Simple Lateral Core Analysis (In SpaceGass)

[Trenno]

Hi all,

Am looking at some preliminary analysis for the lateral core of a 9 story building (relying purely on one core to do all the work). Also earthquake will dominate.

Would be great if somebody could point out any major flaws in my analysis method and/or make suggestions of their own:

> Using Spacegass
> Model core as pure cantilever with correct stiffness properties (can build up cross section in shapebuilder)
> Reduce the flexural rigidity of concrete E by 40% (to account for long term cracking etc)
> Place lumped masses at each floor equal to the seismic weight of each floor
> Have these lumped masses as transnational in XYZ, but no rotational interia because luckily the core is in close proximity to the center of mass of each floor.
> Then run a spectural analysis as per SpaceGass's tutorials.
> Review results for bending, shear and deflection.

Problem is... the bending and shear that results from my spacegass analysis is much lower (40%) than my analysis by hand (equivalent static analysis AS1170.4).

However I understand the AS1170.4 method does not take into account the stiffness of your lateral resisting element (or does this well...)

Thoughts?

 

[asixth]

Looks good. Must be a really tiny floor plates if the building is only being serviced by a single lift. Maybe about 400sq.m.

Firstly I would model the stiffness as 70% for walls.

Modal response will result in lower base shears because the idealized stiffness of the building is used instead of the generic code equations. If you check the period from the code calc would probably be like 1 sec whereas the spacegass model is 1.9sec. It's less stiff, would be lower on that response curve and results in lower base shears.

Also the equivalent static calcs are based on a predominant first translational mode response (and an uperside down trianglular distribution of storey shears). As you go taller and become more flexible the higher modes contribute more, namely second mode so you can see that sort of kick back in the middle level storey shears.

Check your drifts and you need to check the inelastic drifts so they need to be scaled up by sp/mu.

AS1170.4 doesn't have a lower bound limit for minimum base shear but I like to use 2.5% of the building weight cause it was the old robustness minimum in AS1170.0. Anything less than this from a modal analysis I scale it up to the 2.5%.

 

[Trenno]

Thanks for that reply asixth. Much, much appreciated.

Yeah the building is a skinny b*stard... 38m L x 9m W. We also have a services core down one end and a small moment frame on the other. However I want to see how this main lift core stacks up.

Wasn't too sure about how much of the stiffness I should reduce it by. I'll try 70% and see how sensitive it is.

Using the AS1170.4 equations, the fundamental period came out to be 0.751sec, which is obviously why it was attracting more load according to the generic equations.

I'm assuming you have done this exercise (or similar) before. Should I be worried about the rotational mass interia input? Does the 10% x Width eccentricity requirement tie into it somehow?

I understand the inter-storey drifts requirements, but can you please explain the inelastic (structural performance/ductility) drifts a little more?

Good idea on the scaling up of the shears, will keep that in mind.

Thanks again, asixth.

 

[asixth]

Yeah. Have you got a higher level program to perform your lateral analysis like ETAB's where you can put your floor plates and columns into it as well. You could probably use spacegass but you would probably need to use master-slave constraints and throw in some beams to get the slab coupling.

Eccentric cores can be problematic particularly if they are right off to the edge to optimize the floor plate. The core itself will be able to rectify some of that torsion if you use the coupling beams (link beams / header beams / lintel beams) over the top of the lift opening. This will close the C-section somewhat. Also the eccentricity will be taken by the columns are the extremities of the floor plate. The moments shouldn't be that great and probably won't exceed the minimum moment requirements.

The Australian code doesn't really mention much about torsional irregularity other than it should be accounted for. One of the American Codes, I think it is ASCE 12 Seismic Design Criteria for Building Structures, gives some limits of drifts at the diaphragm extreme to the drift at the diaphragm centre. As long as your under 1.2 (Drift at Extreme / Drift at Centre ), then I would think it's okay. You will get some torsion particular when you put the mass out and extra 10% from the diaphragm centre.

If the core is relatively central and the columns are in-situ and detailed properly for moment transfer than you should be okay. Also check the transfer of diaphragm forces into your core. It shouldn't be a problem in your case cause each diaphragm only needs to transfer a max of 220kN into the core.

I have always used 30% stiffness modifier for flexural elements and 70% for compression elements like walls and columns. It really all comes back to how cracked the section is expected to be.

 

[asixth]

Being an Australian educated and practising engineer I probably haven't explore as far into the theory of seismic design as I should.

It's in both the equivalent static analysis part and dynamic analysis part of AS1170.4 Sect. 6.7 and 7.5.

Following thru other posts I have seen on eng-tips over the years it does get drilled home a fair bit. Here's one thread with a similar topic that was floating around at the start of this year.

thread507-355872

 

[Trenno]

Well said. Sometimes when the building is shielded so much, earthquake will just easily dominate, even if it's not an overly massive lateral force.

Here's my next question - if going to a modal analysis (Section 7) do we need to still uphold the 80% requirement of Clause 6.2.3?

We finally finished the ETABS model last night, so hopefully our results aren't too far off.

 

[asixth]

Personally I don't believe that you need to. The 80% limit applies to the equivalent static analysis and there isn't any similar limits required for the dynamic analysis. I use robustness (2.5%) as the minimum. And I have seen many consultants drawings who have done the same also.

 

[Trenno]

Asixth,

Apparently all other major EQ codes require that the modal analysis storey shears not be less than 80% of the static equivalent case.

In addition - apparently this requirement was shown in older versions however removed from the current AS1170.4. There must be a reason. Food for thought, I guess.

 

[Trenno]

 

[asixth]

There were a lot of changes between the '93 and '07 codes. One of the more significant changes where that the magnitude of the equivalent lateral analysis base shears where increase significantly.

I think the Australian earthquake standards gives design forces at or above "other major EQ codes", despite the fact that Australia is not a seismically active country, yet the design base shears are on par with Chile.

 

[Trenno]

Hmmmm, interesting. Thanks for your input and help in this thread, Asixth.

Much appreciated.

 

[asixth]

What I would really like to see is a comparison of the '93 and the '07 codes using practical examples of low-medium rise concrete buildings using equivalent static analysis. My biggest gripe with the code general formulations for the calculation of natural period particularly for low-rise buildings.

 

[Trenno]

Just happened to be reading this today - I think I found it on google some time ago...

 

[asixth]

Yeah, I just ran thru it.

I think the ESA-1993 gives a much narrower band of results and caps the maximum base shear effectively at Z for normal buildings (ground acceleration). The '07 code doesn't have this maximum limit so for low-rise buildings on average soils the base shear goes about 50% higher than the '93 code.

However it does have advantages for framed structures. And the period estimation equations in the '07 code are better but I think they're still a little on the conservative side for buildings braced by a concrete core and even more conservative for framed buildings.

Just because of this I would encourage the use of modal analysis for low-rise buildings but I wouldn't impose a scaling of 80%.

Just my opinion and I will probably keep on designing the way I've been going.

I have been meaning to post something similar to this in the AS/NZS forum for sometime. Just never got round to doing it.