distribution of lateral forces

huangyhg

distribution of lateral forces
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
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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   
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
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.fff">
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...
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.fff">
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
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
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.
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
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.fff">