Unit issue in equation

[Linkanson10]

Hi, im using mathcad prime 4 and I have´some problems with the following equation. This i

This is my input values:

d=314 [mm]

b=200 [mm]

pl=0.006 [Unitless]

Cr=0.12 [Unitless]

k=1.798 [Unitless]

fck=30 [N/mm^2]

V=[Cr*k*(100*pl*fck)^(1/3)]*b*d, this equation gives me the unit [kg^(1/3)]*[m^(5/3)]/[s^(2/3)] but i want in to be in the unit N. I've tried to use [MPa] as a unit for fck and tried to write the unit manually but it doesn't work

[LucMeekes]

Please attach your worksheet. Look in the announcement to the right of this column for further information.

Success!
Luc

[LucMeekes]

Where does the equation come from?
What might be the unit of the number 100?

[Linkanson10]

I'm trying to calculate the dimensional value for tansverse power to be able to calculate stirrups in a beam. The equation comes from eurocode and the number 100 is a constant i guess.

[LucMeekes]

I get an error message trying to unarchive your .RAR (please use .ZIP; it's in windows, free and works).

You formula comes from Eurocode.... Is it a formula derived from physics basics (in which case the units must balance), or is it an empirical formula (one that happens to describe the phenomenon, or just happens to work, but lacks a solid physical background)?

If it is an emprical formula, then you better work without Mathcad's units, and fill in the numbers per the instructions of the formula. If you search this forum for empirical, you will find tips on how to deal with empirical formulae.

If it is physically based, you better look up the meaning of all symbols and constants and their correct (SI) units.

Success!

Luc

[Werner_E]

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@Linkanson10 wrote:

I'm trying to calculate the dimensional value for tansverse power to be able to calculate stirrups in a beam. The equation comes from eurocode and the number 100 is a constant i guess.

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Maybe not, I don't know. Maybe its an empirical equations which expects its input values as dimensionless numbers.

At least you get the expected unit N if you assume that the factor 100 is of dimension pressure^2, maybe Pa^2, maybe something else.

[LucMeekes]

Found it as formula in 6.2.2. of the EN 1991-1-1.

From the description I conclude that it's an empirical formula. Strip your units (by division with SIUnitsOf) of each of the input variables and apply the unit N to the result.

Success!

Luc

[Werner_E]

> Strip your units (by division with SIUnitsOf) 

No, not SIUnitsOf but rather division by the units expected by the empirical formula (whatever they may be).

E.g. SIUnits of fck would be Pa but as you wrote the formula expects the value in MPa.

[LucMeekes]

You're right, Werner...completely right.

Here's a way to work this. From the Eurocode I read:

Success!

Luc