Design load for column/joint retrofitting in case of Strong Beam-Weak Column behavior

[Blackstar123]

BACKGROUND INFO
I am checking the design of an existing G+1 building with a total plan dimension of 25m (L), 9m (W) and a height of 14.8m, as shown in following fig.

There is a standard live load of 100 psf on first floor and, equipment loads (provided by supplier) at roof level. The height of this equipment is almost 13 m and is similar to as shown in the following fig.

The structure of the building is supposed to be IMF moment frame subjected to Zone 2B earthquake loads. The design check of the structure shows that beam column capacities are adequate but structure shows a “strong beam and weak column” behavior. Thus, columns and joints are proposed to be retrofitted using FRP by specialized consultants. I am responsible to provide them the required column and joint capacities for FRP design.

QUESTON

I am using the following methodology to achieve this goal. I’ll be thankful if someone could confirm if what I am doing is right or if I am way off my rockers.

I am using sap2000 to perform a push over analysis and a sort of performance-based design. I am not going too deep into performance-based design because my understanding is very limited. My goal is to find the load at which beams will go into plastic region before the columns.

For push over analysis, I first loaded the structure with D + 0.5L + 1Equip. and then incrementally pushed the frame upto 0.02h. I’ve assigned auto generated plastic hinges as per FEMA-356 to frame members, “M3 hinge” at beam ends and “P-M2-M3 hinge” at column ends. Although I’ve a good theoretical understanding how a M3 hinge behaves. I cannot say the same about P-M2-M3 hinges. I’ll be obliged if someone could provide me with a good reference on the subject matter or can explain the behavior in detail.

Also to provide some of the facts, while modelling this nonlinear behavior,
1. I’ve not taken into consideration the extra rotation due to (i) Cracking at negative moment region and (ii) Shear cracks. At this level, I consider this a conservative assumption for column and its joints, because the more load a beam can take, the higher the design load will be obtained for column design from analysis. I am aware that this might not be the most economical option for client.
2. I’ve considered the true stress-strain curve of the rebar and not the conventional perfectly plastic model because I believe the rebar will be in strain hardening regime at higher EQ loads.
3. I’ve also considered cracked property modifiers for frame sections (0.5 for beams and 0.7 for columns).

I’ll report the forces in column for FRP design at that “step” in which rotation in beams reached the “Life safety” range as per FEMA. These forces will not be increased using a load factor. I’ll be thankful if someone could confirm if what I am doing is right or could suggest a better way to find the design load.

 

[KootK]

Seeing as nobody else has taken a swing at this, you may have to settle for my input. At the least, you'll get a thread bump out of this.

1) If it is at all possible, I would forgo the entire pushover analysis and simply reinforce the columns and joints to make them stronger than the expected beam hinges tying in with overstrenth etc. This wold be much simpler analytically, I feel, since you'd just work out the capacities of the beams and use those for the loads on your columns and joints.

2) I agree that performance based design is a viable strategy here but, if that's your path, then I think that you have to take it all the way rather than in half measures. I think that what you'd want to do with PBD is to convincingly demonstrate that your beams won't need to develop plastic hinges. Once you've concluded that plastic hinges are required, no matter your analysis method, I think that you are obligated to satisfy the strong column / weak beam requirements.

3) Note that your roof level beams do not need to satisfy the strong column / weak beam requirements. That will only be necessary at the second floor framing where those requirements will be much easier to satisfy.

 

[r13]

What is the motivation for the retrofit, and where is the intended FRP application? For industry equipment, stability is often out weight flexibility, is plastic hinge a desirable feature in such a low seismic zone?

 

[Blackstar123]

I was pleasantly surprised when I discovered that someone has indeed replied to my last query. I was quite dejected when no one replied to my post initially and therefore, had conveniently forgotten about the presence of this post and did not bother to follow up with the status.
As always, I am grateful with the thoughts you put into our queries, KootK.

I know it’s a late response, still I do not like it when OPs do not respond to people who took time to think over their queries.

1. Initially, I thought to do it the same way. But then I started over thinking all the probable load distribution scenarios, such as, what if all beam spans/supports yield at the same time or what if they don’t yield at the same time and how would they affect column forces. Now that I have performed the pushover analysis, I can perform the exercise this way as well and compare the differences in results.

2. This is one of the thing that bothers me about my explained methodology that I’ve only a rudimentary knowledge of PBD and thus, do not completely interpret the results and understand the potential of the procedure. However, I am trying to improve my knowledge by studying whenever I get some free time.
Can you explain or give an example of a probable scenario when the following statement will hold true?

I think that what you'd want to do with PBD is to convincingly demonstrate that your beams won't need to develop plastic hinges.

Isn’t the whole point to design for inelastic seismic base shear is that beam should undergo plastic deformation? If hinges were not develop in the beam then how would the excess energy dissipate?

3. I understand that column hinging at roof level is not critical because it cannot lead to story mechanism. But there is a heavy equipment with supporting steel structure resting on roof and it’s presence created no small amount of confusion for me regarding this matter as well.
What I forgot to mention is that, there is a moment connection between steel and RCC column in actual. Since, the adequacy of the steel structure of equipment is not within the scope of our work, only its loads were considered in the analysis. However, there is in fact a steel structure on top of RCC, thus, I rationalized that the roof should be treated as a floor rather than a roof. Do you think I am being overly conservative here?

Also, I think there is a typo here. Do you mean at the first floor framing instead of second floor here? Because second floor is Roof.

… That will only be necessary at the second floor framing where…

 

[Blackstar123]

Retired,
The structures were originally designed for zone 2A. Client wants to check the adequacy of design for zone 2B. His reasons for doing this is that some damages were observed in one line of a manufacturing plants during low to moderate EQ shaking. Now he is reevaluating the strength of all existing building in other lines as well for zone 2B level EQ.

 

[r13]

I think what you were doing are fine. Consider existing structure in zone 2A, it might not have designed for earthquake, but wind. Let us know how extensive is the retrofit turned out to be.