Secret Metric Formula Conversions - Elastic Beam Equations 6

[CrunchBird]

If this has been answered, my apologies and thanks for pointing me to the right forum.

Find the area, given the allowable shear stress and load, A = Vfv. Find the section modulus, given the allowable bending stress and moment... and so on.

It's pretty easy if my forces are in Newtons and section properties are all in m, m^2, m^3 and so on. For example, I just convert from m^2 to mm^2 or cm^2 after I've gotten my answer in m^2. I've come across some direct computations, for example moment in N-m divided by MPa gives cm^3 - without including converting from m^2 to cm^2 by multiplying by 10^6 cm^3/m^3.

I've been working on deriving a cheat sheet on this, but so far I've confused myself to the point where I need assistance. Thanks for any suggestions/help/etc.!

 

[apsix]

" I have gotten confused and wrong in the past by trying to combine Newtons and millimeters. Don't do it."

I don't think that you'll get consensus on this, I do it, and as said above they combine nicely to equate to MPa.

 

[drawoh]

apsix,

I was working out the torque and the bending of a mirror rotating back and forth on a shaft. I was doing a unit balance as I was advised to by one of my machine design teachers, and it did not work out. Note how I have equations combining second moment of area and acceleration.

My solution was to systematically convert everything to MKS. In general, your point is correct. In my analysis, it might still be correct, but I have no intention of checking to find out. A unit balance is an excellent error check. It works better if I keep it simple.

JHG

 

[IDS]

Since codes almost always express loads in kN or kPa, rather than N and Pa, it is convenient to use tonne/m^3 for density, rather than kg.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[BigH]

Why not change to unit weight and use kN/m3 - makes a lot more sense when you are dealing in kPa etc. It is amazing how many mill test certificates I see use non-SI units for test results.

 

[IDS]

Why not change to unit weight and use kN/m3

I usually do for my own calculations (if gravity is the only accelleration I have to worry about), but FEA programs like to have density in mass/volume, so I use tonne, m and kN (and kPa for stresses and pressures).

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[jhardy1]

My $0.02 worth:

a) Always remember that mass and weight are NOT the same thing; try to avoid being loose / sloppy with "everyday" concepts like density (mass per unit volume; e.g. water = 1,000 kg/m^3 = 1 tonne per cubic metre) and unit weight (water = 9.8 kN/m^3).

b) Always use a fully consistent unit system throughout your calculations. If you are only doing static load calculations, you can often get away with being a bit sloppy with "mixed units", but it can sure come back to bite you when you get into dynamic analysis (where the time dimension comes into play), or when you have to deal with parameters with which you are not fully familiar (e.g. what is the correct conversion factor to get the heat flux in BTU per square foot per hour, if thermal conductivity is given in W/mK, temperature is in degrees Fahrenheit, area is in square feet, and thickness is in inches?)

c) There are quite a few common consistent unit systems; e.g. in metric, you can use base SI (m, kg, N, Pa, s, etc) or the N-mm system (mm, tonne, N, MPa, s, etc). Note, however, that when you deviate from base SI, some derived units can have "unusual" consistent units; e.g. in the N-mm system, the base unit for density is tonnes per cubic millimetre (which is a very small number for most common materials).

d) If in doubt, I strongly recommend you revert to basic SI units throughout; in this way, you can be confident that the consistent basic unit for ANY parameter in your analysis will be the corresponding base SI unit for that parameter.

Hope this helps!

 

[BigH]

I'm well aware of the tonne/m3 vs kN/m3 - being a geotechnical engineer, it is much easier for us to deal in kN/m3 than in tonne/m3. Pressure at depth of 5 m with unit weight of 20kN/m3 = 100 kPa. I don't have to go put in the gravity factor. As jHardy1 points out - it is best to get the units right at the beginning.

 

[rb1957]

"right" units are what ever you want to use ... i'd never use tonne/m^3 ... for me it's N, mm, and MPa

the key is to be consistent. and if you're importing an odd unit (like IDS mentioned), i'd convert it immediately to the units i liked, and maybe convert my answer if particular units were required.

 

[IDS]

"right" units are what ever you want to use ... i'd never use tonne/m^3 ... for me it's N, mm, and MPa

Which one of those do you use for mass?

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[BAretired]

It has been noted previously that MPa is the same as N/mm² which is very handy. Another handy identity is that a load expressed in kN/m is the same as N/mm.

For a simple span of L with a uniform load of w, the bending moment is wL²/8. If L is expressed in meters and w is kN/m, then M will be in kN-m.

Deflection is 5/384 * wL⁴/EI. The load, w expressed in kN/m is the same when expressed in N/mm. E is in MPa which is the same as N/mm². So, if span L is expressed in mm, the deflection comes out in consistent units, namely mm. Another huge advantage of the SI metric system over the Imperial system.

BA

 

[rb1957]

IMHO BA's post summarises the difficulty ... spans are big distances, better suited to big units (like m) but deflectiona are small, so small units (mm) are better.

the problem is that you have to be very careful (not saying BA isn't !) ... in one expression L is in m and the other it's in mm. personally i keep the units the same and convert the answer, so a deflection of 0.01m = 10mm.

units of mass ... i avoid mass as much as i can ! but usually it's slugs ('cause i'm on the west side of the pond, and most of the time it's in, lbs, and psi/ksi)

 

[jhardy1]

@rb1957:

OMG! Someone who actually uses "slugs" as a unit of mass! I learnt about slugs at Uni (many,many years ago), but I honestly don't think I have ever come across someone who actually uses them!

w.r.t. the "right" units system - in Australia, conventional engineering drawing practice is to use mm for ALL construction dimensions (including member cross-section data, beam and slab spans, set-out dimensions, etc). About the only exception that I can think of is when dealing with large scale overall site plans etc, in which case the set-out coordinates are generally expressed in UTM (whole metres, with mm after the decimal point), and overall site dimensions / road changes / etc may well be specified in metres, but the mm will also be shown after the decimal point where applicable.

Where we make life a bit hard for ourselves, is that structural design calculations are generally done using kN, m and kNm, but we generally give member cross-section data in mm. By and large, it doesn't create any confusion, because it is generally pretty obvious by inspection whether a dimension is being given in metres or millimetres (or kilometres, when dealing with very large distances) - and of course the beauty of the metric system is that all you have to do to swap between units is shift the decimal point by 3 places one way or the other. I would much sooner work in metric units than have to deal with pounds, tons, feet, inches, 1/64 inch, etc.

While we understand the concept of other metric dimensions such as cm, dm, Dm, etc, you won't generally find them on any of our engineering drawings.

 

[rb1957]

we only use them for inertial loads in FEM ... a 9g load you need mass density, slugs/in^3.

i'm trying to get the guys to understand they can use weight density, lbf/in^3, and then the load is 9 (instead of 9*32.174*12)