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Digging even deeper here. . . . From oltmannd's good comments, it might be useful to find out just how much force the average tie clip must withstand. We'll start by determining how much force it would take to squeeze our heated rail that's expanded by 380 feet back to its original length of 300 miles even. The equation to use here is as follows (again, over simplified): d = PL / EA d is the change in length, 380 feet or .072 miles P is the force, what we want to know L is the original length, 300 miles E is the modulus of elasticity, 30 million pounds per square inch (psi) for steel A is the cross sectional area of the rail, 11.75 square inches for 120 lb/yd rail Solving for P: P = dEA / L = .072 * 30000000 * 11.75 / 300 P = 84,600 pounds So it takes a force of 84,600 lbs to keep 300 miles of rail from expanding over a temperature change of 20 C. Assuming ties spaced 22 inches on center, there are about 864,000 ties in 300 miles of track. Thus, at each tie plate there only has to be 0.1 pounds of horizontal force applied to the rail to keep it in place (84,600 divided by 864,000). But that's horizontal force -- the tie clips hold the rail to the ties using a vertical force. Translating that vertical force into a horizontal force introduces friction (isn't this stuff fun???). Clean steel (big simplification/assumption here) has a coefficient of friction of 0.8. That means 80% of the vertical force becomes horizontal force. However, if the steel gets lubricated (like from grease or oil on a passing train) the coefficient of friction drops all the way to 0.16. If we're going to play it safe, we can only assume that 16% of our vertical force translates to horizontal force. Thus, the vertical force at each tie plate needs to be 0.1 pound / 0.16 = 0.625 pound. Again, this analysis is incredibly over-simplified, but I hope it was still useful. I found some good information on welded rail forces at: http://www.newscientist.com/lastword/article.jsp?id=lw437 Wow, that's the most action my engineering textbooks have seen in months! Thanks, guys. Additions, corrections, questions, etc. welcomed as always, Scott Lothes Cleveland, Ohio
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