Convert Metric Units to English Units

[SunshineTown]

I have this formula from ACI 318-02 for the basic concrete breakout strength Nb = k*(fc^0.5)*(hef^1.5). I am thinking how this formula will led to a result in unit of force (kip)?
This question arises when I tried to use this formula as a reference to double check the concrete breakout strength using the standard in my region which is in English units and the 'timing' of converting the units leads to different results!
For example, say if I have k=24, fc=25MPa and hef=100mm, if I put these values into the formula without converting to metric ones then I will have the result of 120kN (which is 26.98 kips).
However, if I convert the units of fc and hef to psi and inch and then put it in the formula then the result will be 11.2879 which is 50.2kN. Can anyone explain which way is the correct one and why? I am confused...

 

[IDS]

but this describes the imperial units for 318-02

Nice Article, but is it what you meant to post? Table 1 doesn't seem to specify units.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[IRstuff]

Sure it does:

fc’ same Specified compressive strength of concrete, psi,
hef same Effective anchor embedment depth of anchor, in.

Which is consistent with 318-02 Appendix E

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[IRstuff]

This is what I get for the conversion

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[Lomarandil]

I just had this discussion with a young engineer the other day.

I believe this is the simple and robust way to handle equations with implicit/inconsistent units when using MathCAD/SMath. Rather than stripping out and reintroducing units, address the inconsistent/implicit units at the source.

(more in-depth explanation attached)

----
just call me Lo.

 

[IDS]

Sure it does:

fc’ same Specified compressive strength of concrete, psi,
hef same Effective anchor embedment depth of anchor, in.

OK, I scanned it too quickly and read the in. as "in … whatever came next".

So for those who know it matters, the units are given. That's better than the Australian codes, where you are just assumed to know what units to use.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[IDS]

Lo - that works for shear where the shear strength is proportional to fc^0.5, but does it work for the pull out strength where the area term is proportional to hef^1.5?

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[human909]

That's better than the Australian codes, where you are just assumed to know what units to use.

In most situations in Australian codes that I can recall it doesn't matter what units you use. I certainly haven't come across situations where you need to assume what units to use. In fact most forumala are unit agnostic. Keeping track of your units is part of science 101.

IMO Ideally formula should be invariate with the choice of units. Coefficients should either be unitless or the units CLEARLY highlighted.

EG a random excerpt from 4100.

You are free to use whatever units you want and the answer doesn't change.

Even some equations where the units don't seem to line up do if you dig hard enough. Here they spoon feed you the units but it is actually a unit agnostic formula too.

 

[Settingsun]

IDS,
See AS3600 clause 1.7, AS4100 clause 1.4, AS1720.1 clause 1.9. N, mm and MPa unless noted otherwise.

Eg AS3600 clause 9.4.4.1 (slab deflection) uses load in kPa and specifically notes that.

Human909,
Dimensionless is great but I don't think sqrt(f'c) equations (for example) can be. There's no physical meaning without another sqrt(f'c) built into a constant.

 

[human909]

Human909, dimensionless is great but I don't think sqrt(f'c) equations (for example) can be.

If you give the coefficent dimensions then you are covered. If you don't then you are not.

You are correct about AS3600 clause 9.4.4.1. Absurd really because they have MPa/kPa.... All they needed to was have them both consistant and the equation would be unit agnostic! Very poorly written IMO.

 

[IDS]

Steveh49 - OK, my mistake.

Human909 - as stated by Steve, in the concrete design codes the tensile and shear strength of concrete are related to the square root of the compressive strength, which only works if the compressive strength is in the correct units (MPa). The pull out strength formula discussed in this thread is another example where the correct units must be used.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[Settingsun]

Human909,
I think the kPa units are used because engineers are... human. Forgive me.

Everyone calculates floor load in kPa and that's how live load in specified. Guaranteed there would be many instances of people forgetting to convert. The Lef/d would be off by a factor of 10 though so you'd think it would be noticed.

Use MPa without the 1000 factor if you prefer.

 

[human909]

I guess my first degree as a physist is showing through. I'm used to carrying my units through. I also use it as a fundamental sanity check as I compute things and as a final answer. I'm very much human and it helps keep any mistakes in check.

AS1720.1 clause 1.9. N, mm and MPa unless noted otherwis

Oops. All these years I've been using N, m and N/m^2 in my calculations....

Human909 - as stated by Steve, in the concrete design codes the tensile and shear strength of concrete are related to the square root of the compressive strength, which only works if the compressive strength is in the correct units (MPa). The pull out strength formula discussed in this thread is another example where the correct units must be used.

True. True. But it would be nicer if the coefficients had nominated units.

Somewhere between doing plenty of steel and not enough concrete combined with a little cognitive dissodance, I've glossed over such travesties of physics!

 

[Settingsun]

Concrete used in tension = travesty of physics

 

[human909]

No. As a physist I'd just have some funky coefficents. EG instead of
ft = 0.36 √fc in (MPA)

ft = a√fc

where a=360 (N^0.5)/m Now I don't know what a (N^0.5)/m is but I sure can convert it to whatever set of units I need to.