Ductile Design of Gravity dominated frame 1

[Rajshrn06]

Hi

I have Reinforced Concrete frame building, where my beam's hogging moment is higher for gravity case than that for seismic case. If I undertake a ductile design in accordance with NZ seismic code (NZS1170.5), I am required to design my columns for the over strength of the beams capacity, which means that my column would have 4 times the capacity of that required by the actual seismic demand. This also basically means that I have 2 times the capacity of that required under elastic loads. Does this mean that I cannot adopt a ductile design as my columns capacity is in excess of the elastic demands? My understanding is that my columns would behave elastically so there would not be any post elastic deformation to even consider ductility in design.

Thanks

 

[KootK]

1) I can't speak to NZ codes stuff as it's not my turf. Agent666 is the guy that you really want to hear from.

2) Other than at the column bases, where a hinge must form for a frame mechanism to form, you want your columns to remain elastic if possible. It's that whole strong column / weak beam principle. It's really the beam to column joints, on the beam side, that you want to yield and dissipate energy.

3) Because of the 4X over-design, your moment frame joints may remain elastic for more of the seismic displacement history than they otherwise would. Conversely, that means that they'll spend less time being shoved through plastic deformations than they otherwise would. And that feels a lot like less energy being dissipated. That's what's bothering you, right? Code seismic design typically follows the equal displacement principle, as shown below. While the principle is only sort of true, we deem it good enough for most purposes and it implies that, so long as a structure can withstand the imposed displacement that we think it will need to endure, we're not overly concerned with how much of that displacement is elastic vs plastic.

4) Keep an eye on your beam forming plastic hinges within the span under seismic load. That's the usual problem with moment frame beams carrying heavy gravity loads.

5) In my heart of hearts, I do prefer it when seismic moment frame beams are not heavily taxed under gravity. I feel that their behavior is more predictable in that scenario.

 

[fugeeo]

CA Residential Code
R301.2.2.2 Seismic Design Category C. Structures assigned to Seismic Design Category C shall conform to the requirements of this section.
R301.2.2.2.1 Weights of materials. Average dead loads shall not exceed 15 pounds per square foot (720 Pa) for the combined roof and ceiling assemblies (on a horizontal projection) or 10 pounds per square foot (480 Pa) for floor assemblies, except as further limited by Section

R301.2.2. Dead loads for walls above grade shall not exceed:
1. Fifteen pounds per square foot (720 Pa) for exterior light-frame wood walls.
2. Fourteen pounds per square foot (670 Pa) for exterior light-frame cold-formed steel walls.
3. Ten pounds per square foot (480 Pa) for interior light-frame wood walls.
4. Five pounds per square foot (240 Pa) for interior light-frame cold-formed steel walls.
5. Eighty pounds per square foot (3830 Pa) for 8-inch-thick (203 mm) masonry walls.
6. Eighty-five pounds per square foot (4070 Pa) for 6-inch-thick (152 mm) concrete walls.
7. Ten pounds per square foot (480 Pa) for SIP walls.

 

[Agent666]

The usual thing to do here is to redistribute your load under the gravity case as much as you can to reduce the negative moment demand. This will make for a more economic seismic design.

What actual ductility are you getting (actual) vs what are you aiming for design wise in doing the checks you note? What I'm getting at is will it work at mu=1.25? Then you don't need to do the capacity design, just ensure you satisfy CL2.6.6.1 and the hierarchy noted in the commentary?

I'd also hazard a guess that you'll have non-reversing hinges with a gravity dominated frame which comes with its own unique challenges regarding detailing and amplification of the inelastic rotations?

 

[Rajshrn06]

Thanks very much for your responses. My structural background is Australian but I am based in Fiji where we use NZ codes for seismic design. I am still learning some aspects of the NZ code as I am new to this code.

Kootk, those are some great points you mentioned. The actual earthquake load could be of any magnitude. Agent, when I relook at it, my end moments and midspan moments are almost identical but there is a chance of midspan hinging in an Earthquake as there will be counter-moments at ends that will reduce earthquake load.

How do you go about measuring the actual ductility of the structure? Do you carry out a displacement based analysis to obtain global ductility? The process I use is that I assume a ductility and detail the critical regions accordingly, while ensuring that my material strains are within the limits imposed by the kd factor.

I would be able to describe my problem better in a scenario. For instance, lets assume I am analyzing the building as a limited ductile (LD) structure with mu=3.0 and then reanalyzing as nominally ductile (ND) with mu=1.25. With LD my Fixed end moment (FEM) is lets say X, with ND my FEM is 2X and with gravity loads my FEM is 3X. If I carry out LD, my columns need to be designed for overstrength of my beams, where I will use 3X to design my beams. So this may result in my column capacity being in excess of 3.5X, whereas the actual load resisted by my column in LD earthquake is only X. I have designed the structure as LD but it has a capacity to resist earthquake loads in excess of mu=1.25. Can I still treat this structure as LD, since it will only go into post elastic stage if my earthquake loads are nearer to mu=1.25? Does NZS impose a limit on the material strengths? I would eventually design this as nominally ductile as there is not much point in going upto Limited ductile but I am curious to know the understanding behind this.

 

[Agent666]

If you have a non-reversing hinge you need to amplify the inelastic deformations in accordance with 2.6.1.3.2(b)(ii).

Once you consider the overstrength capacities, it could force the hinge to the column face if your analysis showed it was almost at the end, so it turns into a reversing hinge. Typically, you would look at an envelope of overstrength at both ends, nominal moment one end and overstrength the other and opposite case to determine where your hinges might occur.

Also the other limitation for a real ductile design with non-reversing hinges is that you start to become limited in getting bar laps within the spans, as you cannot have laps/splices within any of the Potential Plastic Hinge Regions (PPHRs). If you look at the ductile detailing lengths associated with the column negative hinge and the span positive hinge for each direction of loading you often have no beam left to provide the laps.

Sounds like by virtue of having an oversupply of strength that your frame will never form the beam hinges at a mu=3.0 level of load. The work out the actual ductility, you can compare the sum of your column face analysis moments and max midspan moments form the seismic case (on the assumption of non-reversing hinges). Then compare this to the sum of the positive and negative beam capacities you were detailing (governed by the gravity case of course). Compare the two numbers and you can work out a ductility/equivalent base shear by working backwards from the analysis base shear times ratio of the analysis moments/capacities. This level of lateral load would cause all of your capacities to be achieved and form the ductile beam hinge mechanism.

Based on what you have described with the excess strength your frame will either respond elastically, or at a ductility of 1.25. Therefore the only requirement you need to satisfy with respect to the hierarchy of strength between your beams and columns is to ensure that should your frame actually form a beam hinge mechanism (i.e. much larger than design level earthquake). Then you still need to ensure you achieve a permissible mechanism, i.e. weak beam/strong column. This is covered in CL 2.6.6.1, have a look at the commentary, it is satisfied as long as the sum of your column strengths is 15% higher than the sum of the beam strengths. Because you have not done capacity design, then thi sis basically saying you probably have enough strength to get to MCE level event loads, but they want to make sure it doesn't fail in some brittle non-ductile or non-permissable way (like columns hinging or shear failure or similar).

It sounds like you have a reasonable handle on things already if you are new to seismic design.

Does NZS impose a limit on the material strengths

Wasn't quite sure what you meant by this?
There are some limits on concrete strength for a Nominally ductile design and ductile design. Main reinf is limited to 500MPa, shear reinf to 800MPa.

 

[Rajshrn06]

Thanks Agent666, that is very fruitful. I try and read as much as possible. Seismic capacity design is on a very different level altogether.

By material strengths, I meant the individual member capacities. You have somewhat touched on it in your 4th paragraph. I was thinking that if NZS ensured that the capacity is very close to strength, than we can ensure that hinging does occur at the load level we are designing to. I have seen people do ductile design where capacities are way greater than strength, particularly in wall only buildings where minimum reinforcement criteria governs, but as you and Kootk mentioned, we don't need to worry about this as it basically means the structure will stay elastic for a greater return period earthquake. We just need to ensure a ductile failure mechanism.

 

[johnie134]

Use a Q factor equal to 1

 

[Agent666]

Use a Q factor equal to 1

What is a Q factor Johnie134? There is no such factor in the NZ codes. Maybe try expand on your answer, like why you are suggesting this, how does your random one liner reply address the OP's situation?

 

[johnie134]

Agent search the code, don;t ask me to do that.

 

[Agent666]

All I'm asking is for you to explain yourself and your statement to which I get a nonsense reply.

If you're not going to be helpful, then please refrain from posting garbage statements.

 

[Agent666]

I'm not asking anyone to do my work. I'm asking you to explain yourself. Why comment your one liner comments if you are so unprofessional that you can't even take the time to reply and explain your thoughts in a logical & professional manner.

But you're incapable of that obviously based on your typical questions and replies on eng-tips. Don't bother replying, go play your silly games elsewhere.