deflection analysis of a 12 metre concrete beam

huangyhg

deflection analysis of a 12 metre concrete beam
i was doing a deflection check on a 12 metre reinforced concrete simply supported beam.in the code it says compliance with the span/ effective depth ratio (20 for simply supported) will generally limit total deflections to span/250.
when i checked the actual span depth ratio for a 1 metre deep beam, the result was  simply 13.3 ( ie 12000/900 ), hence this means this is well below the allowable basic span depth ratio of 20.
however, when i used the formula 5 wlxlxl/(384ei), the max deflection came out to be 54.6 mm, whereas, as mentioned above, the  allowable limit is span/250 = 48 mm.
do i have to increase the beam depth ?

if you have complied with depth/span ratio you do not need to check deflection, unless you have other requirements.
i had the same results before. i looks like this ratio established based on tests, not on elastic behavior (code is not based on elastic behavior of concrete).
deflection check of a 12m beam is not very simple.  you cannot rely only on span-depth ratio.  i would suggest to consider post-tensioning.  the span is too large for reliable calculation of deflection in ordinary reinforced concrete.
emil,
i disagree.  12 meters is well within the bounds of common practice for which standard span/depth ratios have performed well for many decades.
now for the disclaimers...
of course, this is assuming typical values for concrete weight, reinforcement strength and loading.  and you would not rely solely on span/depth ratios if you have brittle finishes, partitions, or equipment attached to the slab that are sensitive to displacements.  if any of these conditions apply, deflections should be calculated, and the effects of cracking and creep should be included.
azh,
what did you use for the "i" of the beam?  did you include an integral cast slab?  did you use the aci effective moment of inertia, ie?  (are you using aci or some other code?).  are your deflections total load or dead load?
if you are under aci, whymrg is right in that you really don't need to check deflections if you meet the general criteria given.
dear jae and others,
the code i am using is bs8110 (british standard).
i=bdxdxd/12 where b stands for the rectangular width of the beam, in this case b=350mm and d is the effective depth of the beam =900mm in this case.the deflection i calculated was based on the ultimate (factored)load of the dead and imposed load (i.e total load).
am i doing the right thing? for your information i am not familiar with the aci ( is it an american code)
actually, i did analysed a 1100mm deep beam and the deflection was within the allowable limit.but the architect may not be in favour of this. taro was right, in saying that post tensioning is not practical.
helpful and ethusiastic engineers, please reply!
here is how i can be of help: not on the subject but on where the subject gets talked of.
if you are using bs8110, then that code does have very simplified deflection checks. check out for example t.j.macginley and b.s.choo reinf. concrete design theory and practice if you are having trouble following the "law" kind of prose in codes(joke intended).
if you are in u.k, the visit rcc website, they even have free spreadsheets for offer within uk(never abroad though), written specifically for bs8110.
aci318 is a strong us code worth your time to check on. not really different from bs in principle but material quality differences and perhaps more emphasis on lateral resistance of structures is placed in us than is in uk.
good luck.
ijr
i've used regular reinforced 16" x 36" deep conc beams for spans as great as 58' for parking structures.  a portion of the moment is taken by the columns.
deflection calculations are fairly involved to accommodate long term effects and account for t-shape (due to slab), percent of steel and concrete strength.  reinforcing is often in several layers.
crack widths also checked.
long term deflection not an issue since there are no partitions.
thanks dik ! 58 ft seems very long.what is the spacing of these beams ?
the aci is the american concrete institute.  aci provides the modulus of elasticity (ec) for concrete, and an effective moment of inertia (ie) for computing deflections.  ie is a combination of icr (moment of inertia of cracked section transformed to concrete), mcr (cracking moment), ma (maximum moment), ig (moment of inertia of gross concrete section neglecting reinforcement).  ie should be less than ig.  the formula for ie is too long to type into words.  its found in aci 9.5.2.3  (aci 318-95).
just 2 things to check for your deflection analysis.
azh
excuse me if i am wrong, but i think your problem is not in the analysis for deflection but rather you seem intrigued by the span of your beam. you are not sure it will work and you are sharing the typical set of worries we all experience.
and none of us can really tell you much since we dont have sufficient input.
however, with my assumptions stated above, let me tell you this: 12m is not a big deal. i know a stadium wing with rc frames spaced 9m apart and one span of a beam in this wing crossing over some 15m, the beam is 1.4m deep, 60-70cm wide and is stuffed with high strength steel reinforcement in double layers, like dik mentioned.
another one is a coach(bus) terminal with roof supported by rc beams again spaced some 6-7m apart and crossing real distance. this one is about 1.2m deep and some 0.40m wide and supports roof slab.
both seem perfectly well.
as for the architect- with such a span to cross and whatever loading conditions you have, he is supposed to co-operate or change the design.
well, i just thought without numbers i can help.
regs
ijr