## Von Mises in Hand Calc?

## Von Mises in Hand Calc?

(OP)

Hello everyone,

I'm contributing a small section to a colleague's report that is showing compliance with structural aspects of FAR 23 for a fixed wing aircraft's control system. The control system is fairly agricultural, i.e. cables, bellcranks, pushrods and the like.

One component subject to analysis is a torque tube that features drive arms welded to it, with the drive arms being simple 4130N square tube. My colleague has analysed these arms as a cantilever beam.

The colleague remarked that he "had to go to Von Mises" to show the arms good, which got my attention. I've been around the proverbial block a couple of times, and have seen a reasonable number of hand stress calculations from various sources including 'heavy metal' manufacturers, however I cannot immediately recall a time where I've seen Von Mises stresses determined in said hand calcs. I have, of course, seen VM stresses and their related brethren used when reporting FEM results.

Is my sample size too small? Would anyone like to comment regarding the use of Von Mises stresses in hand calculations?

Thank you,

Greg

I'm contributing a small section to a colleague's report that is showing compliance with structural aspects of FAR 23 for a fixed wing aircraft's control system. The control system is fairly agricultural, i.e. cables, bellcranks, pushrods and the like.

One component subject to analysis is a torque tube that features drive arms welded to it, with the drive arms being simple 4130N square tube. My colleague has analysed these arms as a cantilever beam.

The colleague remarked that he "had to go to Von Mises" to show the arms good, which got my attention. I've been around the proverbial block a couple of times, and have seen a reasonable number of hand stress calculations from various sources including 'heavy metal' manufacturers, however I cannot immediately recall a time where I've seen Von Mises stresses determined in said hand calcs. I have, of course, seen VM stresses and their related brethren used when reporting FEM results.

Is my sample size too small? Would anyone like to comment regarding the use of Von Mises stresses in hand calculations?

Thank you,

Greg

## RE: Von Mises in Hand Calc?

TTFN (ta ta for now)

I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg

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## RE: Von Mises in Hand Calc?

The Von Mises technique is just a different, slightly less conservative failure criterion.

Basically, using a stress vs strain curve with some yield stress from uniaxial test data is very conservative because the area below said curve represents the total strain energy per unit volume stored in the material. Basing the notion of failure on this is not entirely accurate (although as mentioned it is conservative) because there are two components to this total strain energy. That is, the hydrostatic, and distortion components. The distortion component comes from the intergranular shear and is what is key to failure.

The Von Mises effective stress is the equivalent uniaxial tensile stress on a member which would create the same distortion energy as created by the actual applied stresses. But it's calculation may be formulaic if you have determined the critical stress location and critical stress element of the part, depending on the situation (again, we have no details of the actual analysis this person performed).

Most design books should develop the VM stress from first principles based on strain energy of a stress element.

Keep em' Flying

//Fight Corrosion!

## RE: Von Mises in Hand Calc?

STF

## RE: Von Mises in Hand Calc?

but as a calc, sure; I guess the max principal was too high, and he was "smart" enough to see a tensile (or same sign, whatever) min principal would give a lower von Mises. So he's looking at a web ?? still don't see it ... on a cantilever arm, the caps take the bending (as a couple) and the web takes the direct shear. If you have too you've got bending and shear interaction ... all simple calcs, not seeing it still !?

another day in paradise, or is paradise one day closer ?

## RE: Von Mises in Hand Calc?

## RE: Von Mises in Hand Calc?

Probably a valid reason, but I would want to understand the rational.

## RE: Von Mises in Hand Calc?

another day in paradise, or is paradise one day closer ?

## RE: Von Mises in Hand Calc?

The VM yield criterion itself is not being questioned, nor how to calculate it - my interest is whether it regularly appears in the typical aircraft hand calcs that many of us are familiar with.

My reaction upon first reading was not unlike these:

which lead me to posting here to see whether I required calibration, or perhaps the use of VM in this type of calculation was slightly amiss.

An example of how said colleague has attempted to use VM in this situation is attached in the file below - unfortunately the report is bereft of FBDs. Please note during reading that I am not the preparer, checker nor approver of said information; I am just an interested observer.

## RE: Von Mises in Hand Calc?

If I were preparing I would

1. Show the component overview with free body diagram

2. Find and show the critical cross section

3. Find and show the critical point in that cross section (where stresses are highest). This is where your stress element of interest will be.

Any time I've ever found a principle or Von Mises stress, it is related to a stress element with applied axial and shear.

Also, it would be helpful to get some context on the shear stress. In the notes, the calc is simply (Vmax / Ashear) but this is only true for direct (transverse) shear, so it depends on what we are talking about here.

For shear due to bending you would have Tau = (V*q)/(I*b)

And for torsional shear, you would have Tau = (T*r)/J

Keep em' Flying

//Fight Corrosion!

## RE: Von Mises in Hand Calc?

bending stress is calc'd at max fiber, shear stress at NA ... why combine them ?? ok, at 2nd glance, for a square tube not unreasonable.

uniform shear stress ? with such a small margin, a better shear stress calc is worth it, and uniform is probably unconservative.

what about plastic bending ? (much higher allowable)

instead of principal (note the spelling) stress I'd use bending/shear interaction ...

Rt^2+Rs^2 = (83.7/85)^2+(4.4/50)^2 = 0.98 ... MS = 0.02

what about fitting factor ?

note his von Mises stress is higher than max principal (so why mention it ?)

I wouldn't've considered a 0.75" tube as a biaxial member.

another day in paradise, or is paradise one day closer ?

## RE: Von Mises in Hand Calc?

"von Mises is lower than max principal if the other principal stresses are the same sign, and larger when there are different signs. But as you say, where is a simple control system would you find multiple principal stresses.."

Von mises would be applicable for an arm for simple strength/margin check.

However, if it were to go beyond this and was to be checked for fatigue, then max/min principle stresses might have been needed to be calculated.

But again, it really depends on the type of the part: (casting, sheet metal, machined part?)

If it is a simple strength check as SWComposites had mentioned it before, without "beating every stinking little fitting to death with a complicated FEM", we might apply this rule of thumb on this as well :)

In automotive, they'll mostly use von mises stresses to calculate fatigue life on parts. And it gives reliable results. In aerospace they will extract every element load from a "good" quality shell element and calculate every stress in detail and check it accordingly. So, it really is up to the complexity of the FEA model and the assumptions. But with rb1957's explanation and von mises checks in most cases where the structure isn't a "primary/secondary" structure, they might be taking the shortcut. They might have been good with Von Mises so far. If they had no problem with it, then it would be experimentally approved as well.

You might wanna check it with other stress engineers there to see if that's the general practice.

I really think every stress department needs weekly meetings of 1 hour to discuss their know-how and to agree on their methods. That's what we used to do when I worked for the wing-box structure. It helps not only at an individual level but at a team level.....

Spaceship!!

Aerospace Engineer, M.Sc. / Aircraft Stress Engineer

## RE: Von Mises in Hand Calc?

Brian

www.espcomposites.com

## RE: Von Mises in Hand Calc?

another day in paradise, or is paradise one day closer ?

## RE: Von Mises in Hand Calc?

Interaction Equations are normally used when combining stresses in a hand calculation, so that's probably why you don't recall seeing von mises in hand written analysis. The interaction equation for a beam stressed in torsion + bending is:

R

_{b}^{2}+ R_{st}^{2}= 1Some notes:

If your control rod has a hollow tubular cross section, don't apply plastic bending. tube walls collapse well before you can develop the plastic bending allowable. Use elastic bending, or look it up on a test derived curve. there are curves in Bruhn and Mil-hdbk-5 for limited materials.

If your control rod is also in compression, VM is

NOTa good assumption, since the tube can buckle before rupturing. In that case use the appropriate interaction equation.