Bending Moment confusion.

[sumo70]

Hello all,

I have been given the task of comparing some calculations regarding the stress on a sheet metal flange. The theory given states that the flange is subjected to three forces. One from friction and the other two are as a result of the pressure of oil the flange is subjected to. The 3 forces impart bending moments on the flange and it is the sum of all three bending moments that the stress on the flange is calculated. My confusion is as a result of the calculations sheet I was given that shows the three separate bending moments with units of Nmm/mm? As far as I understood, a bending moment had the units of the applied force and a distance such as Nm or Nmm. Can anyone shed any light on what the units Nmm/mm refer to in the case of a bending moment?

 

[JStephen]

I would assume it is the bending moment per unit length of flange, Newton-millimeter per millimeter of length.

 

[GBor]

It looks like the calculation sheet is based on a "per unit length" of metal flange...it is probably making a "plane stress" assumption for it's calculations and using the associated plane stress equations.

 

[rb1957]

or it could be out of an FE program ... NASTRAN reports plate bending moments as moment/thickness (= Nmm/mm)

 

[drawoh]

sumo70,

Warning!

A Newton is a derived unit. The units it is derived from are kilograms, meters and seconds. Do not use millimeters in expressions involving Newtons.

In your expression above, the millimeters cancel out, but this is still bad practise. A "correct" torque unit would be N.mm, which creates a good chance of a three order of magnitude error.

JHG

 

[GregLocock]

Hmm, now translate that comment into traditional units.

Almost every car company I have worked in has used N and mm quite happily for FEA and real world test data.





Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[BillBirch]

Correct Greg,
Designing pressure vessels in Australia, using N and mm in formulae conveniently yielded MPa.

 

[rb1957]

i took it as abit of a "rant", but i think drawoh has a point about mixing units ... the number of times i've seen "g" as 32.17 in a model in "inch" units.

but then drawoh says "the correct unit for torque is N.mm" ... i'll assume he meant "N.m" and up it down to keboard stammer.

anyways i thin N.mm is a prefectly valid unit for torque ... it implies that some thought when into the definition (a force in N and a distance in mm). i quite happily (if misbegottenly ??) use N.mm^2 for stress, and interchange this with MPa.

 

[drawoh]

rb1957,

Note that I placed the word "correct" in quotes. I was pointing out that N.mm is a better unit for torque than N.mm/mm.

I think you are relying on the FEA software to convert everything into standard units of some sort, probably meters. I was trying to do McCauley's double integration method at one time using N and mm. Values of x² and x³ yielded some interesting results.

You can mix inches and feet in English units to your heart's content, as long as you methodically do a unit balance and convert everything. The derived English unit is slugs, and I cannot remember if this is based on pounds or feet. It is so much easier and safer to replace m with w/g.

JHG

 

[rb1957]

N.mm/mm is not the dimension for torque (as i'm sure you know). a (the ?) problem with N/mm is what dimension has been used ... in "normal" calcs it would be a length, in some FE programs it is thickness (and oddly enough it's still called "moment").

i agree you can mix units to your hearts content, so long as you either ...
are very careful, or
happy to live with chaos

 

[JStephen]

To be honest, I can't think of any reason not to use millimeters with newtons, regardless of whether it's a derived unit or not.

In usage, I generally associate "moment" with beam bending and "torque" with twisting of a shaft, although there's not necessarily a rigid distinction there. But in plate and shell bending problems, it is normal to derive the bending moment per unit length. The units technically cancel, but are usually left uncanceled to show that it is a moment per length, rather than a force. Similarly, membrane forces will be calculated as force per unit length, rather than just force.

 

[drawoh]

JStephen,

If you multiply force in Newtons by length in millimeters, you get valid units, used on a lot of torque wrenches. If you multiply by length in millimeters again, you get a unit conversion, as noted above. Multiply once more, you get another unit conversion. Double integration beam analysis has at least two ways of elevating units to a fourth power.

A Newton equals a kg.m/s². You are multiplying meters by millimeters.

JHG

 

[zekeman]

If I were Sumo70, I would be thoroughly confused by all these "answers" to a simple quiry that that was thoroughly answered by Jstephen's response.

The guy/gal probably wanted to understand how Nmm/mm should be called moment when it looks like the the mm's cancel out dimensionally and you are left with a force, not a moment.
All those extraneous responses don't help that understanding.

Now we all know, the practical application is to simply take the numerical value of that Nmm/mm input and apply it to a 1 mm length of that flange.

 

[rb1957]

zekeman, i think you need to be careful about which length dimension has been used ... length, width, or thickness

sumo70, can you give us a clue ... is it something out of an FE program (which i think would tend to be thickness) or is it a running load ?