# Formula & Conversion with a square root

## Main Question or Discussion Point

I'm comparing the shear formula for a beam in english and metric. But it seems the
formula or result don't match.

In English, the formula is Vc=2*b*d*sqrt(Fc)

Given
b=11.81102 inches
d=18.11024 inches
fc=4000 psi
Vc=2*b*d*sqrt(Fc)=27056 lbs

Now converting the units in metric.

b=300mm (11.81102 inches)
d=460mm (18.11024 inches)
fc=27.5 Mpa (4000 psi)
Vc=2*b*d*sqrt(Fc)=45.8 Kilonewton

To convert Kn to lbs. Divide Kn by 4.448 and multiply by 1000.
Doing that to the metric result. 45.8 Kn / 4.448 x 1000 = 10304 lbs

But 10304 lbs is not equal to the result in the english formula? Why?
Note this is not a homework. I just want to compare the two units in the formula.
Thanks.

SteamKing
Staff Emeritus
Homework Helper
Not familiar with your formula. It doesn't seem to have consistent units:

lbs = in * in * SQRT (lbs / in^2)

Can you provide a source for this formula?

please also see page 16 of the above for an actual example of it. Why, what is wrong with lbs = in * in * SQRT (lbs / in^2)? Won't LBS result with the in^2 being cancelled by in * in?

SteamKing
Staff Emeritus
Homework Helper
lbs is not equal to SQRT (lbs).

SteamKing
Staff Emeritus
Homework Helper
It seems that some of the formulas in the ACI 318 standard are unit specific, IOW, the standard you are using is meant to be used only with Imperial units. I understand from doing a web search that the ACI has a separate publication which is meant to be used with SI. I would refer to that SI version to find an equivalent formula for the max. compressive shear.

Chestermiller
Mentor
Expanding on what SteamKing said, the 1.9 and the 2 in these equations are not dimensionless, and depend on the particular properties of concrete. If they had been expressed with units, then it would be possible to make the conversion.

When you get the square root of something, you are getting the sides (say 3 inches) of a 9 square inches area. So when you are getting the square root of pounds. What sides are you getting? Can you give another example where you need to get the square root of pounds or mile?

SteamKing
Staff Emeritus