Moment Equation for Concrete Beams?

[kvazipecaros]

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?

 

[BAretired]

A quadratic equation has two solutions, one of which is usually nonsensical. Why don't you give us the equation you are attempting to solve and the answers you are getting?

BA

 

[JoshPlumSE]

Manually enter in the quadratic formula yourself. Provide the two distinct solutions in different cells.

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.

 

[rb1957]

sorry if this is obvious but remember a quadratic is Ax^2+Bx+C = 0
and you'll have problems (ie no real solution) if B^2 < 4AC

 

[JLNJ]

I always solve the quadratic for concrete beams. I like the exact solution. You might have a sign problem.

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.

 

[fancypants]

Assuming that the section is tension controlled which is what you want, I would solve for rho

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.

 

[kvazipecaros]

thanks guys, i will look into it and post the formula i'm having troubles with...

thanks again!

 

[rscassar]

I just record a macro with a goal seek function. If your starting guess for 'a' is 0.1*d then it should solve the correct equation. I have not had any issues with it yet.