Maximising Torsional Stiffness

[awemawson]

I've bitten the bullet and ordered the steel to re-make the attachment of my hedge flail that I've been banging on about in various other posts, and as I start to build it I will start a suitable thread - however this is more a theoretical question.

Imagine a ladder like structure - two parallel rails joined by 'rungs' for half the length, but the other half only joined at the extreme end. This end can (hopefully) be regarded as firmly fixed. The end where the 'rungs' are has a very uneven load creating a significant twist or torque.

Am I correct in thinking there is virtually nothing to be gained by adding rungs to increase the stiffness to resist this twist, and about the only way is to add a third member parallel but above (or below), and triangulate the structure ?

Conceptually imagine two rails, built into a wall, projecting horizontally out from the wall, joined together for the outer half of their length, then a force trying to twist them along their length.

(The 'rungs' are the main body of the flail and the extreme ends will be joined to the tractor axle. The flail head and arm weighs perhaps 75-100 kgs and project only to one side)

[vtsteam]

The longer the span the easier the twist. I'm assuming a welded structure. And pin ends at the wall instead of fixed.

So I think more rungs will help some. But not as much as substantially increasing thickness of the structure (ie. your diagonals out of the plane of the ladder.)

This is very general talk, on my part.

[Pete W.]

Hi there, Andrew,

Make the stiles high and add rungs both top and bottom AND herringbone strutting.  (Analogy - floor joists.) 

[PekkaNF]

Not very sure if I follow it completely, but if I got the question right:
* Plate (thin but wide) is very stiff on one direction and very floppy on other directions.
* Perfectly round tube has same torsional restistance on every point of it's circumsfere, I.E. same stiffnes in every direction.
* Closed profile tends to be more stiff to twisting than open. Compare pipe and C.
* Generlly more you have dimenssion of the profile in one direction, more stiffness you have for weight....until the structure collapses when a rock, dent ot angly sparrow hits it and it collapses. You see aluminium pipe bike bodies, If only strength were only consideration, beer can thikness would be pretty close, but it would collapse when something touches it.

You are right on geodesic ladder format, ancient aeroplane fuselages are good eaxample and modern radio masts. Booms on mobile devices tend to be hight strengt square steel structure that properties are optimized and their edge is reinfoced. Round shape would be great, but terminating ito an actuator or pivot is not nice. Square tube is a very good compromize.

I could not find any paper...but I'm not mechanial engineer, I see engineers calculating and dimenssioning this kind of structures (different steel and different product) all the time. This is example of steel/section type that is used. I have seen some modern ones and wall thiknesses look pretty thin. Joints and hard points have cast or welded reinfosments of rather big dimenssions.

http://www.ruukki.us/~/media/Files/Steel-products/US%20Tubular%20products%20-%20Brochures/Ruukki-Optim-High-strength-hollow-sections.pdf
http://www.ruukki.us/References/Lifting/Time-Manufacturing---Aerial-lifts-that-lift-more-and-reach-higher
http://www.ruukki.us/Products-and-solutions/Steel-products/First-class-steel-products-and-services-to-a-wide-range-of-customer-industries/Lifting

Not sure if I'm answering the question at all?

Pekka

[vtsteam]

There are traditional engineering formulas for calculating deflection in trusses to give specific answer to a problem. But to try to speak on the level of intuitive understanding of what happens with a mental picture, a simple ladder with two people at both ends can be twisted to some degree with reasonable strength.

If you remove several of the rungs toward one end, the holders will be able to twist it further using the same force. The two stiles will deflect more in the area where the rungs have been removed. They will deflect oppositely, and attempt to form a helix in that section. The degree of deflection is the part that is important to Andrew, but that is not possible say without doing the formulas, or relying on experience of a similar setup and set of forces.

I do think, also just intuitively, that the end with the single rung should have triangular corner gusset plates for longer life since fatigue from flexing is going to be a consideration at those welds.

[awemawson]

The "end with rungs" is actually not rungs at all but one solid hydraulic tank structure made from very heavy steel plate (it is also used to mount the pivots for the arm - so I'm pretty certain that end will not twist.

The pair of stiles projecting towards the tractor axle is where the problem will probably arise if at all, and as I don't know how long they originally were, I'm working to make them the absolute minimum length that will fit. A wooden mock up is in construction to ensure clearances are ok. These stiles are 100 mm box section with a 6 mm wall so pretty stiff and are spaced with about 30" between them. The problem is that I need clear space between them, as a large hydraulic pump directly mounts onto the PTO output shaft - it's all rather tight ! The other modification I'm working on is to give this pumps hydraulic pipes some form of quick release coupling, so that it can be mounted first, then the tractor reversed onto the flail, rather than having to maneuver the heavy pump onto the shaft at arms length between the stiles. However there is considerable flow which mustn't be restricted - the motor that the pump drives on the flail head develops 24 horse power !

[vtsteam]

4" x 1/4" square tube is stiff. I think triangular gusset plates at the end, displaced in from the corner a bit, and lapped over the tubes would help in avoiding fatigue at those particular tube joints. If you have the clearance for it, I mean.

[mattinker]

How about some photos so that we can really understand what's going on.

Regards, Matthew

[Lew_Merrick_PE]

The angle of twist resulting from a given torque applied to an element is: Theta = (Tau * Length)/(PolarMomentofInertia * ShearModulus)

Theta is the angle of twist in Radians.
Tau is the torque in appropriate units as used in the Length, PolarMomentofInertia, and ShearModulus.
The Length should be obvious.
PolarMomentofIntertia is the area polar moment of inertia of the element (which can be a compound assemblage).
ShearModulus is a value inherent to the material of the element.

Thus, to limit twist, you want to minimize torque, minimize length, maximize the Area Polar Moment Inertia, and/or use a material with a greater Shear Modulus.  These are the variables you have to play with in minimizing twist.

[vintageandclassicrepairs]

Hi Andrew,
Would it be possible to add  a further section centerally  but below the two parallel arms ( to avoid PTO etc)
This (say similar material to the parallel arms) would be held in place by angled members welded to the parallel arms  forming a triangulated  cradle below the mounting arms to the tractor
the welded in pieces would be alternatively at right angles and 45degrees to the main arms forming a cradle of triangles ?
OK difficult to picture ?? imagine 3 vertical members of a radio or power mast forming a V shape
The bottom member of the cradle would just serve to carry the triangulation from one arm to the other

Hope my  ramblings make sense??
John

[awemawson]

Thanks one and all for your suggestions - I've started another thread covering the hedge flail installation so link it here for others following in future:

http://madmodder.net/index.php?topic=9925.msg111235#msg111235