hw12sol.Fall.2010x - ME 452 Machine Design II Solution to...

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1 ME 452: Machine Design II Solution to Homework Set 12 Problem 1. (Problem 8-34, page 463). The figure below illustrates the connection of a steel cylinder head to a grade 30 case-iron pressure vessel using N bolts. A confined gasket seal has an effective sealing diameter, D. The cylinder stores gas at a maximum pressure, p g . For the specifications given in the table for the specific problem assigned, select a suitable bolt length from the preferred sizes in Table A-17, then determine the yielding factor of safety, n p , the load factor n L , and the joint separation factor n 0 . Assume the joint is permanent. A B C D E F N pg grade spec 0.5 in 0.625 in 3.5 in 4.25 in 6.0 in 8.0 in 10 bolts 1500 psi SAE 5 ½ in-13 SOLUTION: First, we determine the length of the bolt . Bolts are generally not threaded for their entire length, but are only threaded a standardized length near their free-end. If the bolt selection is too long, the bolt will not have enough threaded length, so the nut will bottom out on the end of the threads before it tightens on the members. This can be checked by calculating the length of the bolt that is unthreaded, called l d , and making sure it is less than the grip. Conversely, if the bolt is too short, it may only partially engage the nut. That is, there may not be enough bolt length to stick all the way through the nut. This can be checked knowing the thickness of the nut, and calculating to make sure a couple of threads of bolt extend beyond the end of the nut. Usually two or three threads is enough.
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2 Since the member thickness (grip) is given, and the bolt size is given, we can estimate the needed length of the bolt ensuring that a couple of threads stick out beyond the end of the nut. From Table (8-7), page 426, the length of the bolt should exceed the grip, l, plus the nut thickness, H: L l H + From Appendix Table (A-31) page 1055, for ½ in bolt, the height, H, of a regular hex nut is 7/16 inch. The grip, called l or L G , is the total thickness of material between the nut and the bolt head, 0.5 0.625 1.125 in G l L = = + = Therefore, the bolt length, L, needs to be 1.125 7 /16 1.5625 in L + = From the standard lengths normally available (See Table (A-17), page 1035), choose L = 1.75 inches . This needs to be checked to see how many threads are showing beyond the nut, but it also needs to be checked to make sure the unthreaded part of the bolt does not extend beyond the grip (that is the threads on the bolt need to extend far enough so the nut does not bottom out on the threads before the members are gripped.) Since the bolt specification is ½ in-13, this indicates 13 threads per inch, the thread pitch. (See Table (8-2), page 413.) Therefore the threads showing beyond the nut are: [ ] [ ] ( ) 13 1.75 1.5625 13 2.44 threads showing N L l H = - + = - = This is enough threads showing (2 or more is adequate). From Table (8-7), page 426, the threaded length, L T is 2 1/ 4 2(0.5) 1/ 4 1.25 in T L d = + = + = So the length of bolt that is unthreaded is (also from Table (8-7)):
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hw12sol.Fall.2010x - ME 452 Machine Design II Solution to...

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