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Posted by Administrator on 10/26/2011 to Information Worth Bookmarking
I can't give you a full lesson on Mechanics of Materials here; it is a little involved- 4 hrs per wk for a semester. I will give you a little info though.
If you can find an engineering textbook on Machine Design or Mechanics of Materials, read up on stress and strain. It is very simple and you do not need to be a calculus whiz to understand it; it is basic math only.
The basic material properties are given in lb/sq in for English (inch) fasteners. So, whether it's a 1/4 or 1/2 screw (bolt) it will have the same properties as long as it’s the same material. Don’t confuse properties with strength; the larger fastener will fail at higher loads because it is larger. It's the same as a 2x4 and 4x8 board cut from the same tree: same *properties*, different strengths.
If you have a half inch bolt, basically .5 diameter (but not .500", max diameter is actually slightly smaller), and want to know its strength, don't figure the "area" as Pi(.5*.5)/4; this is incorrect. You must use its smallest diameter- basically the diameter at the "root" of the thread. This smallest area is commonly called the "tensile stress area", or just the "stress area" and there are tables that list this area so you don't have to do the math- tables are in Machinery's Handbook and other "engineering" books, or do an online search for “fastener tensile stress area”. Fine thread bolts have a greater root diameter than coarse, so the stress area is greater and they are stronger than a coarse thread fastener if they are the same material and basic size.
Note that the stress area is not exactly the root diameter on a threaded fastener because threads are rolled and not cut on commercially produced fasteners. Because of the rolling method of manufacturing, the stress area is actually slightly larger than the root diameter; think of the material compression at the root diameter from the rolling process and that this would increase the strength over a cut thread where material was solely removed by cutting it away.
(~ means "approx" as I'm going to round to make it easier on me)
Sooo, a 1/2 UNC bolt has a stress area of ~.142 sq in, and a 1/2 UNF bolt has a stress area of ~.160 sq-in. Multiply the stress area by the Ultimate Tensile Strength and you will get the load, in lbs, when the bolt will fail. For UTS=120,000 lb/sq-in material, basic SAE grade 5, the 1/2 UNC will fail at 17040 lb, 1/2 UNF at 19200 lb. See how the units cancel out? Multiply strength in (lb/sq in) * (sq in) stress area and you are left with lb at failure. A decent *rule of thumb* (not exact!) is UNF is ~10% stronger than UNC for the same basic size and material. 1/4 UNF is almost 20% stronger than UNC, same material.
You can search the net for "tensile stress area table" and can do the math yourself.
Yield strength: the load in pounds (lb; technically lbf) to make it the item stretch 0.2% (not 2%). Take the load and divided by area of the item. Units are lb/sq in for english units. Note it is *usually* 0.2%; this is the most common value by far. So, assume 0.2% unless otherwise noted. This would be stretching a 1.000 lg item to 1.002.
If you load a bolt and stretch it, and plot stress (load/area, or lb/sq in) on the Y axis and strain (change in length/original length) on the X axis you will have a "stress strain curve" for the bolt. For a portion of the loading, the stress strain curve is linear; then at the end of the linear portion you will have the Sp, Proof Strength; then it will turn to a "curve" (not a line) and you will have the Sy, Yield Strength; and finally the Sut, or UTS, Ultimate Tensile Strength, where it fails (breaks).
please see this for a stress strain diag:
Instron is a mfg of testers that can be used to load bolts, etc, and measure stress/strain
Tensile Strength is when it breaks; this is the UTS I mentioned.
Proof Strength is max load it can take without undergoing plastic deformation- aka, permanent stretching or a permanent change in length. This is usually ~.9 times the yield strength. Divide Proof Strength by Yield Strength and you should get about .9, but this does vary slightly.
If you are tightening a bolt, it will eventually stretch some value. This is the most accurate way of preloading a fastener. A torque wrench is a *highly approximate* method of preloading, but it's good enough for most applications. Basically all you are doing with a torque wrench is approximating the stretch of the bolt. If you have ever used ARP rod bolts you will see that they really want you to use the stretch method as it's the most accurate; there are too many variables with the torque wrench method. Type of plating on a fastener can produce a major difference in the torque applied vs. actual preload- zinc and cad are very different with cad having a much lower coefficient of friction. So, a cad plated fastener will stretch more than a zinc plated one when the same torque is applied to it. A few other common error introducing items are fastener cleanliness and lubrication. Since these variables can introduce errors of over 100% in torque applied versus preload, you can see the possible problems with relying on a torque wrench.
~60ksi, or 60,000 lb/in sq is the stress to properly preload a grade 5 bolt in a non-permanent connection- bolt may be reused. Permanent bolts- like in structural steel connections in buildings, are stressed (stretched) more.
To Be Reused: stress to .75 proof strength
Permanent: stress to .90 proof strength
Threaded Fasteners in Shear
There is a lot of incorrect information on fasteners “in shear” on internet mailing lists and message boards. I have seen in more than one location where people claim you should use a grade 5 bolt in a “shear” application instead of a grade 8 since the grade 5 is softer and will take more loading to fail in shear than the more “brittle” grade 8 bolt. First off, a little information on shear strength: shear strength is the strength (lb/sq in) when the element is loaded in shear will fail; shear being when the load is applied perpendicular to the axis. Shear strength is usually calculated as a percentage of the Ultimate Tensile Strength, about .5-.6X the UTS. So to debunk the myth of a grade 5 bolt failing at higher loading in shear than grade 8 is very simple: The higher UTS in the grade 8 bolt gives a higher shear strength than the grade 5 bolt- end of story. So, a grade 8 bolt is stronger in both tension and in shear than a grade 5 bolt; remember that one. Also, grade 8 bolts are harder than grade 5 by definition, but this greater hardness does not make them shatter like glass when loaded in “shear” as some people seem to think.
Notice that I have written “shear”, in quotations, many times. Why? Because bolts will never actually be in shear in a properly designed, properly preloaded (torqued) assembly. Why? Well, if you insert the bolts, finger tighten the nuts, then load the junction in shear then the bolts will be in shear; however, this is ignoring a major part of a bolted joint: clamping force that is exerted when a fastener is preloaded. When a fastener is tightened it exerts a clamping force on the items that it connects. This clamping force is surprisingly high; please check out a fastener torque and preload chart:
That is a great chart to print out and put on your garage wall.
So, if you have a two elements connected by four grade 8 ½-20 fasteners that are properly preloaded, each fastener will exert over 14,000 lb of clamping force; for four (4) fasteners, that is 56,000 lb total clamping! Think of it as having a large flat horizontal plate and sitting another flat plate on top of it that weighs 56,000 lb and then trying to slide that top plate on the bottom plate. So, in order to actually shear load the 4 fasteners mentioned you will have to first overcome the 56,000 lb clamping force. Only once the 56,000 lb clamping is overcome will the fasteners be actually loaded in shear. Going back to the horizontal plates, reasonably assuming dry steel on dry steel, with a coefficient of friction of 0.5, you will have to apply a force of F=uN; F=0.5*56,000=28,000 lb of force to move the top plate on the bottom plate. The same force would be required to shear load the four ½-20 bolts that have been properly preloaded.
(F= force; u= coefficient of friction; N= weight)
Bolt Or Screw Loosening And The “Split” Lockwasher.
Most people believe that vibration causes a bolt or nut to loosen, however the most common reason, which has been verified through extensive testing, is that the nut or screw moves “sideways” relative to the fastened joint. The sideways motion (force) is then applied to the threads and the bolt or nut will unthread itself if the sideways force is greater than the friction force between the screw/bolt or nut and the element that is fastened. There are several reasons the bolt/screw or nut moves sideways: bending in the fastened joint which applies force that can loosen the element, thermal expansion, and shifting of the joint surfaces. If a clamped joint relaxes over time then the fastener will no longer be properly preloaded which can cause the fastener to loosen.
If you are a fan of the split lockwasher, think of the some most important bolts in an engine: connecting rod bolts, main bearing cap bolts and flywheel bolts, none of which use a split lockwasher (none that I’ve seen). The fact that these bolts/screws don’t use a split lockwasher should tell you that it is not a necessary item. So then why are they still used? Good question, but read below, taken from www.boltscience.com.
“Work completed during the 1960's in Germany indicated that transversely applied alternating forces generate the most severe conditions for self loosening. The result of these studies led to the design of a testing machine which allowed quantitative information to be obtained on the locking performance of self locking fasteners. Such machines, often called Junkers machines in the literature - after it's inventor, have been used over the last twenty years by the major automotive and aerospace manufacturers to assess the performance of proprietary self locking fasteners. As a result, a rationalisation of the variety of locking devices used by such major companies has occurred. For example, conventional spring lock washers are no longer specified, because it has been shown that they actually aid self loosening rather than prevent it.” (1)
There are, however, many worthwhile locking devices available, the main three types being:
Free Spinning: Serrated flange nut or a serrated washer head screw
Friction Locking: Plastic insert locknuts, flexloc nuts, interference thread lock nuts...
Chemical Locking: Loctite, etc.
“In general terms, the key to preventing self loosening of fasteners is to ensure that:
1. There is sufficient clamp force present on the joint interface to prevent relative motion between the bolt head or nut and the joint.
2. The joint is designed to allow for the effects of embedding and stress relaxation.
3. Proven thread locking devices are specified. Specifically, thread locking compounds - such as "Loctite", flanged fasteners such as "Whizlok" or torque prevailing fasteners such as "Nyloc". In general, loose washers, of the plain or spring variety, are not generally advisable.” (2)
above are the *basics* of fasteners. Of course, there is more to it than that, entire books, but that will get you started.
Mechanical Engineering Design, 5th edition, by Shigley and Mischke
(1) (2) www.boltscience.com
Thanks to Resto Rick (Restorations by Rick Kreuziger) for the great info!