Materials Engineering - Aluminum Tubing Strength

[Axecutioner]

Background info: This is for a trebuchet I plan on building. Obviously lighter is better especially for the throwing arm which is why I need your help in figuring out that problem, so I can get it as light as possible without it having even a remote chance of failing. If there's information missing from the problem just let me know and I'll try to reword it if needed. The pic below is kind of another example of what's going on, but slightly different with the forces involved.

Assume the following:
-Aluminum has a max tensile strength of 18,000 psi (125 MPa), max yield strength of 8,000 psi (55MPa), and elongation (stretch before ultimate failure) of 20%.
-The steel rod is infinitely strong and won't bend or break (so it isn't a factor in the problem)
-The length of the aluminum tubing is 50 - 150cm (just to eliminate any weirdness with really short or really long lengths), I don't think the actual length matters in this.
-The aluminum tubing is free to rotate about the steel rod.

Question: If rectangular aluminum tubing width W (W ≥ 1.27cm), height H (H ≥ 1.27cm), and thickness T (T ≥ 0.15875) has a radius R (2R ≤ 0.75W) hole drilled through it's width, and a steel rod radius R is put through that hole, and the aluminum tubing undergoes a peak net torque F ( about the steel rod, what is the lowest mass per unit length of aluminum tubing that can hold that torque F before bending, breaking, or losing structural integrity, and what are the dimensions of that tubing?

Very lame and basic pic: http://img854.imageshack.us/img854/5247/badexampledrawing.png

Please show all work involved in this problem. Thank you very much in advance for any help!

 

[berkeman]

Background info: This is for a trebuchet I plan on building. Obviously lighter is better especially for the throwing arm which is why I need your help in figuring out that problem, so I can get it as light as possible without it having even a remote chance of failing. If there's information missing from the problem just let me know and I'll try to reword it if needed. The pic below is kind of another example of what's going on, but slightly different with the forces involved.

Assume the following:
-Aluminum has a max tensile strength of 18,000 psi (125 MPa), max yield strength of 8,000 psi (55MPa), and elongation (stretch before ultimate failure) of 20%.
-The steel rod is infinitely strong and won't bend or break (so it isn't a factor in the problem)
-The length of the aluminum tubing is 50 - 150cm (just to eliminate any weirdness with really short or really long lengths), I don't think the actual length matters in this.
-The aluminum tubing is free to rotate about the steel rod.

Question: If rectangular aluminum tubing width W (W ≥ 1.27cm), height H (H ≥ 1.27cm), and thickness T (T ≥ 0.15875) has a radius R (2R ≤ 0.75W) hole drilled through it's width, and a steel rod radius R is put through that hole, and the aluminum tubing undergoes a peak net torque F ( about the steel rod, what is the lowest mass per unit length of aluminum tubing that can hold that torque F before bending, breaking, or losing structural integrity, and what are the dimensions of that tubing?

Very lame and basic pic: http://img854.imageshack.us/img854/5247/badexampledrawing.png

Please show all work involved in this problem. Thank you very much in advance for any help!

What is the context of this project? Is it for schoolwork?

 

[Axecutioner]

I'm building a trebuchet using aluminum tubing, and I want to know what size tubing I can use to keep it as light as possible without breaking. No school involved.

 

[pantaz]

From a practical standpoint, aluminum is a poor choice, IMHO. The arm of a trebuchet tends to act somewhat like a spring. Aluminum will work-harden and develop stress cracks pretty quickly.

Regardless of the material, if you must have a hole through it, add reinforcements.

 

[SteamKing]

If you have access to steel that is infinitely strong, I would definitely go with that material.

 

[Axecutioner]

So what metal should I use to keep the weight down but still hold strong?

I'm dropping a max of 50-60 lbs from 4 ft high. What material and dimensions should I use? Rectangular tubing or circular tubing?

Thanks

 

[pantaz]

... I'm dropping a max of 50-60 lbs from 4 ft high. ...

That is a considerable mass to be using on a "lightweight" trebuchet. What is the maximum machine weight (less counterweight) you hope to achieve?

What is the throwing arm length? Can the machine be anchored to the ground during use?

Are you going to use it just a few times for a demonstration, or do you expect to use it repeatedly?

What construction methods are available to you? (Welding, machining, etc.)

 

[RocketSci5KN]

If you want to lighten the structure, choose a better Alum. alloy like 6061-T6 which has a yield strength of about 35ksi. This assumes creep won't be a factor. Add back in whatever safety factor you require.