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'K' tables for concrete
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- Subject: 'K' tables for concrete
- From: Roger Turk <73527.1356(--nospam--at)compuserve.com>
- Date: Mon, 10 Apr 2000 21:51:39 -0400
Robert Rollo wrote: >>In our office we have K-charts for use in reinforcing selection for concrete and in fact have a spreadsheet that publishes these values for different combinations of conc and steel strengths. These charts have 3 lines on them, rho min, rho max, and an intermediate line. When I first was introduced to the chart, it was explained that the intermediate line represented a rule-of-thumb "you might want to change your section if your k value is below this line." There are notes on one of our older charts saying that a cracked section deflection computation should be used beyond the intermediate line. Seems like this line was based upon research by some individual, but i cannot recall the name or locate any published reference material on this. Does anyone know what i am referring to and/or have a reference that would detail exactly what the line really represents, and a formula that would give us the correct intermediate line?<< Robert, It sounds like you had one of my students (or one of my student's student) working for your firm. In 1993, I was asked as adjunct faculty to teach Advanced Reinforced Concrete Design. In order to find out how well schooled the students were in Elementary Concrete Design, I gave a homework assignment that involved flexural design of some slabs and beams. They spent so much time iterating and not designing that I had to spend two weeks reviewing elementary concrete design. In the review, I had the students develop a chart similar to what you describe. The chart is based on calculating Ksubu for rho min and rho max for various concrete and steel strengths where, Ksubu = Phi*f'subc*q*(1 - .59q) and, d^2 = Msubu/(Ksubu*b) where Msubu is in inch-pounds This gives the range of depths a slab can have for any permitted ratios of reinforcing. I usually take a nice number (400 or 500 is pretty good) in the middle to see if I have sufficient depth, d, for the concrete strength I would be using. A second part to the chart is the value of asubu for the same range of permitted reinforcing ratios. asubu = Phi*fsuby*(1 - .59q)/12,000 and, Asubs(required) = Msubu/(asubu*d) where Msubu is in ft-kips. This gives you the amount of reinforcing (more or less) that is needed for flexural requirement. asubu doesn't really vary very much based on concrete strength so you can use asubu as 2.5 or 2.6 for grade 40 reinforcing, and as 4.0 for grade 60 reinforcing. Hope this helps. A. Roger Turk, P.E.(Structural) Tucson, Arizona
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