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Registered Member #190
Joined: Fri Feb 17 2006, 12:00AM
Location:
Posts: 1567
I have a steel plate that is 2" x 3/16" x 3'. Let's say the steel has a tensile stength of 30,000psi. 7/8" from one end and centered on the midline axis I have drilled a 1/2" hole. The circumference of the hole is 3/8" from the end of the plate. There will be a chain linked into the hole with a tensile force exerted on the fixed plate. I know how to determine the maximum tensile load for the plate, but how do I determine if the chain will be ripped through the end of the hole? The chain is more likely to get ripped through the hole than for the steel to get pulled apart below the hole. Do I determine the compression capacity for the 3/16" x 3/8" section of steel?
Registered Member #72
Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659
Tensile and compressive strength only work for very simple geometries. In most real world situations, shear strength also counts, and is often the limiting factor. The Youngs, bulk and shear moduli are related by the poison (sp?) ratio for any material, knowing two will let you calculate the other two. However, the elastic yield points are not calculated as simply.
There are two limiting definitions of failure for the situation you describe. The first is any yielding at all that changes the original dimensions, and the second is complete failure where the chain and the plate part company.
Of the many types of steel, almost all will have a ductile failure mode, whereby the hole will elongate and the plate material thicken under the point of chain contact, and thin where it is stretched. Unfortunately for calculation, the area around and under the hole suffers from tensile, compressive and shear stresses in different parts, and these change as the material yields. Fortunately, as the hole elongates and the material thins, the situation will more closely approximate a tensile failure, unfortunately the amount of thinning is not easily calculated.
A passable first approximation can be had by considering the 3/8 x 3/16 cross section below the hole as a link of chain. Assume that it will end up carrying the load of the chain as tension in the cross section, because any shear stresses will have caused the material to yield until the load is carried by tension. This link will fail at 30kpsi x 3/8 x 3/16 lbs x 2 for both sides of the link. This is an upper bound, so knock a bit off for thinning and a bit more for the non-parallel geometry.
Short of some very serious finite element modelling, and knowledge of the whole tensile/elongation graph for the particular steel, you are not going to get a better ball-park figure.
Registered Member #30
Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706
There are lots of textbooks, and just to confuse the student, they're all called "Engineering Mechanics: Statics". I had the one by Meriam & Kraige inflicted on me as an undergraduate.
I also have Spooner's "Machine Design, Construction and Drawing" from 1910-ish, and it looks at this problem in the context of rivets in boiler plate. The chapter on motor cars is hilarious, it discusses things like the best kind of leather to use for clutch linings.
I'd say that you want to calculate the compressive force over an area equal to the thickness of the plate, times the diameter of the rod the chain links are made from. If this is greater than the crushing strength of the plate, then the metal will crush and the chain will rip through the hole.
Also calculate the tensile stress through a cross-section of the plate halfway through the diameter of the hole. This is where the amount of metal is least (you drilled away 1/2" of it) so this is where the other failure mode would be: the plate would crack in half through the diameter of the hole.
Off the top of my head, I'd say that if the allowance between the edge of the hole and the edge of the plate is greater than the diameter of the chain stock on all three sides, and the plate is also thicker than the diameter of the chain, and they're both made of the same kind of steel, then the chain will snap before the plate breaks in any possible way. (this advice is of course provided with no warranty of any kind)
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materials science
