy at the MCE level (primarily related to making sure thing supported on ledges like stairs and ramps don't fall off, and things like precast panels have sufficient clearances to not participate as part of the lateral system).

Some of the stuff being posted in this thread is utter rubbish, misinformed or about as incomprehensible as the original quote.

Quote:

If the code allows plastic deformation/behavior, the Fult will replace wherever the Fy is in use.
This is completely wrong, plastic design is not about replacing f_y with f_u. Please don't do this. Look up the difference between the elastic and plastic section moduli for steel design for examples of the differences between elastic and plastic design.

Instead of talking about 15% this 15% that, it's the wrong terminology. The way codes work is maintaining a suitable 'target safety indice', the development of the number to use is codified in ISO standards, search google for 'ISO Bases for design of structures'. For members subject to gravity loading this might be in the range of 2.5-3.0, meaning in reality you can increase the load by this factor before something truly fails. This maintains a traditional 'safety factor' in ULS/LFRD design.

Another way to look at it is that considering capacities determined using lower characteristic material values which are factored down by strength reduction factors, being compared to upper limit loads (dead/live/snow, etc) which are also then load factored to arbitrarily increase them. On the basis of probabilistic methods we then ensure that there is a sufficiently small overlap between the distribution of reduced capacity and the load factored loading, demonstrating that there is a sufficiently low probability of the member failing under any real world loading.

This might help explain some of the concepts better than I can put it into words.
https://www.youtube.com/watch?v=itie93Adetc

RE: Question regarding Ultimate Limit State Design

From ISO 2394:1998:

2.2.9 limit state: A state beyond which the structure no longer satisfies the design performance requirements.

NOTE — Limit states separate desired states (no failure) from undesired states (failure).


2.2.10 ultimate limit state: A state associated with collapse, or with other similar forms of structural failure.

NOTE — This generally corresponds to the maximum load-carrying resistance of a structure or structural element but in some cases to the maximum applicable strain or deformation.


2.2.11 serviceability limit state: A state which corresponds to conditions beyond which specified service requirements for a structure or structural element are no longer met.

RE: Question regarding Ultimate Limit State Design

Moving on to routine design, the exact capacity of structures can't be determined by calculation. Too many variables. Design codes typically use some lower-bound estimate, eg plastic moment based on minimum yield stress. The actual plastic moment is expected to be higher because 350 MPa steel will probably be 370 MPa or more then have strain hardening above that again. Then there are reduction factors to go from lower-bound ultimate capacity to design capacity. That is expected to be substantially below the real ultimate limit, enough to give the target reliability when combined with design (ultimate) loads.

RE: Question regarding Ultimate Limit State Design

retired13- I have just had a look at the link you posted on 23 Jan 20 21:41.

I'm tempted to give you a little pink star, but perhaps I shouldn't ;)

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Question regarding Ultimate Limit State Design

IDS,

If I can persuade a single person to think and act elastically, I would be honored. Thanks for your thought though :)

RE: Question regarding Ultimate Limit State Design

After another smoke and though through again, I have doubt that my advocation of ULS been "purely elastic" is flawed for regions with high seismic activity and intensity. The newer philosophy in earthquake resistance design that says "a structure is allowed to fail but collapse" has sounded triggered the alarm. I still don't think the codes allow structures go plastic for places outside of the high seismic zones, or for cases that seismic force is not controlling, though.

Note, the word "fail" means irreversible deformation has occurred. On that stage and after, the structure is not to be used for human occupancy until problem removed/corrected.

RE: Question regarding Ultimate Limit State Design

Agent666,

Your rubbish could be others treasure. Give some self-restrain and civility when comment on others opinion.

If the codes encourage/allow the venture into plastic range, look at the stress-strain curve, the stress continues increase until hitting the ultimate stage, why code specifies a lower bond stress, Fy in this case, instead of using higher bond stress (say 1.1*Fy, 1.2*Fy, if not Fult) to compute ultimate resistance?

RE: Question regarding Ultimate Limit State Design

I dont know what I'm sharing is a general condition or not. But may be if someone has time they can research about this in further detail,
For advanced steel structure coarse, my professor gave us a simple assignment to draw a M-phi curve for a given W Section of A36 steel. The intersting thing about this was that the strain at the extreme fibre, at which almost all the section was yeilded, that strain was still within the flat plateu of stress strain curve and no where near tha strain hardening regime.

Euphoria is when you learn something new.

RE: Question regarding Ultimate Limit State Design

Rubbish is rubbish, retired13. You made an assertion that was incorrect, and Agent666 explained why it was incorrect. I don't believe it was meant to be personal.

Rod Smith, P.E., The artist formerly known as HotRod10

RE: Question regarding Ultimate Limit State Design

Quote (Blackstar123)

...almost all the section was yeilded, that strain was still within the flat plateu of stress strain curve and no where near tha strain hardening regime.

I noticed a similar phenomenon when checking haunched concrete slab bridges. The haunches at the supports were deep enough that the bottom reinforcing was slightly above the neutral axis into the tension zone. I had to satisfy myself that it would yield before the top layer of reinforcing reached strain hardening. It did. The yield plateau for mild steel is actually much longer than most of the diagrams I had seen published (around 10 times the elastic range). Apparently, it's common for those diagrams to be pictorial and not to scale.

Rod Smith, P.E., The artist formerly known as HotRod10

RE: Question regarding Ultimate Limit State Design

I am holding my position, except the 15% which I don't think is an exact citation, after watched the youtube presentation provided by Agent666.

Correct or not, the presentation is about the background in probabilistic and risk based evaluation of structural design, and a method to justify the design, new or existing, when DCR > 1 (Demand Capacity Ratio), by adjusting load factors for known certainty of loads (DL, LL, WL), and resistance factor for known material strength, such as the steel supplied has a tested yield of 58kai vs the nominal 55 yield strength. Most notably, at the conclusion, the presenter states:

- LRFD invented to provide a rational and consistent way to set margins of safety for structural design, and
- LRFD was calibrated back to historic levels of safety accepted in ASD methods.

From conclusions above, same safety level is achieved no matter the design methods (ASD and LRFD), since both are operated within the same universe, with the same upper limit.

RE: Question regarding Ultimate Limit State Design

Rod,

I didn't make any assertion, all quotes are gathered from other sources but align with my thought. For the Fult, if that's what you are pointing to, I am sorry, it was representing my doubt on the others opinion, and expressed in a question form. I think we can agree that a question does not make it a declaration of matters.

RE: Question regarding Ultimate Limit State Design

Quote:

If the codes encourage/allow the venture into plastic range, look at the stress-strain curve, the stress continues increase until hitting the ultimate stage, why code specifies a lower bond stress, Fy in this case, instead of using higher bond stress (say 1.1*Fy, 1.2*Fy, if not Fult) to compute ultimate resistance?

The higher capacity in plastic design comes from utilising the full yield strength over the full section (plastic vs elastic section moduli). It is not a function of using a higher yield stress or the ultimate tensile strength.

Quote:

I still don't think the codes allow structures go plastic for places outside of the high seismic zones

This isn't correct, codes generally allow plastic design methods as a valid design method. Redistribution of design moments under gravity load is one case. Provided a mechanism doesn't form, just follow code provisions.

RE: Question regarding Ultimate Limit State Design

Agent666,

As mentioned back and forth, Fy is a border line condition, I consider within and at it, it is elastic. In order to go to the next level, the stress must be greater than Fy, say Fy + 1psi (an exaggeration here). Thus the yield design method still results in an elastic structure if stability is maintained. A simple example is a beam can have both supports at yield but stable until a hinge is formed in the mid-span. And, a cantilever is not allowed to have plastic hinge at the support, why, if plastic deformation is permitted?

RE: Question regarding Ultimate Limit State Design

Agent666,

I think I've found something in between our believes.

Quote (Wikipedia)

Plastic section modulus

The plastic section modulus is used for materials where elastic yielding is acceptable and plastic behavior is assumed to be an acceptable limit. Designs generally strive to ultimately remain below the plastic limit to avoid permanent deformations, often comparing the plastic capacity against amplified forces or stresses.

I cease my case, and back to adjust (moderate) my thought a little.

RE: Question regarding Ultimate Limit State Design

The assertion you made, retired13, that Agent666 referred to as "rubbish" was:

Quote:

If the code allows plastic deformation/behavior, the Fult will replace wherever the Fy is in use.

That is not true. The codes have separate and distinct equations and provisions for sections designed to a level that exceeds first yield. Most of them still use Fy in the capacity calculations, while in some places there are additional checks to prevent fracture at the tensile strength limit. I'm not aware of anywhere, at least in the AASHTO spec, where Fult is substituted for Fy. If that is not what you intended to convey, then you should clarify your statement.

Rod Smith, P.E., The artist formerly known as HotRod10

RE: Question regarding Ultimate Limit State Design

Rod,

Consider Fy is the border line stress, Fy*SP gives a resistant stress level still in elastic range, albeit it sits on the border. So if we/the code want (no, we don't, nor the code) to go beyond the elastic range and utilize the ultimate strength of the material, then it should be something like Fult*Sp to take the advantage of the higher stress, instead of the lower bond permissible stress, in this case, Fy. I doubt this is the position of the code, AASHTO included, thus I question the claim that the ULS is computing resistance in the plastic range, which demonstrates un-tolerable/un-recoverable strain/deformation. You need to stare at the stress-strain curve, and have a clear vision on the division of elastic region and plastic region, and the limiting stresses the regions associated with.

RE: Question regarding Ultimate Limit State Design

That's what occurs to some degree in reality (some strain hardening if your strains get you past the yield plateau for carbon steel), but as you approach Fu failure rapidly occurs as section is necking reducing its cross area and concentrating stress. Even though this effect occurs in reality it's not how we design at the ULS using LFRD techniques. If we did stuff would be falling down all the time, last time I looked around me most stuff even if overloaded was still standing.

RE: Question regarding Ultimate Limit State Design

Quote:

Even though this effect occurs in reality it's not how we design at the ULS using LFRD techniques.

I think we are on the same page regarding this.

RE: Question regarding Ultimate Limit State Design

Quote (retired13)

...utilize the ultimate strength of the material, then it should be something like Fult*Sp

No, no, no, no no! Designing within the elastic range utilizes Fy*S (S being the elastic section modulus). Designing in the plastic range utilizes Fy*Z (Z being the plastic section modulus). The only time I've ever used Fu (ultimate tensile strength) is in the design for tension at the net section of a bolted connection.

Rod Smith, P.E., The artist formerly known as HotRod10

RE: Question regarding Ultimate Limit State Design

There are various definitions of 'elastic' and 'plastic' being used in this discussion. You can't all be using those words properly...

RE: Question regarding Ultimate Limit State Design

Rod,

Yes, my mistake in didn't use the proper symbol for plastic modulus "Z". Did I type "S" instead of Sp in my thought during a short elapse of my memory.

RE: Question regarding Ultimate Limit State Design

Three points:
1. The design "Ultimate Limit State" for bending is defined by strains, not stresses, and the maximum strains are far greater than the elastic strain limit. The associated stresses are derived from conservative simplifications, and are then factored down some more, but that doesn't make the analysis elastic. How can it be when large parts of the section with greatly different strains are treated as having equal stress?

2. "Limit State Design" also puts limits on stresses at the "Serviceability Limit State" with lower load factors (often but not always 1.0), and these limits ensure that the actual maximum load on the great majority of structures will result in both strains and stresses within the elastic limit. The point of ULS design is to cover the rare case where applied loads are much greater than expected, and the actual section capacity is less than assumed in the analysis.

3. The fact that ULS factors were calibrated against existing ASD limits does not mean they will always give the same results. Detail differences in the loading and in sections being analysed will often give different results, and the Limit State Design results will be more reliable because they consider the ULS, and the actual failure mechanism, and they also consider the SLS behaviour with lower loads, where strains are within the elastic limit.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Question regarding Ultimate Limit State Design

Quote (retired13)

If I can persuade a single person to think and act elastically, I would be honored. Thanks for your thought though :)

Just in case it wasn't clear, the reason for no little pink star was that the link was to my blog, so it would have been a bit self-promotional.

I'd be interested to know what conclusions you drew from the link though.

https://newtonexcelbach.com/2010/12/21/uls-design-...




Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Question regarding Ultimate Limit State Design

I didn't know there were alternate definitions of elastic and plastic. Elastic means it returns to its original shape when the stress is removed; plastic means it stays in its deformed shape when the stress is removed. In the case of mild steel, the dividing line between the two is the yield point.

Rod Smith, P.E., The artist formerly known as HotRod10

RE: Question regarding Ultimate Limit State Design

Quote:

I didn't know there were alternate definitions of elastic and plastic. Elastic means it returns to its original shape when the stress is removed; plastic means it stays in its deformed shape when the stress is removed. In the case of mild steel, the dividing line between the two is the yield point.

What was that in response to?

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Question regarding Ultimate Limit State Design

Perhaps I was too gentle. Retired13 is including the plastic yield plateau in his definition of elastic. This is largely why this discussion is not going anywhere.

Quote (Retired13)

Fy is a border line condition, I consider within and at it, it is elastic. In order to go to the next level, the stress must be greater than Fy, say Fy + 1psi (an exaggeration here). Thus the yield design method still results in an elastic structure if stability is maintained. A simple example is a beam can have both supports at yield but stable until a hinge is formed in the mid-span

RE: Question regarding Ultimate Limit State Design

IDS,

Internet made the world so small. If I am still practicing, that would be one of my reference regarding reinforced concrete design. Too bad, I couldn't give myself a star for finding/linking the useful information from the vast public domain though:) Nice to know that with respect.

RE: Question regarding Ultimate Limit State Design

Quote (BridgeSmith)


I didn't know there were alternate definitions of elastic and plastic. Elastic means it returns to its original shape when the stress is removed; plastic means it stays in its deformed shape when the stress is removed. In the case of mild steel, the dividing line between the two is the yield point.

Quote (IDS)

What was that in response to?

It was in response to:

Quote (Steveh49)

There are various definitions of 'elastic' and 'plastic' being used in this discussion. You can't all be using those words properly...

Rod Smith, P.E., The artist formerly known as HotRod10

RE: Question regarding Ultimate Limit State Design

Quote (steveh49)

Retired13 is including the plastic yield plateau in his definition of elastic.

steveh49,

Please point out the elastic yield point and plastic yield plateau in the diagram below, as I have never heard of "plastic yield" before, and would like to know/learn more. Thanks in advance.


RE: Question regarding Ultimate Limit State Design

Quote:


I still don't think the codes allow structures go plastic for places outside of the high seismic zones]

I don't know who said the above, i saw this quote and want to comment on it.

I do think that it is the intent of the code to allow us to use the plasticity of the material in regular design by ULS method.

In Working stress design method, stresses were not allowed to exceed the elastic stresses or surpass the yield point. For example, allowable stress in concrete was limited 0.45 f’c, which almost lies near the linear portion of the curve, and stress in steel was limited to Fy.

Whereas, in Ultimate limit state method, stress in concrete can reach the maximum stress f’c, and strain in steel is allowed to exceed the yield strain. Stress in steel is not increased more than Fy because of the elastic perfectly plastic idealization of stress strain curve of steel.

I consider this idealization perfectly reasonable because we do not design our beams to undergo a very large tensile strain such that it reaches the strain-hardening regime. However, if someone is interested in taking into account the strain hardening effect of high strength steel, various bi and tri linear models have been proposed in the research works in past several years.

In addition, serviceability of building designed by working stress method is so much better than ultimate limit state method. Because in working stress, frame sections were designed so that the stresses remain less than the elastic stresses which results in large cross-sections and small displacements. Compare to this in ULS method, frame sections are allowed to deform past their yield points.



Euphoria is when you learn something new.

RE: Question regarding Ultimate Limit State Design

IDS,

In your blog, I am confused with the statement below, can you clarify? Thanks.

Quote:

The two BS codes are limited to a concrete cube strength of 65 MPa, which is equivalent to a cube strength of a little over 50 MPa. The other codes have modifications to the concrete stress block for higher strength grades, to account for its reduced ductility.

RE: Question regarding Ultimate Limit State Design

Retired13, in answer to your question on the yield plateau, as a number of people have stated that stress strain curve is not representative of a real stress strain curve for structural steel. One reason is it doesn't contain a defined yield plateau. I think someone mentioned earlier that this plateau is maybe 15 times the yield strain.

This is what I'd expect a real structural steel stress strain curve from testing to actually look like:-



Quote:

In addition, serviceability of building designed by working stress method is so much better than ultimate limit state method. Because in working stress, frame sections were designed so that the stresses remain less than the elastic stresses which results in large cross-sections and small displacements. Compare to this in ULS method, frame sections are allowed to deform past their yield points.

This is simply not true. There is another limit state called the serviceability limit state under which the serviceability of a structure is checked (deflections, fatigue, durability, vibration, etc) The intent of limit state design is that under the serviceability load cases (SLS) that structures remain in the elastic stress range and hence remain serviceable. This has nothing to do with ULS which is separate limit state.

RE: Question regarding Ultimate Limit State Design

Interesting diagram. I wonder the deformation in that plateau is recoverable or stay permanent.

Yield Plateau

RE: Question regarding Ultimate Limit State Design

Quote (Agent666)


This is simply not true. There is another limit state called the serviceability limit state under which the serviceability of a structure is checked

May be you didn’t understand my point. I didn’t say the beam designed by ULS are not checked for their serviceability.

I was comparing the serviceability of old method (Working stress) and new method (Ultimate limit state).
I think you can well imagine the magnitude of deflection in a design method in which stresses were not allowed to exceed their elastic stresses VS the design method in which members are allowed to crack at their ultiamate life but are supposed to be within well defined deflection limits in their service life.

It’s obvious to me the serviceability of the old method will be better than the new ULS method. However, it will not be an economical option for sure.

Euphoria is when you learn something new.

RE: Question regarding Ultimate Limit State Design

Simeone answered the question on importance of the yield plateau in structural engineering, the answer may not be written perfectly, but I think it makes sense. Please read on. Note he use "yield area" instead of yield plateau.

"I´d rather say yielding stretch is a feature, a characteristic of most of metal material.

Most of structural assumptions( at least for civil engineering purposes) take in account yielding point rather than rupture point.

Because most of structural calculations are made in the dominion of elastic field. Considering the mentioned graphic of Stress X Strain, beyond the yielding part, steel( or other metal) don´t behaves on elastic way, but on plastic mode. The yielding point it´s somehow safer to calculations, because close to such "yielding area" the strains grow without additional efforts, what it is a warning about complete "burst"( or rupture) is close.

More...most of calculations are made inside the "elastic area" which follows Hook´s Law. At elastic area, strain can be recovered if load is withdrawn. At the plastic area strains are permanent( it is the anticipation of the rupture).

I wish I could be understood ."

RE: Question regarding Ultimate Limit State Design

I am going to make my closing call to end my journey on this subject.

Maybe caused by my poor writing skill, thus led to misunderstandings on my stance, that stated below:
- For typical structural steel, elastic behavior stops at "yield, Fy". Beyond the yield point, plastic behavior starts.
The current code specified structural resistance capacity calculations are well remain in the elastic range, thus the use of Fy in the equations. I don't know where is the future heading toward, but at this moment of time, none of the codes allows the venture into the plastic range (except the high seismic zones mentioned before), whether through a ladder/escalator up or down as shown on the diagrams above this thread.

It is interesting to know so many different opinions on this subject though.

RE: Question regarding Ultimate Limit State Design

2

Quote (retired13)


The current code specified structural resistance capacity calculations are well remain in the elastic range, thus the use of Fy in the equations.

ok.. This just made me sad that's why I've gone to the following trouble.

Euphoria is when you learn something new.

RE: Question regarding Ultimate Limit State Design

retired13: "none of the codes allows the venture into the plastic range"
If not into it, very close to it. With rectangular sections the shape factor Mp/Me is 1.5. With a low load factor, DL being 1.25 and material factor of 0.9... you may be into the plastic range.

Blackstar123:
Once the section is unloaded, with the residual stresses, Hooke's law is applicable up to the latest 'plastic load'.

With rolled sections you are not likely in the plastic range for service loading with a shape factor of about 1.15 for rolled sections and material factor of 0.9 and DL factor of 1.25.

This has been a great thread... one of the more interesting ones...

Dik

RE: Question regarding Ultimate Limit State Design

Blackstar,

It is transition from the proportional point to the yield point, that can be called non-linear elastic zone, which is located between points A & B on the first stress-strain curve I posted on 21 Jan 20 23:04 (first post down from the OP) I don't think Hooke's Law is applicable after the proportional point.

RE: Question regarding Ultimate Limit State Design

Dik,

The case you described could be fall in the risk category with DCR > 1. I recommend the video (NASCC Steel Conference) originally provided by Agent666, and linked here. Link

RE: Question regarding Ultimate Limit State Design

Thanks for the link... I'll look at it later today... this has been a really 'fun' thread.

Dik

RE: Question regarding Ultimate Limit State Design

Blackstar,

You brought up a very interesting question on the "plastic capacity". Now let's go one step further, op top of Mp, sometimes we will have axial load too. Assume superposition is valid, what is the result when a hinged location subjects to both Mp+T, or C, simultaneously? May this phenomenon will never occur, or there is a simple explanation? Maybe you, or someone can help me to get over it.

RE: Question regarding Ultimate Limit State Design

dik,

Be prepared, it is an hour long video, coffee break excluded :) But it's quite valuable in knowing how to squeeze a few drops out from the code to add some extra strength for the design. Enjoy it.

RE: Question regarding Ultimate Limit State Design

I'm about half way through it... it's a great discussion on probabilistic design...

Dik

RE: Question regarding Ultimate Limit State Design

Quote (Retired13)

The current code specified structural resistance capacity calculations are well remain in the elastic range, thus the use of Fy in the equations

The use of Fy does not imply the elastic range.

If you use plastic section modulus (eg Blackstars diagram) you are assuming the section has gone past the pure elastic zone, and is sufficiently plastically deformed that the entire section is now yielding, is now plastic. Hence “plastic section modulus”.

RE: Question regarding Ultimate Limit State Design

Codes limit the stress at ultimate to the yield stress. That does not mean the section does not go into the plastic range. Just that you cannot benefit from the increased steel stress. Unless a designer does a Balanced Design (concrete strain of .003 - .0035 and steel strain of .002 - .0025), the strain in the steel will be greater than the yield strain, so the section will be in the plastic range. Very few designs are Balanced Sections. A design with minimum tension reinforcement would normally have a steel strain at ultimate in the order of .04 to .05 while the yield strain is .002 - .0025 (that is why low ductility reinforcement is a problem!).

The important thing is for the section not to go into the plastic range under service loads. Some codes specifically do not allow this. AS3600 and Eurocode specifically limit the steel stress at service to 80% of the yield stress. In most situations, this will be controlled automatically by the load factors at ultimate compared to service and the material/capacity factors at ultimate. With those set to normal design values, the steel stress at service would normally be in the range of 60-65% of the yield stress.

RE: Question regarding Ultimate Limit State Design

Just find this.

k = Mp/My = Z/S
k = 1.5 for rectangle shape, and k ≅ 1.1 for I (W) beam
So, for steel wide flange shape, Z ≅ 1.1*S
LRFD Moment Capacity ∅Mn = = 0.9 Mp= 0.9*Fy*Z = 0.9*Fy*1.1*S = 0.99*FY ≥ Mu

Someone may want to try other shape.

RE: Question regarding Ultimate Limit State Design

Quote (retired13)

In your blog, I am confused with the statement below, can you clarify? Thanks.

Quote (ids)


The two BS codes are limited to a concrete cube strength of 65 MPa, which is equivalent to a cube strength of a little over 50 MPa. The other codes have modifications to the concrete stress block for higher strength grades, to account for its reduced ductility.


Eurocode2 allows ULS design using a parabolic-linear stress block, or a rectangular stress block that will generate approximately the same force and moment (on a rectangular section). They also have a triangular-linear stress block, but this is just a conservative simplification of the parabolic-linear case.

As the concrete strength increases from 50 MPa to 90 MPa:
- The maximum strain reduces from 0.0035 to 0.0026
- The strain at the start of the constant stress region increases from 0.002 to 0.0026
- The exponent of the "parabolic" region reduces from 2 to 1.4
- The depth and maximum stress of the rectangular stress block is factored to be equivalent to the modified parabolic-linear stress block

See graph below.


The Australian code does not have any provisions for a parabolic-rectangular stress block, but it does modify the rectangular stress block factors to have a similar end result.


Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Question regarding Ultimate Limit State Design

Or the one I've been using for the last 50 years... I was introduced to it in 1st year engineering by the late Al Lansdowne, who would become my thesis adviser.



Dik

RE: Question regarding Ultimate Limit State Design

Quote (retired13)

k = Mp/My = Z/S
k = 1.5 for rectangle shape, and k ≅ 1.1 for I (W) beam
So, for steel wide flange shape, Z ≅ 1.1*S
LRFD Moment Capacity ∅Mn = = 0.9 Mp= 0.9*Fy*Z = 0.9*Fy*1.1*S = 0.99*FY ≥ Mu

There is no dispute that in most cases if a load equal to the factored down design capacity is applied to a section then, the stresses will be less than the yield stress. The point is that this requires that the load does not exceed the design load, the load is distributed as assumed in the design analysis, and the section is constructed exactly in accordance with the design, with materials that meet or exceed the design assumptions, and with no degradation over time. If all that is true, the section is not approaching the Ultimate Limit State. The whole point of the ULS check is to allow for cases where some or all of those assumptions are not met.

It's not just seismic loads that may cause problems. For instance differential settlement, corrosion, or another section on the load path being stiffer or less stiff than assumed can all cause significant overstress, even with loads within the design limits.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Question regarding Ultimate Limit State Design

Quote (dik)

Or the one I've been using for the last 50 years... I was introduced to it in 1st year engineering by the late Al Lansdowne, who would become my thesis adviser.

As mentioned, the Eurocode also includes a triangular-linear stress block.

Rather strangely, the way it is implemented makes it not only more conservative than the parabolic-linear stress block (which is reasonable), it is also more conservative than the rectangular stress block. For a given depth of neutral axis, both the force and moment are reduced.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Question regarding Ultimate Limit State Design

Eurocode clause 3.2.7 also allows a designer to take into account strain hardening as long as the reinforcing strain is limited.

RE: Question regarding Ultimate Limit State Design

IDS:
"Rather strangely, the way it is implemented makes it not only more conservative"

I still feel comfortable with my 'over design'... and have been using plastic design for nearly 50 years. I have little use for the increased UTS above yield since deflection usually 'kicks in'. Thanks for the added info, though. I wasn't aware other codes make allowance for the stain hardening.

The only thing this thread is missing is the inclusion of Luders bands and body centered cubic lattices...

Dik

RE: Question regarding Ultimate Limit State Design

dik - it was just the Eurocode formulation that I was saying was more conservative. It all depends where you take the end of the elastic strain, and what you use for the constant stress. For a rectangular section it's quite easy to work out numbers for a rectangular block that will give exactly the same results as the parabolic-rectangular block. For a non-rectangular section, or rectangular under bi-axial bending, the parabolic-rectangular gives much better results than the rectangular though, and the triangular-rectangular would be very close.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Question regarding Ultimate Limit State Design

Thanks, Doug... I'm just a tekkie junkie.

Dik

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