Formula & Conversion with a square root

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Discussion Overview

The discussion revolves around the comparison of a shear formula for beams in English and metric units, focusing on the discrepancies in results when applying the formula to both unit systems. Participants explore the implications of unit consistency and the validity of the formula used.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant presents a shear formula Vc=2*b*d*sqrt(Fc) and calculates results in both English and metric units, noting a discrepancy in the outcomes.
  • Another participant questions the consistency of units in the formula, suggesting that the units do not align correctly.
  • A participant provides a source for the formula, referencing a specific equation from a document, but others challenge the validity of the formula's unit consistency.
  • Some participants argue that certain formulas in the ACI 318 standard are unit-specific and should be used with their respective unit systems.
  • There is a discussion about the implications of taking the square root of units like pounds, with some participants asserting that it leads to meaningless results.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the validity of the formula or the implications of unit consistency. Multiple competing views remain regarding the interpretation and application of the shear formula in different unit systems.

Contextual Notes

There are unresolved questions regarding the assumptions behind the formula, the specific properties of the constants used, and the implications of unit conversions. The discussion highlights the need for clarity on the applicability of standards across different unit systems.

violt
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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.
 
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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 canceled by in * in?
 
lbs is not equal to SQRT (lbs).
 
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.
 
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?
 
That's just it: the square root of pounds is meaningless.
 

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