I have some similar charts from ACI that I have updated with a spreadsheet.
The middle line you refer to is probably the value for one half of rho
balanced. The 2.5-2.6 and 4 values that Roger Turk referred to (below)
represent these approximate same values. The formulas for the balanced rho
value can be found in most any good concrete textbook. If you can't find it
let me know and I will give you the formula.
From: Roger Turk [mailto:73527.1356(--nospam--at)compuserve.com]
Sent: Monday, April 10, 2000 6:52 PM
Subject: 'K' tables for concrete
Robert Rollo wrote:
>>In our office we have K-charts for use in reinforcing selection for
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?<<
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
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
design. In the review, I had the students develop a chart similar to what
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)
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
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
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)