ponding analysis by manual calculation

huangyhg

ponding analysis by manual calculation
i have a project where an engineer used an in-house procedure to check some long span roof joists for ponding loading.  
the roof uses primary drains only and then depends upon over-the-roof flow of water to scuppers at a far end of the building.  there are about 4 to 5 valleys that have these primary drains and the water must flow over the various ridges which about 3" high or so, to get to the scuppers.
i honestly don't know what the exact procedure is but i think it is essentailly this:
1.  load up the roof joist with the initial water assuming the drain is clogged.
2.  the joist deflects downward some initial amount.
3.  recalculate the new depth of water based on the now-deflected shape of the joist.
4.  re-calculate the new deflection of the joist based on the re-calculated depth of water.
5.  repeat until convergance.
i don't know the validity of this process.  
i checked the joists against aisc for ponding (9th edition and second edition section k2 or appendix 2 in the new 13th edition).  this check revealed that the joists were no good in terms of ponding control.  
however, the engineer states that the aisc provisions only determine if you need to further check for pondingfff">....not whether there is a problem with ponding.  he claims that his method above then satisfies the code with respect to ponding.
the actual language that aisc uses is:  the roof system shall be considered stable for ponding and no further investigation is needed if both of the following two conditions are met:....
this seems to imply a "further investigation".
i've never thought of it like this before.  i've always taken the aisc provisions as determining if the joists are inadequate for ponding or not.  
i've never heard that they simply determine whether a further check is required.
thoughts on this?
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i don't know anything about the aisc provisions, but your five-step procedure looks reasonably sound.  but it would be tedious, particularly if you were close to a ponding situation (for which the convergence would be very slow).
under many circumstances the differential equation governing the deflection of a beam subject to ponding is identical to the differential equation for a beam on an elastic foundation.  the only difference is that the ponding case has a negative "foundation stiffness".  if the resulting de has a solution then ponding will notfff"> occur.
if you have access to any software for the bef problem that allows you to specify negative bef foundation stiffnesses then you might be able to use that software to solve your problem in the one pass.
alternatively, if you have a simple beam program that allows negative nodal support springs, you could approximate the "true" bef situation through modelling a series of closely spaced (negative) springs.

if you cannot satisfy the ponding requirements using equations k2-1 and k2-2 in aisc (9th edition), then you can use the curves in the aisc commentary.
i think the approach this engineer used is valid as long as the stress in the joist does not exceed 0.8*fy.
daveatkins
thanks for the replies.
while his approach does seem reasonable, i guess i'm confused by my main question:
if the aisc ponding checks show no good...does this imply a need for "further investigation" or does it mean the joists are no good?  
it would seem strange to have both the main body check and the aisc curves in the commentary as well - but with these only serving to determine if you're close and have to check further....and then for aisc to not offer a "real" check procedure.

asce 7-05 recognizes aisc methods on page 337 (refs. c8-5 and c8-6) but i don't read it anywhere in asce that the aisc methods must be followed exclusively.
i don't have asd 9 right at this minute. by the 13th manual, i read that section 2.1 is simplified and section 2.2 is more exact. if section 2.1 shows that ponding may be a problem, the engineer has the option to use the more exact method of section 2.2 to check the roof system (this is where the curves show up in the 13th manual).
but the way i read asce 7 is that you are not limited to using only the aisc ponding checks (example, if sji had a method you might choose to use it). example, page 95 of asce says "it shall be investigated...." but doesn't state a required method.
so an alternate "in-house" investigation may be allowed even if both aisc methods do not work unless you are for some reason (building department, goverment ufc criteria etc.) required to meet aisc. right?

sounds to me like the engineer's "in-house procedure" meets the definition of "further investigation."  if aisc meant that the system was unacceptable if it didn't meet the two conditions, then they wouldn't have left the door open.  sounds like aisc is saying "the exact analysis is complicated/time consuming."  in lieu of performing an exact analysis, a quick and dirty conservative method is to meet these two conditions.  as always, when the designer deviates from the accepted method, it puts an extra burden on the checker.  i once was the checker for a brilliant, innovative designer. he would design stuff in half the time, and it would take me twice as long to check it.
if you are going specifically by aisc, then it says method 2 is "permitted" when a more exact determination is required over method 1. but to me, you don't have to check aisc's methods at all according to asce. or am i missing something? maybe you could argue it is standard practice in your area that it should be upheld.
  
jae - though it might seem odd, i believe that both the aisc procedures are just simplified procedures, one grossly simplified, and one closer to the real deal.  i have generally used the same "rigorous" analytical procedure as outlined by the engineer in lieu of the aisc simplified procedure(s) when i get close to having a problem.  the code language appears to bear this out..   
so the key here is that if you use a homegrown procedure it must include an iterative/converging approach that takes into account second order effects, etc.?
the thing that the aisc approaches tend to do is include an aspect dealing with the water flowing - sort of a dynamic effect.  the engineer's approach that i listed above seems to be more static.  i don't feel that water behaves itself that much....but maybe i'm wrong - i have a question posted to aisc so we'll see what they say.
haynewp - whether asce 7 requires the aisc procedure or not may be valid, but for a steel roof it seems to me that aisc shouldfff"> be the authority.
do you all agree with the engineer, though, that the aisc checks are onlyfff"> checks used to determine whether you need to investigate ponding?  
or are the aisc checks a check on ponding itself?  
or both?   
well that is what i was saying with the "standard practice" regarding using aisc. but there is the sji technical digest #3, could this be what he is basing his method on? i have never actually used it before.
jae - its both.  if you pass simplified 1 no need to look at simplified 2.  if you pass simplified 2 no need to look for further analysis.  if you fail simplified 1 and 2 - look at an interative technique as described.  if that doesn't work...make it bigger.