# Axial Compression Strength Table?

#### mccordmw

##### Well-Known Member
I finished calculating the total force of drag plus inertia for my rocket. I want to make sure I'm well within the safety margins for current and future motors.

Does anyone have a good link to the strengths of various airframe tube materials? I can find aluminum, but that's not too hopeful to me right now.

#### mccordmw

##### Well-Known Member
Thanks. I totally forgot about that site. While it doesn't have the tube I'm looking for, I can use the estimate that the cardboard shipping tubes have a fail rate around 1200 psi. I'll play it safe and go down to 1000 psi.

Sanity check here. Based on the data on crush tests for cardboard tubes this is what I calculate.

Real Test: Cardboard shipping tube
OD: 2.120"
ID: 1.994"

Back-calculating:
Area: pir2 (outer) - pir2 (inner) = 3.52 in2 - 3.12 in2 = 0.407 in2 area
Calculated load = 1160 psi * 0.407
in2 area = 472 lbf

Makes sense.

So if I use an 8 inch mailing tube with a 0.25" wall, and I use a safer limit of 1000 psi, I get:

OD: 8"
ID: 7.5"
Area: pir2 (outer) - pir2 (inner) = 50.3 in2 - 44.2 in2 = 6.1 in2 area
Calculated load = 1000 psi * 6.1
in2 area = 6100 lbf

So a standard 8" mailer tube with a 0.25" wall and 4' length can support 6100 pounds of force? Does that seem sane?

The measured strength of a thin walled fiberglass tube was super strong itself:

Real Test: fiberglass tube
OD: 3.128"
ID: 3.005"
Wall Thickness: 0.123"

wow...

So I suppose it's not that unrealistic?

#### Nytrunner

##### Pop lugs, not drugs
TRF Supporter
I'd do a double check for buckling. The longer a structural object gets, buckling will become more of a factor under compression loads. The layered nature of cardboard may present another variable too.

#### mccordmw

##### Well-Known Member
Trying to calculate Euler buckling now...

Pcritical = &#960;2EImin/L2

#### Nytrunner

##### Pop lugs, not drugs
TRF Supporter
Hmmmm. Young's Modulus of shipping tube cardboard may be difficult to find.

#### mccordmw

##### Well-Known Member
Bank, L. C., E. Cofie, T. D. Gerhardt "A New Test Method for the Determination of the
Flexural Modulus of Spirally Wound Paper Tubes." ASME Journal of Engineering
Materials and Technology, Vol. 114, p. 84-89, 1992.

Might be a good start.

matweb.com

#### mccordmw

##### Well-Known Member
Ok. So I checked the weight of a section of mailing tube and cross-checked it with the table on the link I proided. It has a modulus of elasticity of 10 MPa. Assuming that, I can calculate Euler's buckling for a cylinder's moment of inertia. For an 8" cardboard tube, I came up with a load limit before buckling for a 8" x 48" tube as 1,249 lbf.

#### mccordmw

##### Well-Known Member
Oops. That's for a rod, not a hollow cylinder. A hollow cylinder has a moment of inertia of &#960; (do4 - di4) / 64 .

So the allowable force before buckling is only 284 lbf.

#### dhbarr

##### Amateur Professional
TRF Supporter
Oops. That's for a rod, not a hollow cylinder. A hollow cylinder has a moment of inertia of &#960; (do4 - di4) / 64 .

So the allowable force before buckling is only 284 lbf.

Want me to carefully step on a 2.5" coupler? :-D

#### Nytrunner

##### Pop lugs, not drugs
TRF Supporter
Nice investigation and work-check!

My Mech. E sanity check was refusing to be quiet at the thought of a cardboard tube holding 3 tons.

#### Ravenex

Another thing to consider though is buckling strength goes down rapidly as a beam bends even a little. The slight slop between a coupler and airframe could cause enough misalignment to reduce your strength on a long rocket significantly.

#### mccordmw

##### Well-Known Member
Heh. Yeah. Been there with super long LPR rockets. This airframe has axial support structures inside with forces supported from thrust plate through to the bulkhead of the payload bay. Still in planning which is why I'm calculating this here.

#### mccordmw

##### Well-Known Member
One more thought. Since the motor mount is epoxied to the airframe at many points in short spans axially, it should be a point of strength. I can assume that the thrust of the motor is being applied to the airframe starting at the topmost centering ring then. Any point below that has so many force distribution points via epoxied rings and ttw fins, that they can be treated as a single body of force?

So don't count the whole 4' frame for buckling. Instead only count the distance from the top centering ring to the end of that frame.

#### Ravenex

That sounds like a valid assumption.

#### OverTheTop

##### Well-Known Member
TRF Supporter
That sounds like a valid assumption.

Yep. Sounds like a very reasonable simplification.

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