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prestressed inverted t-beam
i have a prestressed inverted t-beam that is supporting very large loads. none of the proprietary shapes can handle this loading. i tried to work out the example by hand, but i am even beyond the design aid charts limits.
i am using the flow-chart in the pci handbook, and need some information.
i am using a 1/2" dia. 7-wire strand with an ultimate tensile strength (fpu) of 270 ksi. what is my yield strength (fpy) of this tendon?
also, is my effective stress in prestressing steel after losses (fse) equal to 270ksi - 50ksi = 220 ksi?? (with effective losses being about 50 ksi)
does anyone have a design example (by hand, not using design aids) or know where to find one of a prestressed inverted t or rectangular beam?
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several good books are available for your endeavor. two of the ones that i use quite a bit are nawy's and the other by mitchell.
to answer your questions, fpy is dependant on using stress relieved strands (fpy =0.85fpu) or low relaxation strands (0.9fpu).
using a lump sum of losses, the effective prestressing is the initial prestress (fpi)-losses = effective prestressing. check your code for the value of fpi. it will be in the neighborhood of 0.7fpu or 0.7(270).
once you have your parameters for design you can check your beam by using sheets i posted in the mathsoft collaboratory site.
service level status, adequacy of stresses to the limits in the circumnstance, shear strength and moment strength should be ascertainable from the sheets. for shear there are also sheets from aci's viewpoint and collins&mitchell's.
pylko,
the jacking forces is usually 70% or 75% of fpu (0.75x270=203 ksi) then you need to deduct your prestress losses, as qshake indicated. for first trial "guess" 20% losses (eg fpe = 0.80x0.75x270 = 162 ksi, or 24 kips for 1/2" strand).
prestressing strand does not have a definate "yield point". for ultimate moment calculations based upon strain compatability go thru the normal motions that you would for rc but include the effect of prestressing strain on the strand (initial strain due to effective prestress and those resulting from ultimate strain at prestress level at a concrete strain of 0.003).
from this value of strain in the prestressing, calc the corresponding stress from the approximated stress strain curve for the strand - see pci handbook 5th edition (page 11.22) - where the approximated equation for the strand is presented.
also, low-relaxation strand (it is also stress relieved via heating and cooling to 600f, but under tension) is just about exclusively used today - and i am not aware of those using just stress relieved only.
check out example 4.2.6 of pci 5th edition - it does a long hand calc for mu using strain compatability without using design aidsm except the equation for the stress-strain curve for strand. it is an inverted t-beam too.....
you will also still need to check stresses for serviceability etc...but that is just p/a +/- my/i assuming the section us uncracked.
becareful on your level of prestress verses beam depth - you indicated that you are off the pci charts for standard sections - better to increase beam depth than have it over-prestressed.
hth
thanks. unfortunately, i only have the 4th ed of pci. any way to fax or email the stress-strain diagram and that inverted t example?
plyko,
sure - i am in hawaii, so give me you fax number an i will send it to you. i guess you are in the us mainland?
you only require ultimate moment calc and stress-strain equation, right? i guess flexural strength is governing for the large loads imposed.
yes, in the continuous 48. fax - 203-639-8384. thanks, greatly appreciated.
must be nice engineering in hawaii.
i wonder if they're lookin for engineers in the bahamas...
thanks again.
pylko
a prestressed inverted tee-beam is a very unefficient section, that is the reason you are out of the charts.
take a section at mid-span, where the stresses are the highest: the thin concrete stem is resisting the compressive stresses, while the prestressing strands (assume you draped them) are very close to the concrete section centroid.
i would recommend a regular tee or a rectangular beam section instead. of course, some other considerations may been having you to select the inverted tee.
aef
dlew,
i agree that with a reduced compression area the inverted t is not very efficient, but most often the precast inverted t is made composite with the topping slab (effective flange equal to bw + 2x8t ) so you gain a significant compression flange, and increased flexural capacity. most often the na is in the web of the inverted t, and you have to deal with two different f'c of the precast inverted t, and the topping, but no real problems with this.
the reason for inverted-t is that i am limited in depth of the girder due to height restrictions in a parking garage. the flanges of the t support box beams. if i had the clearnace, i would have liked to sit the box beams on top of the girder, not flush with it.
yes, i agree with you. the inverted t is not the best shape. my initial calculations have been seriously limited by the relatively small compression block.

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