Question regarding Ultimate Limit State Design 12

[fracture_point]

I was doing some additional background reading on ULS design, and found the following quote on 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.

 

[Settingsun]

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.

 

[IDS]

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/

 

[r13]

IDS,

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

 

[r13]

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.

 

[r13]

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 F_ult) to compute ultimate resistance?

 

[Blackstar123]

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.

 

[BridgeSmith]

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

 

[BridgeSmith]

...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

 

[r13]

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.

 

[r13]

Rod,

I didn't make any assertion, all quotes are gathered from other sources but align with my thought. For the F_ult, 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.

 

[Agent666]

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.

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.

 

[r13]

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?

 

[r13]

Agent666,

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

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.

 

[BridgeSmith]

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

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

 

[r13]

Rod,

Consider Fy is the border line stress, Fy*S_P 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 F_ult*S_p 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.

 

[Agent666]

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.

 

[r13]

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.

 

[BridgeSmith]

...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

 

[Settingsun]

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

 

[r13]

Rod,

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