Reinforcement Ratio?

[jeb6294]

I'm working on problem number 111 in the NCEES Sample Questions concerning minimum area for reinforcing steel.

Working backwards from the solution, I've got most of it figured out except where they are figuring the reinforcement ratio. I have absolutely no idea where they are getting it from, but I'll try and give you an idea of the formula they're using:

=(fc'/Fy)[1-(1-4*0.59*a/fc')^0.5]/(2*0.59)

fc'=normal weight concrete
Fy=reinforcement bars
a=Mu/(phi*b*d^2)

I'm taking the Water Resources PE Exam so can anyone tell me where this can be found in the CERM or do I just need steal it from the sample book if it shows up on the exam?

 

[chicopee]

I dont know anything about your problem but if my recollection is right there are guidelines to minimum amount of steel cross sectional areas in reinforced concrete. I also remember from strength of material that there are several examples on bending and compressive stress analysis of reinforced concrete beams , retaining walls, columns fand pilasters. Check out any related references.

 

[DaveAtkins]

It looks like they are solving for the required reinforcement ratio, based on Mu.
I was taught differently--to assume a steel area, solve for phi*Mn, and compare it to Mu.

DaveAtkins

 

[crossframe]

It appears to be Equations (3) and (4) in Chapter 10 of PCA's "Notes on ACI 318-99" (1999 is most recent I have, but these equations haven't changed).

I always use this to directly solve for As (especially when doing hand calcs), rather than assuming As.

 

[archeng59]

the equation appears to be a strain compatibility derivation. if you have access to a Wang Salmon concrete design text (I have the fifth edition), chapter 3 shows several equations for designing a rectangular section.

I also solve for As based on a calculated Mu = phi*Mn. the equation I use is:

phi*Mn = phi*As*Fy(d-0.59[(As*Fy)/(f'c*b)])

all variables are known except As. you end up with a polynomial (ax^2+bx+c=0, where As = x) to solve on the calculator. the first root is the required As. once you solve for As, use the equation rho = As/(b*d) to get the reinforcement ratio (rho) for the member cross section.