How much will threaded rods flex?

[chutes123]

I am designing a rather complicated system that needs a certain level of precision. The design includes four (probably aluminum, possibly steel) threaded rods (1/2" diameter, 15" long) in the formation of a square that will support a load of around 6 pounds (load may vary). The dimensions of the centers of the four rods is 1.6" X 1". How much flex will I see from the aluminum or steel rods and what kind of stiffness should I expect? Since the load will be changing, I would appreciate any formulas that might apply. Thanks.

 

[Mech_Engineer]

Why can't you make it a triangulated truss structure? Why threaded rods instead of straight?

 

[chutes123]

Why can't you make it a triangulated truss structure? Why threaded rods instead of straight?

I need lateral stiffness as well as vertical stiffness. Wouldn't a triangulated truss structure compromise the lateral stiffness?

Threaded rods are for ease of design, assemble, and use. The original design has 15 inches of threaded rod so that the load on the end can be adjusted with nuts. I could shorten the rods and only thread the ends where they need to be threaded. Would that be a more stable structure? The compromise in that situation would be its fixed length.

 

[Mech_Engineer]

Any chance you can give us a picture of your specific geometry? That might help with detailed feedback...

 

[chutes123]

Any chance you can give us a picture of your specific geometry? That might help with detailed feedback...

Per your request, I included my best computer rendition of the design I have right now. I have another design that I redid with the triangular truss as well. I can include that in another post if necessary. The important thing to remember is that I need up to a foot of reach from the rods. My boss asked for 15 inches, but I can probably talk him down. I added two plates to the rods spaced equally for added stiffness as well. Let me know what you think.
Thanks

 

[AlephZero]

As a conservative estimate I would assume it has 4 times the stiffness of a single cantileverred rod. Your plates connecting the rods wll distribute the loads between the rods, but IMO they don't look substantial enough to make the structure iact like one composite beam (whilch would be orders of magnitude stiffer).

You don't say what deflections are acceptable but a 1/2 in rod should be plenty stiff enough to support a few pounds weight at 12 inches offset.

If you want to be ultra-conservative, take the radius at the bottom of the threads (i.e. the solid section) rather than the nominal 1/2 in.

The above assumes the vertical support is stiffer than the rods. If not, making a simple finite element model will be easier than doing the calcs by hand.

 

[nvn]

chutes123: Using fully-threaded rod is fine. Using your diagram in post 5, and using your dimensions and applied load (P = -26.69 N) in post 1, if all parts are made of steel, then the vertical deflection will be y = -0.0513 mm, not including any deflection of your vertical support. This is 63.7 times less deflection (or greater stiffness) than a single cantilevered threaded rod.

If all parts are instead made of aluminum, then multiply the above deflection value by 2.90. Therefore, y = 2.90(-0.0513) = -0.149 mm.

If you change the applied load value (P), then y = P/(520.4 N/mm), for steel.

 

[AlephZero]

This is 63.7 times less deflection (or greater stiffness) than a single cantilevered threaded rod.

I'm guessing that you got the factor of 63.7 by calculating the I value of the 4 rods as a singlle section?

I don't agree with that assumption, because there is nothing in the structure to carry the shear between the rods (i.e. to do what the web of a conventional I-beam section does).

The square plates will have a small effect stiffening up the beams, but nothing like the same effect as a continuous web, or a warren girder type of structure connecting the rods. (But as I understand the OP, that type of structure would interfere with the purpose of the screw threads.)

 

[nvn]

AlephZero: The 63.7 factor is for a single threaded rod, not four threaded rods. Four threaded rods, with no composite action, would have 63.7/4 = 15.9 times more deflection than the structure in post 5.

The structure in post 5 has 1.452 times more deflection than if the threaded rods had fully-composite beam action. In other words, the composite action of the structure in post 5 is quite good, about 97.9 % of a fully-composite beam, which is more than one might guess. What it means is, the plates are providing pretty good shear resistance. And the nuts play a fairly big role in this.

 

[chutes123]

What about a three beam structure? Mech_Engineer recommend that I look into using a "triangular truss structure." I drew it out and included pictures. Would this design increase stiffness or have any benefit over the four rod design? The dimensions are the same, just three rods in an equilateral triangle instead of four.

I forgot to mention that there will also be the two plates spaced equally on the rods just like in the last picture.

 

[nvn]

chutes123: The structure in post 10 would decrease stiffness.