Moment Equation for Concrete Beams?
Moment Equation for Concrete Beams?
(OP)
Hello again,
This time I'm trying to program a short script in excel to calculate needed reinforcement in simply supported concrete beams.
According to the Canadian standards, the moment resistance formula for a beam is Mr = PHI x As x fy x (d - a/2) where the "a" variable also contains "As"...making this a quadratic equation in terms of As. I work with metric units and I'm trying to basically equate the Mr equation with applied moment, and solve it for As (area of steel reinforcement) which I would round up and figure out the way to propose a certain number of rebar to cover it...
The problem I'm having is that I can't seem to get a meaningful solution to this quadratic equation...it's always nonsensical...
Does anyone have any tips for me?
This time I'm trying to program a short script in excel to calculate needed reinforcement in simply supported concrete beams.
According to the Canadian standards, the moment resistance formula for a beam is Mr = PHI x As x fy x (d - a/2) where the "a" variable also contains "As"...making this a quadratic equation in terms of As. I work with metric units and I'm trying to basically equate the Mr equation with applied moment, and solve it for As (area of steel reinforcement) which I would round up and figure out the way to propose a certain number of rebar to cover it...
The problem I'm having is that I can't seem to get a meaningful solution to this quadratic equation...it's always nonsensical...
Does anyone have any tips for me?






RE: Moment Equation for Concrete Beams?
BA
RE: Moment Equation for Concrete Beams?
Then compare that to what you get when you use Excel's built in quadratic solver. It may just be that Excel is returning values with a different format than you expect.
RE: Moment Equation for Concrete Beams?
and you'll have problems (ie no real solution) if B^2 < 4AC
RE: Moment Equation for Concrete Beams?
A and C will always be one sign for you and B will be the other. I set it up with A and C positive and B negative.
If I remember correctly, in (-B +or-(B^2-4AC)^.5)/2A you will always be taking the minus of the root. If you take the positive root you get an absurdly huge number.
RE: Moment Equation for Concrete Beams?
rho = {(0.85f'c)[1-{1-(Mu/bd^2)/(0.383*f'c)}^1/2]}/fy
then As = rho*b*d
Otherwise is you want to solve the quad, you could try it in an iterative manner and supply rho(min) as an inital guess.
I assume you know Mu and the beam size.
RE: Moment Equation for Concrete Beams?
thanks again!
RE: Moment Equation for Concrete Beams?