MadSci Network: Engineering

Re: Is a 1/4 in thick pipe strong enough not to buckle

Date: Thu Feb 8 12:37:15 2001
Posted By: Chris Seaman, Staff, Electrical Engineering, Materials Engineering, Alcoa Technical Center
Area of science: Engineering
ID: 981044030.Eg

For your math project, you are designing a "pressure vessel".  A pressure 
vessel is any leak proof container.  Choice of material and design is 
determined by the internal pressures that must be withstood.  Aerosol cans 
are pressure vessels.

Pressure vessel design is serious business, because pressure vessel 
failure is generally spectacular.  Building steam boilers that failed have 
destroyed the buildings they were in.

From the nature of your question, I think you are planning a controlled 
leak, i.e. send the "tennis" ball sized object into the neighbor's yard.  
(I was a teenager, too.)

The basic design equation you want to work with is for "transverse hoop 
stress".  For a unit length section of a cylindrical vessel, the 
simplified form of the equation is:

stress = pressure * radius / wall thickness.

For your example, 1000psi, 1.5inch radius, and 0.25inch wall thickness, 
the hoop stress is 6000psi, or 6ksi.  (For more details, see "Pressure 
Component Construction, John F. Harvey.)

In choosing your material, the key factor to consider is the yield 
stress.  This is the stress that will begin to stretch the material.  

Choose a material that has a yield stress MUCH less than the calculated 
hoop stress.  MUCH less means a factor of 5 or 10 times less.  You want to 
do this for the following reasons.

1)  Published yield stress values represent "typical".  Due to defects in 
the material any particlular sample could yield and break at stress levels 
much less than "typical".  A defect in a tube could be in the weld seam if 
it is a rolled and welded product; it could be along the region where the 
metal has flowed around a die and joined together in an extruded product.

2)  You must consider the "rate" at which the pressure is applied.  The 
faster the force is applied, the lower the level of stress before 
failure.  You may have experienced this phenomoenon when breaking a 
string: pull slowly and the string can support a lot of weight; give it a 
quick yank and it snaps.

Now, on to material choice.  There are many "kinds" of aluminum, called 
alloys.  An alloy is a base metal with other metals added to give 
different properties, such as increased strength.  Each alloy can have 
many "tempers" which is an indication of processing done to the alloy.  If 
you take a paper clip and begin bending it, you'll notice it gets harder 
to bend, then eventually breaks.  You have changed the "temper" of the 
paper clip in the area of the bend through "work hardening".  The 
following is a list of alloys (the number) and temper (the letter/number) 
and "typical" yield stress.  (All values are from the Aluminum Association 
handbook of Standards and Data.)

Aluminum foil aluminum:
1100-0 -- 5ksi
1100-H12 -- 15ksi
1100-H18 -- 22ksi

Conduit aluminum, beverage can aluminum:
3003-O -- 6ksi
3003-H12 -- 18ksi
3003-H18 -- 27ksi

Bicycle frame aluminum:
6061-O -- 8ksi
6061-T6 -- 40ksi

I hope this gives you an understanding of what you are trying to design.  
6061-T6 would be a safe material to use, but make sure you do your 
research before you launch any tennis balls.

Christopher M. Seaman
Alcoa Technical Center

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