huangyhg

calculating rho prime for long-term deflections
this might sound like a silly question, but i have to ask. the question is which b to use when calc'ing rho prime in order to get the long term multiplier for long term concrete deflections.
let's say you have a concrete t-beam with a flange width of 120" and a stem width of 36". you will get a significantly different rho prime depending which b you use for as/(bd).
i have always used the flange width, but have never had such a big disparity before and needed so much compression steel to cut down the long term deflections so this is the first time i've thought this much about it.
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i would go with flange width as well. b it typicaly defined as the width of the compression face, which will primarily be the flange of the t in this case.
i have to think that if you used 120" to compute short term deflections, then you need to use 120" for ρ'. however, if using b=36" for short and long term deflections results in a lower long term deflection, then i'd use 36" for both. are you considering the longitudinal slab steel in your as'?
ρ' is based on bd where b is the compression flange and this is taken at the midspan (by definitions from aci 318).
so you'd use the 120" and the area of compression steel at midspan.

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