Safety of Elastic vs. Inelastic Design 1

[Robbiee]

Hi all,
The requirement for providing a minimum level of ductility for structures in certain seismic areas or for certain types of structural systems is to justify the reduction of design earthquake loads for economic reasons and to prevent certain types of materials such as unreinforced concrete block walls to be used. However, for steel and reinforced structures, what I don’t understand why the inelastic design, i.e. design for reduced load with the reliance on inelastic energy dissipating detailing, is safer than elastic design for the full calculated loads. One might say that the design loads could be exceeded in a server event. But, we know that steel and reinforced structures have inherent over strength of a minimum of 30% and if the design load is exceeded, wouldn’t mean that higher than designed ductility is required to dissipate the additional load.
The reason for the question is two conversations I had recently; one with a professor researching the use of carbon fibre as slab reinforcing and concrete reinforcing in general, who agreed that elastically designed structures are not less safe, and the other conversation with a very experience engineer who has won almost every engineering award, who laughed when I said that elastic design is not less safe that in-elastic. Please comment. I wish to know what I am missing here.

 

[frv]

You are thinking about this incorrectly. Seismic loads aren't really loads. They are displacements. What we do as engineers is try to equate those displacements to loads on a SFRS.

The key concept to remember is that the displacements have to be accommodated or resisted (i.e., either your building is ductile or its SFRS is strong enough to resist the forces resulting from not accommodating the displacements). Taken to the extreme, think of buildings on rocker foundations. What that is doing is preventing the displacements from being transmitted to the building.

 

[PicoStruc]

There are many reasons other that economic, but one of them that I see really often in my job is :

If you dont reduce the lateral force using ductile energy dissipation, you may not be able to acheive a shear resistance.

I mean, the shear demand would be soo high, that you would exceed the maximum permissible shear resistance for a single wall.

Even if that shear resistance limit would not exist, the spacing for reinforcement would be too small.

 

[PicoStruc]

Note : I was refering to ductile shear wall.

 

[Robbiee]

Thank you frv. I thought we design for the forces generated in the building due to the acceleration of the ground movement which will cause the building to deflect. Yes, that load we calculate is the equivalent load that will generate the same displacements. What interested me is your statement: “either your building is ductile or its SFRS is strong enough to resist the forces resulting from not accommodating the displacements”.
How can I make the SFRS strong enough?

 

[EngineeringAdam]

Designing structures to exhibit elastic behavior in a design level earthquake is not economical as you state and just because there is inherent over strength in a design load doesn't mean your system is safe.

Before anything can be said about why and how inelastic behavior is beneficial it should be noted that the economic impacts of designing without ductile-inelastic behavior is cost prohibitive in high seismic regions.

If a seismic event exceeds the 30% over strength in your elastic detailed structure then you have no method to dissipate your energy safely. Therefore, the structure could exhibit a collapse mechanism.

Take the same structure and design with a lower design load, but with ductile detailing that can withstand inelastic behavior, and your system can dissipate energy.

Its true that a sever seismic event the ductile-detailed system could collapse as well, but energy dissipation is still ideal.

Your professor is correct, depending on what you consider safe. Remember that the design level earthquake is determine through probabilities, so there is a chance a greater than design level earthquake is exhibited. In that case, you would hope your structure has a means of dissipating energy.

Also, your professor could be addressing the fact that design is performed in the elastic range using R factors, and the deflections then amplified to approximate drift in the inelastic range.

 

[Robbiee]

PicoStruc,
You are talking very specific. Theoretically speaking, any shear force can be resisted by providing the adequate capacity. For example: if you can use carbon fiber reinforcing instead of the steel and larger concrete sections, you can always meet the demand. My problem is in understanding why “strong enough" members that aren't detailed to be ductile are not safe.

 

[EngineeringAdam]

I should clarify, that your professor is right depending on what you consider safe, but your engineer friend is right in my opinion in that ductile behaving structures are ideal in seismic regions.

 

[frv]

I'm not sure what you mean by making the SFRS "strong enough". It needs to be sufficiently "strong" to resist the anticipated loads.

Another way of phrasing my previous statement is that a structure needs to be either ductile enough or strong enough to resist the seismic displacements, not both.

In other words, if you detail your structure such that it can experience inelastic behavior, the structure no longer needs to displace elastically (read: large loads) in order to properly resist the ground movements. The more energy that can be dissipated within the structure, the less needs to be taken to the foundation (in a dumbed-down sense, less "a" in F=ma).

 

[Robbiee]

EngineeringAdam,
Thanks. My last post was just before reading yours. I understand from your post that the SFRS detailed as ductile can handle loads higher than the design loads better than a SFRS designed as elastic.
frv,
Some code don’t allow designing members to be strong enough to resist the loads. As an example: a one storey fire station that has concrete shear walls and steel roof is required by the Canadian building code to be designed with a minimum ductility of R=2.0 in order to remain operational post the sever event.

 

[frv]

Your terms are a bit misleading. "not strong enough" implies that the code is leading you down a dangerous path.

It's not that the code prohibits something from being strong; rather think of it as the code requiring yielding (i.e. ductility). Feel better?

 

[Robbiee]

frv,
In dead it is and really did not mean it. I should have said: " don't allow.....to be only strong enough..." Thank you for your patience. I was trying to understand.

 

[JoshPlumSE]

When comparing Elastic vs. Inelastic methods of seismic design, I try to think of the "Energy absorbed" by the structure.

By this I mean that the seismic event is going to impart a certain amount of dynamic energy into your structure. If you look at force deflection diagram for an Inelastic structure, the area enclosed by the hysterisis loop represents the energe absorbed by the structure. If your structure can go through a buch of these cycles, then it can absorb alot of energy and can be considered safe / ductile. If it deflects nicely for the first cycle, but the behavior degrades quickly in subsequent cycles, then it may not be able to absorb much energy.

Now, if you have a perfectly elastic structure, then how does the structure absorb the energy? By pure deflection only. Elastic strain energy. The area under that curve will usually be significantly less....hence less energy absorbtion. But, you still can design the structure to absorb the energy...then you should be okay.

What makes "inelastic" design superior (IMHO) is that structures designed elastically tend to experience brittle failure when they do fail. So, if the earthquake is stronger than you designed for (or the structure has been weakend over the last 30 year) then people will die. If an structure has been designed with lots of ductility, then you have designed in the failure mechanism. A failure mechanism that results in significant monetary damage, but not total collapse / death.

 

[DST148]

@Ailmar: Ref Seismic Design of Reinforced Concrete and Masonry Buildings by T. Paulay and M.J.N.Priestley - In certain cases the response of the superstructure to the largest expected earthquake will be elastic. This could be the result of a design decision, or of code requirements for minimum levels of reinforcement in the superstructure providing adequate strength for true elastic response. Usually, this occurs in regions of low seismicity or in low-rise buildings with structural walls.

The authors further add: With increased awareness that excessive strength is not essential or even necessarily desirable, the emphasis in design has shifted from the resistance of large seismic forces to the "evasion" of these forces. Inelastic structural response has become an essential reality in the structural design of earthquake forces.

 

[SAIL3]

what about using R=1 and elastic design?......

 

[Robbiee]

Sorry, somehow deed became dead in my last post. Thanks to all who contributed.

 

[Robbiee]

Now in a related topic, if you were asked to evaluate a 50-year old building for earthquake loads and found that the building elastically meets the strength requirements of the current code but doesn’t meet the ductility requirements. For example: the column/beam joints are not reinforced and beams don’t have the required stirrup spacing. Would you consider this building unsafe and require to be upgraded?

 

[PicoStruc]

In that case, the building meet the requirement for RdRo = 1.0, so what is the problem ? No reinforcement required !

 

[frv]

You cannot separate ductility requirements from strength requirements. They are intimately intertwined.

IF you are referring to structures not specifically detailed for seismic (in steel), then either the building is capable of resisting the loads (it's strong enough) or it isn't. If you use these systems, then you assume your R is 3 and the only ductility that considered is the inherent ductility in all steel systems, but you don't specifically detail your structure for more ductility. Keep in mind, however, that these systems are prohibited above SDC C.

I'm not as familiar with concrete systems, but I believe the equivalent is called ordinary plain (or reinforced) concrete shearwalls, and there are similar restrictions.

 

[EngineeringAdam]

Ailmar,

To answer your question...

The ASCE 31 is used to seismically evaluate buildings, and the ASCE 41 is used to seismically rehabilitate existing buildings.

Following these two standards you will find that: if your building doesn't have ductility-detailing but is strong enough to resist the design level earthquake, then no retrofit is required. However, most of the time you will discover some elements to be deficient, and then a retrofit will be needed for those elements.

So as you can see these standards allow brittle failure mechanisms to exist, assuming the design level earthquake is exceeded. Why is this? Because it doesn't make sense to retrofit every single structure out there. It's cost prohibitive and doesn't make sense if the structure can resist the design level earthquake.

So while I agree that ductility detailed structures are safer, other structures that have no means to resist force in the inelastic range can still be considered safe after a thorough analysis (i.e. ASCE 31, ASCE 41)