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'K' tables for concrete

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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