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hercek
TheTechnicalNoob: thanks for the link.
Hell, that documents must be writen by heretics of physics. Not only the authors use "hogshead" units, but they cannot even get it right, even with them. Ok, so they define modulus as lb/in² but (based on the formula (in note 7) for ussage of their modulus values) the unit is actually only lb. Or at least I hope this is what they intended (one cannot be completely sure when they have contradictions even in such a simple document).
Ok, so for GT2 belt it would be 18000 lb for 1" wide belt. Based on note 4, that is 18000/25.4*6*0.82 ≅ 3486.6 lb (or about 15509 N) for the common 6mm belt repraps often use. That means the elongation for 1m long belt and 57N force change is 1 * 57 / 15509 ≅ 0.0037 m = 3.7 mm.
hercek...as I constantly have to tell my 11yr old daughter, "It is ok to be wrong, but it is NOT ok to assume you are correct." And there are no "hogshead" units in that document.
First you must understand the definition of Young's Modulus (aka tensile modulus or elastic modulus) and the methods of testing and calculations for determining the value of E (the symbol for Young's Modulous). In the equation to determine the value of E, the dimensions of the sample material are removed so the value will be representative of the "material" and not the "material at a particular size." See where the author inserted (1" Width)? That is why there is an extra "/in" in the row stating his unit of measures. Though it should read, "((lb/in2)/in)" or (psi/in). Remember...when there is no value in front of a unit of measure, it is understood to have a value of one. Therefore if his GT2 belts were 2" wide, then the value would have been 36,000 psi/2in.This is a unique case where the units of measure do not cancel because the author must show the derivative value of E to avoid confusion.
The author gives an equation of BE = ((BSL) x (TL)) / TM. Your equation above is BSL = TM / ((BSL) x (TL). Why did you use the reciprocal of the author's equation? ATTENTION TO DETAIL!!
*Edited for spelling and to cite my source as one of my mechanical engineering textbooks: Black Kohser DeGarmo's: Materials Processes Manufacturing 10th Edition (John Wiley and Sons, Inc.) I'll post screenshot of the textbook if requested.