Metric Conversions 1

[Davybeano]

Hey all

I seem to be having some problems converting Imperical units to metric as i am a uk engineer. The problem is to do with Shear in a flat slab.

Allowable Vc=4*sqrt(Fc)*bo*dv

Imperical Units
Vn=102,000lb
fc=4000psi
bo=83in
And the imperical depth for the slab is given as 4.86in

Mertic units
Vn=451kN Conversion factor = 4.448222
fc= 27.576Pa Conversion factor = 6.894757e-3
bo=2108mm Conversion factor = 25.4
Yet my depth is coming out at 10.18mm

I can't seem to figure out the problem
Any help would be much appreciated.

Many thanks in advance
Regards

 

[henri2]

I performed a crude metric conversion of the equation

Try Vc = 3.3 EE-4 sqrt(Fc)*bo*dv

dv = Vc/[3.3 EE-4 sqrt(Fc)*bo] in mm

where Vc = 451 KN

fc = 27.576 MPa (your conversion factor was for psi to MPa)

bo = 2108 mm

 

[Beggar]

I don't know this formula but its units don't work out. That is, Force / [sqrt(Force/Length^2)*Length] does not equal Length.


--------------------
Bring back the HP-15

http://www.hp15c.org

--------------------

 

[PeterCharles]

Check out the unit balance in the original equation

I don't think 4*sqrt(Fc)*bo*dv equals pounds?

lb^0.5 * in * in lb^0.5 * in * in
------------------ = ----------------
(in^2)^0.5 in

= lb^0.5 * in ????????????????

 

[henri2]

Beggar, check ACI 318 Sec 11.3 and commentary..ACI 318 equation 11-3 is similar to the one posted by Davybeano.

We must not forgert that many of these equations are empirically derived based on research data and mathematical modelling to test validity of data. Often several contants (Davybeano's case the number 4) come into play. Use of and MLT (mass, length, time) units appraoch to check validity thus may not always work.

 

[haynewp]

With d=4.86in, I get Vc=102,048lb=453.9KN.

I think that equation is set up to use f'c in units of psi only. (You'll always have to convert your final answers to metric and use f'c in psi).

 

[rapt]

Daveybeano,

The 4 has to be converted also by dividing by the sqrt of the conversion factor = sqrt(144.----) = 12

so
4*sqrt(Fc)*bo*dv
with Fc in psi

becomes

4/12*sqrt(Fc)*bo*dv
with Fc N/mm2

 

[henri2]

That's right rapt.

Vc = 0.333*sqrt(fc)*bo*d with fc in MPa, bo and d in mm gives Vc in N similar to what I posted earlier when solving for Vc in KN.

Another easy method of verifying equation

If you do not have the metric version of ACI 318, just look at equation 11-3 in the 1997 UBC Sec 1911.3.1.1/ACI 318-05 Sec 11.3.1.1...compare the imperial and SI versions of the equation...substitute fc for f'c, bo for bw and dv for d. Now the imperial version looks similar to Davybeano's except the constant is 2 instead of 4....while in the SI version, the constant is 0.166.

Therefore if the constant in the imperial version were doubled to 2*2 = 4 (Davybeano's eq was Vc=4*sqrt(Fc)*bo*dv) , it follows the constant in the SI version would also have to be doubled to 2*0.166 = 0.332

Finally plug Davybeano's numbers in the imperial version of the equation he provided...then try it with the metric version indicated in first paragraph. Do it again with a different fc (say 6,000 psi/41.4MPa)and repeat with both imperial and SI equations. It'll check out.

 

[haynewp]

I see, the "4" requires converting also.

 

[rb1957]

maybe the "4" isn't just a number, but a dimensional co-efficient, to fix the units it would be lb^.5/in, so 4 in imperial units would become 4*4.45^.5/25.4mm = 0.332 ...

 

[henri2]

rb1957, clearly the number "4" is a dimensional coefficient (and not a non-dimensional one) as you and rapt have demonstrated with the MLT analysis.

 

[trainguy]

You should consider that in some concrete design codes, such as the Canadian one, srqt(Fc') is in the same units as Fc'.

This may be the issue.

I would do the whole calc in imperial, then convert your result to metric, not trying to convert all terms in these empirical equations.

tg

 

[transmissiontowers]

I rarely (never) design in concrete but am always ammused that the concrete guys have the square root of Pounds per square inch in their design equations. The units make no sense to an old steel stress guy, but I always say that I proudly display my mistakes up in the air for all to see and don't bury them underground.

_____________________________________
I have been called "A storehouse of worthless information" many times.

 

[jdonville]

Check out the following website for conversion factors.

http://www.onlineconversion.com/

Very useful.

Jeff


Jeffrey T. Donville, PE
TTL Associates, Inc.

http://www.ttlassoc.com

 

[sqrt]

I think the following statement is both extremely important and is also extremely profound.

ALL UNITS ARE COMPARISONS AND ARE THEMSELVES DIMENSIONLESS.

Merry Christmas