# Thread: Deflection on rods and tube steel.

1. ## Deflection on rods and tube steel.

Having a hard time finding a guide to working out the weight to deflection ratio on travel rods. I bought 1.25" dia 4' long rods hoping their wont be any deflection under the wieght of the X znc Z axis combind. Would be nice to know if my 14 gauge sqaure tube steel would deflect too.

In other words would like to know how much deflection my 1.25" dia 4' long rod would have with 50lbs right in the center. Or if I need 1.50' dia? Or maybe I'm over built.

2. ## beam bending

The bending formulas are pretty straightforward but you did not give enough information to know which formula to apply. They all depend upon E, the Young’s modulus for the material (where steel is 29*10^6 in Imperial units) and the area moment which for:
1. A Rod is I =.25 * pi * r^4
2. While a hollow square tube is I= (a^4 –b^4)/12 (if rounded corners are ignored) where a is outside dimensions and b is inside dimensions both across the flats.

But you need to think about how the rod or tube is supported at the ends to select the bending formula. Simply supported means the beam can have deflection slope at the support and with a midpoint load the maximum deflection is (W*L^3)/(48 *E*I). Rigid support means the beam is held to allow no bending at the support (like it was cantilevered at both ends) and for that situation the maximum deflection is (W*L^3)/(96*E*I). You may need both formulas. Suppose the steel tubing base is welded then the top member is effectively rigidly supported and the bending length( L) is the distance between the supports. But if the round rail is supported by relatively small standoffs then it is simply supported and L is the center to center distance between standoffs.

Tom

3. Here's a great(to me) link for doing beam and other calculations; http://www.engineersedge.com/ It will automatically do the calculations after you put in the parameters. All kinds of other engineering calculations too. Hope it helps you

4. Great feedback. Much more than I expected.

TomB,
I'm sorry but I'm way too many years out of school to know what ^ means. And I just started on the search to find E. Thank you very much.

packrat,
Great link, Just what I was looking for. Still I'm on the search for E though.

Pic when my cnc router was being built. Its a fail cnc router because of the play in the Y axis towards the support rob. Being rebuilt ATM with gantry style X axis. The small support rod is only 0.5" and has very bad deflection. The 1.25" large rod seam to have no deflection.

5. This doesn't answer your question directly but if you get these books and read them you will be well on the way to understanding deflection of beams and a lot more things.

The New Science of Strong Materials or Why You Don't Fall through the Floor (Princeton Science Library) by J. E. Gordon and Philip Ball (Paperback - Jan 30, 2006)

Structures: Or Why Things Don't Fall Down by J. E. Gordon (Paperback - Jul 8, 2003)

Metals In The Service Of Man by W Alexander And A Street (Paperback - 1956)

6. Thankx, Geof.

Found this on the wed.
Modulus of Elasticity, E

The Modulus of Elasticity (E) is a measure of a material's axial stiffness. Stiffness and strength are not the same thing. As it turns out, the value for the modulus of elasticity (E) is the same for all steel types. There is no difference in stiffness with type of steel. The value used by the SCM is 29,000 ksi. (See SCM pg 16.1-xxx, the symbols section.)

Shear Modulus, G

The shear modulus, G, is a measure of the shear stiffness of the material. It is a constant for all steels and has the value of 11,200 ksi (see SCM pg 16.1-xxxii).

The fact that all steels have the same E and G means that for members whose design is controlled by a stiffness limit states (i.e. deflection or vibration), the type of steel used is unimportant. In these cases, there is no advantage to using a higher strength steel over one with lower strength. You will particularly notice this in long span beams where deflection becomes the controlling limit state.

7. Originally Posted by TomB
The bending formulas are pretty straightforward but you did not give enough information to know which formula to apply. They all depend upon E, the Young’s modulus for the material (where steel is 29*10^6 in Imperial units) and the area moment which for:
1. A Rod is I =.25 * pi * r^4
2. While a hollow square tube is I= (a^4 –b^4)/12 (if rounded corners are ignored) where a is outside dimensions and b is inside dimensions both across the flats.

But you need to think about how the rod or tube is supported at the ends to select the bending formula. Simply supported means the beam can have deflection slope at the support and with a midpoint load the maximum deflection is (W*L^3)/(48 *E*I). Rigid support means the beam is held to allow no bending at the support (like it was cantilevered at both ends) and for that situation the maximum deflection is (W*L^3)/(96*E*I). You may need both formulas. Suppose the steel tubing base is welded then the top member is effectively rigidly supported and the bending length( L) is the distance between the supports. But if the round rail is supported by relatively small standoffs then it is simply supported and L is the center to center distance between standoffs.

Tom
This is really great help. Were did you get these formulas?
Do you have the formula for hollow round tube?

I worked out that 14gauge 2"x2" tube steel has a I=0.31 and my solid 1.25" rod has a I=0.11984

I think 29,000,000 lbs per inch is a amazing number.

With this internet calculator. I'm not understanding X or C. Not sure what values to put in for a 2"x2" square tube 24' long with 1000lbs in the middle.

http://www.engineersedge.com/beam_be...flection_2.htm

8. Originally Posted by FunnyDream
...With this internet calculator. I'm not understanding X or C. Not sure what values to put in for a 2"x2" square tube 24' long with 1000lbs in the middle....
X is the distance from the end to the point where the load acts so for your example it will be 12'.

C is the distance from the top to the center point of the cross-sectional area; for a symmetric shap that means the centerline so for your example it is 1".

Do you really mean 24'? In other words twenty four feet?

1000lbs in the center of that length of 2" x 2" 14 gauge tube is going to bend it into a deep U shape. It would sag several inches just from its own weight.

9. Originally Posted by FunnyDream
This is really great help. Were did you get these formulas?
Do you have the formula for hollow round tube?
I may have pulled the formulas out of a engineering class 'Strength of Materials' textbook or I may have done a google search for 'beam deflection Wikipedia'. I just did the search and the result includes the formulas as well as a link to the area moment of inertia formulas. Although its been 50 years since I took the class once learned you can recognize the same material from any source. The difficulity for somebody that does not have some formal background is that the formulas build on each other and so just seeing a bending formula does not help since terms like I and E can be misterious. But get past that point and even the correct application of the formula become problematic because the formula's derivation incorporates specific boundary conditions related to beam support. In the respone I gave I tried to illustrate that difficulity.

Today much of that complexity gets embedded in application softwear. There is a good piece of freeware called 'Beamboy' that will calculate deflections. As for the area moment formula for a section of pipe I seem to remember that you just subtract the area moment of the inside from the area moment of the solid rod.

Tom

10. Those formulas were exactly what I've been looking for! Glad I spotted these useful links.

cheers,
Ian