Distribution of Lateral Forces 2

[GalileoG]

I have two different lateral force resisting systems along my N-S direction of my building. On one end of the building, I have shear walls, on the other, I have concentric cross bracing. I'd like to analyze and distribute my lateral forces without the aid of an analysis software. Usually, for shear walls, I would distribute my lateral forces according to relative stiffness. However, I have no clue how I can go about calculating the relative stiffness of a steel braced frame? How do I determine how much goes into my braced frame and how much goes into my shear wall?

Is it enough for me to assume a beam with supports placed at the location of my lateral system, and the resulting shears would be the force that my LFRSs will experience? I don't like this method at all, but its expediency is very tempting.

Any input is appreciated.

Clansman

"If a builder has built a house for a man and has not made his work sound, and the house which he has built has fallen down and so caused the death of the householder, that builder shall be put to death." Code of Hammurabi, c.2040 B.C.

 

[DaveAtkins]

To determine the stiffness of a braced frame, assume a 1 kip horizontal load is applied at the top of the frame. Determine the force in the diagonal member(s). The elongation (or shortening) of the diagonal(s) is equal to PL/AE. Convert this elongation (or shortening) into a horizontal movement. The inverse of this movement is the stiffness of the frame, in kips per inch.

Your question about modeling the diaphragm as a beam does not take relative stiffness into account. It just distributes lateral load by tributary area.

DaveAtkins

 

[youngstructural]

This still has to be distributed in terms of relative stiffness... The easiest way to do this is to check the deflection at the knee for each system under the same load (say 10kN point, or 100kN point; Whichever would give a "sensible" result for the size of the bracing elements).

Thus, if your brace frame deflected 15mm and your shear wall only 7mm, a total of 1/Rt = 1/R1 + 1/R2... This is simple spring stiffness addition.

Now, two caveats:

1. This is only valid if the system tying the two together can take the unbalanced force, and of course the deflections of the combined system can only be described as "weird". Further, the bracing units need to be in a line and joined by a stiff system (floor, beams, etc); Otherwise your good old length squared or length cubed distribution of forces is probably more accurate.

2. The "correct" way to handle this analysis is available on eng-tips and discussed briefly in thread

http://www.eng-tips.com/viewthread.cfm?qid=214448&page=27

Be sure to note that your stiffer element may take all the load in lower level events. Thus the stiffer system takes most of the load, most of the time. I perfer to use an overstrength factor for all connecitions to the stiffer frame, given that it will take the majority of the loading over time with the less stiff elements kicking in for P-Delta and Ultimate effects.

Hope that helps,
Cheers,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[GalileoG]

Thanks Dave, that was very helpful.

I have a metal deck as my roof diaphragm, though I am not sure whether its behaviour will be that of a flexible or that of a rigid diaphragm. Is it reasonable standard practice for someone to analyze it as both and to take the worst case scenario?

Clansman

"If a builder has built a house for a man and has not made his work sound, and the house which he has built has fallen down and so caused the death of the householder, that builder shall be put to death." Code of Hammurabi, c.2040 B.C.

 

[youngstructural]

Darned it Dave; I was writing my answer when you posted your elegant, and short, reply.

I also agree with you, but hopefully the more detailed explanation will be useful anyway...

Cheers,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[GalileoG]

A star for both of you!

Thank you for the very detailed response YS, now I have to read it over again to digest it.

Clansman

"If a builder has built a house for a man and has not made his work sound, and the house which he has built has fallen down and so caused the death of the householder, that builder shall be put to death." Code of Hammurabi, c.2040 B.C.

 

[msquared48]

I agree with Dave here - I had to do a hospital expansion over 20 years ago that involved integrating the same elements.

The computer run will have to be done a few times though as it is a hit and miss process. Assumptions have to be made regarding the relative stiffnesses and changed and re-run in accordance with the results, checkng to see that stress and deflection limits are not exceeded and that the stiffnesses assumed are correct.

I think you get the picture here

Mike McCann
MMC Engineering

 

[DaveAtkins]

Now that all of us have discussed relative stiffness, I will backtrack by saying a steel deck is generally considered to be a FLEXIBLE diaphragm. Therefore, in this case, lateral loads should be distributed by tributary area.

DaveAtkins

 

[bigmig]

Clansman,

A flexible diaphragm is "one that has a maximum lateral deflection more than 2x the story drift" according to a seismic book I was reading (Lindeburg/Baradar chapter 7 Diaphragm Theory. I believe the reference, albiet old, is UBC '97 Sec 1630.6. I haven't tried finding the reference in IBC. One key difference between rigid and flexible is that flexible doesn't transfer torsional shear stresses. For this reason rigid diaphragms track loads to the shearwalls/frames etc. via rigidity, like everyone is showing you above, and flexible diaphragms track loads to their respective elements by tributary areas.

 

[msquared48]

Depending on the thickness and the depth of the metal deck with respects to the diaphragm shape, I think that the situation could be argued either way.

So, either determine whether it is flexible or rigid and proceed accordingly, or figure out the worst condition of both cases here and use that envelope for your design.

Mike McCann
MMC Engineering

 

[GalileoG]

bigmig,

A flexible diaphragm does not transfer shear stresses? How then can the lateral loads be transferred by my flexible diaphragm? Does that also mean that my flexible diaphragm will not have any torsion?

Thanks.

Clansman

"If a builder has built a house for a man and has not made his work sound, and the house which he has built has fallen down and so caused the death of the householder, that builder shall be put to death." Code of Hammurabi, c.2040 B.C.

 

[youngstructural]

Not that it doesn't transfer shear stresses, but that it is how much it puts where which is in question.

Any element will transfer some load; From sheetmetal roofs (poor diaphragms, low stiffness) through to concrete cast insitu floor (normally very stiff), they all transfer loads. The concrete floor will just force all of the frames to deflect a similar amount, so the most load goes to the stiffest one (ie: the one that didn't want to deflect along with the others).

So it is a matter of how stiff, always. We often make simplifying assumptions which are not wrong, they just aren't very accurate. At the end of the day this is going to be akin to moment redistribution: As long as the system as a whole has the reserve strength SOMEWHERE and the overstrength to hold itself together, you're going to be fine.

You should be, in general, more concerned when it comes to seismic loads. Wind loads, while very important, are usually not in the catastrophic building-wretching category, without being long and sustained (so the building is going to be in a great deal of trouble anyway). We can permit ductility in seismic because the peak loads are not long and sustained, or as tremendous, as with cyclones.

Cheers,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[bigmig]

Clansman,

Flexible diaphragms are assumed to not transfer TORSIONAL shear stresses. This means there is no torsional shear stresses from eccentric mass placement in either walls/frames etc. or diaphragm. You will have horizontal shear in the plane of the diaphragm. This is what you design for.

 

[sundale]

Most SE's treat a metal roof deck as a flexible diaphragm. This is what I learned from my mentors.

However, if you bother to calculate the diaphragm midspan deflection in relation to average drift deflection of the vertical lateral elements, these things are really quite stiff. My experience in the few times I have run these numbers is that a metal deck diaphragm will numerically meet the definition of a RIGID diaphragm per ASCE 7 Figure 12.3-1.

ASCE 12.3.1.1 and IBC 1613.6.1 will both let you idealize a metal deck as FLEXIBLE. I think this is a nod to SE standard practice. So it is equally valid in the US codes to treat this metal deck diaphragm as either rigid or flexible.

Treating it as rigid diaphragm will induce added torsional shears into your lateral design. You will need to calculate frame and wall stiffness if you are distributing forces from a rigid diaphragm analysis.

You do not need to know the frame or wall stiffness to distribute the forces if you are doing a flexible diaphragm analysis, because this is simply based on tributary width. You will still need to know the stiffness of these lateral elements from a servicablity perspective in order to see of your drift will be cracking finishes, cladding, etc.

As other posters have said, virtual work is a good way to calculate the stiffness of a steel brace. Perhaps consider cracked section properties for your shear wall.

 

[msquared48]

Yea. There's a lot of us doing virtual work nowadays...

Mike McCann
MMC Engineering

 

[zeemas]

CY

I tried the method you mentioned in your previous thread regarding distribution of lateral forces including torsional cases

http://www.eng-tips.com/viewthread.cfm?qid=214448&page=27

But i am unable to match the numbers with ETABS. I dont know how ETABS is distributing forces.

Any input please!!!!
Zee

 

[youngstructural]

How far out are the results?

Have you checked the method against something VERY SIMPLE? IE: I can only assume you have written a spreadsheet; Did you check the spreadsheet against a known solution? Did you thereafter check your Etabs modelling skills against the same, known, problem?

Hang in there... Different methods are not always going to give dead accurate results; You're looking for CLOSE, not exact.

Cheers,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[zeemas]

I just created the spreadsheet and i was able to calculate center of rigidity exactly same as ETABS and then i tried to distribute the forces but i got different result than ETABS. I am going to model a very simple model now to check my results.
By the way check the Rigidity topic in ETABS help,

Thanks for your reply.
I will share my excel sheet tomorrow.

Zee

 

[youngstructural]

Okay, that sounds good; I look forward to seeing your spreadsheet (even just a screen capture output).

One thought: Could there be an issue with your diaphragm stiffness in ETABS?

Note that it is Friday where I am, and I probably won't be as quick to reply until I get back to the office. I'm usually on here during my coffee breaks! *smiles*

Cheers,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[zeemas]

I am sorry i didnt get chance to upload the spreadsheet.
Check the attached. We will discuss about this later.