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# Deflection of spring tempered stainless steel rods

## Deflection of spring tempered stainless steel rods

(OP)
Dear All,

I am involved in a rather unusual sculpture project.

The concept is to create a large assembly of 20+ feet high vertical rods that sway with the wind but always return back to their (perfectly) vertical resting position if there is no wind.

I assume using spring tempered stainless steel rods, probably 302/304, is the best economically speaking and in terms of longevity outdoors. What’s the best way to predict their deflection other than trying out different rods from let’s say 3/8 to 3/4 inch diameter? Is there a (not too complicated) way to calculate their deflection? Any application where I could plug in different diameters and lengths that would visualize the swaying of the rods?

Erwin
Replies continue below

### RE: Deflection of spring tempered stainless steel rods

"Machinery's Handbook" has simple equations for stress and deflection of cantilever beams, which is sort of what you're talking about.

Worst case stress won't be from the wind, but from the local high school football team pulling on the bar at head height, roughly speaking. That would be the load case of a concentrated load at a specified intermediate point along the bar. The problem may not even be soluble if you include this load case, but you can't reliably prevent it from happening. Maybe if you put the base of the bars on a tall pedestal surrounded by a deep moat of raw sewage, but even then it's still susceptible to a lasso and a pickup truck...

The wind will apply, roughly, a uniform load along the length of the bar; maybe some CEs will chime in with a transfer function between wind speed and loading.

You have to allow a foot or two of embedment in, e.g., concrete at the root of the bar to resist the applied moment. You can't just weld the bar to a plate, because the welding heat will anneal the bar and you won't know what the real properties are at the point of highest stress.

Mike Halloran
Pembroke Pines, FL, USA

### RE: Deflection of spring tempered stainless steel rods

(OP)

As a base I thought about something like two horizontal steel plates, each with a hole the size of the vertical rod. The two steel plates would be spaced apart about a foot with threaded rods (or simply with welded stand-offs). The vertical rod sticks through the steel plates and everything is buried below ground and put in concrete. The steel plates would hold up the rod vertically and in addition to the steel itself the concrete would weigh everything down.

### RE: Deflection of spring tempered stainless steel rods

(OP)
Some completely different idea: How about fiberglass or carbon fiber rods? Very light therefore less sagging under their own weight. No rusting...
I've got a couple of carbon fiber paddles for my kayak. They are totally amazing - super light and almost indestructible...

PS: Sorry for suggesting this in a stainless steel forum :)

### RE: Deflection of spring tempered stainless steel rods

That sounds like a plan; just don't weld the rods to the top plate.

There may be a way, but just virtually eyeballing it, I don't think you can make the subject sculpture sufficiently vandal- resistant to survive for long and still flexible enough to sway in the wind.

Mike Halloran
Pembroke Pines, FL, USA

### RE: Deflection of spring tempered stainless steel rods

Carbon fiber will be far stiffer than steel in loading due to self weight. It will also be far more expensive. Also, tapered tubing can be made much taller than straight rods or tubes before it falls over or flexes from its own weight (like fishing rods). The sway frequency will also be higher.
Your idea for supporting the rods with two plates is a good one, particularly if the space between the plates is left open. this allows the rods to flex in the top support hole and greatly reduces the stress concentration at that point.

### RE: Deflection of spring tempered stainless steel rods

ErwinRedl-

Your sculpture sounds like an interesting concept. However, in order to accurately simulate how a vertical array of 20ft long stainless steel rods would sway in response to wind flows would require a fairly complex coupled aero-structural analysis. While it is fairly simple to calculate the bending in a single cantilevered rod based on a distributed normal force, it is far more complicated to calculate what the aerodynamic forces produced on any particular rod in the array are under various conditions.

The spacing and relative positioning of the rods in the array will have a big effect on the airflow turbulence/velocity between leading and trailing rods. Long, slender, cantilevered rods will likely experience all sorts of extreme dynamic responses due to flutter or coupled structural modes. I could easily imagine a situation where the rods at the leading edge of the array are gracefully bent in the direction of the wind flow, while the rods at the trailing edge of the array are whipping wildly side-to-side due to flutter instability caused by wake turbulence.

If you have funding to build your sculpture, I would suggest that you contact the engineering dept. of a local university to find an undergrad willing to work on your project. The opportunity for an engineering undergrad to do a coupled aero-structural analytical model of your sculpture, and then be able to validate their work after you build the sculpture, is too good to pass up. A perfect combination of art and science.

### RE: Deflection of spring tempered stainless steel rods

On possibility is to make the rods tapered, this way they would be stronger near the ground where people can mess with them but thin enough toward the top that they would sway.
You may need to put a small stainless ball on the tips to create enough aerodynamic drag to get them to sway in the wind.
It would be possible to make tubes that are constant OD with a tapered wall, getting thinner toward the top. But this would not be low cost.

= = = = = = = = = = = = = = = = = = = =
Plymouth Tube

### RE: Deflection of spring tempered stainless steel rods

I tend to doubt that a cantilvered 3/4 dia x 20+ ft solid metal rod can be induced to remain vertical for any meaningful period of time.

Regards,

Mike

### RE: Deflection of spring tempered stainless steel rods

Since this is a dynamic sculpture that is intended to capture peoples' attention as it continually changes form/pattern/shape in response to wind flows, then I would suggest adding some capability for the rods to actively change their aerodynamic characteristics, structural stiffness or orientation. For example, how about a system of parallel links that connect adjacent rods near their root ends? This will result in all of the rods in the array swaying in unison, rather than randomly, in response to wind flows. To me, an array of rods swaying in sync in response to the wind would be far more intriguing than an array of rods swaying randomly.

Just a suggestion. Best of luck with the project.
Terry

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