Question

**Use Shigley's Mechanical Engineering Design, McGraw-Hill textbook as a reference

Problem 4: For a bolted assembly, the stiffness of each bolt is k, = 5MIbf/in and the stiffness of the members is k,m= 15MIbf/in per bolt. The joint is subject to occasional disassembly for maintenance and should be preloaded accordantly. A fluctuating external load is applied to the entire joint with Pa= 100kips and Pnia= 20 kips. Assume the load is equally distributed to all the bolts. It has been determined to use 1/2 in-13 UNC grade 8 bolts with rolled threads. a) Determine the minimum number of bolts necessary to avoid yielding of the bolts Determine the minimum number of bolts necessary to avoid joint separation b) c) Determine the minimum number of bolts necessary to avoid bolts failure due to fatigue.

Answer 1

p.4 Saln's Giem Stilfneiof lach belt, K 5 mthflim Stillmiss of mumbl&, Km 15 Pman Mibtlim -100 ki Ps 20 kiPs Pmim CRy wing Shigley Design Machamical Engimutimg A feimce) (a) ramtable 8-2, tunsil stess a&ia At im2 -O.141g lrom table 8-9, mimimum Preaf steength Sp 120k Psi Fi o.75 EP Nous Fi O.75 At. Sp) Fi O.75 (0.1419 12.77 ki Ps 4120) Fi Stiffmeus conitamt =O.25 5+15

Dee J 2 im equation mp Sp At CP+ Fi Nows with np- we gut Ptotal = NSp At-Fi 0-25 N Sp At C Ptotal Ptotal C O.25 Sp At N- (100) CO.25) O.25 C120)(o 1419) N 5.87 OR 6 Bolts mimimum No. a balts niceiioky to araid yeildiang af the balts is 6 Ralts with maI (b2 Nout im ea Fi Ptotal N. wl gety Fi Ptotal (1-C) Fi 1o0(1-0.2 5 12.77 N-5.87 OR 6 Bolts Mimimum Noa bolts micwaky to avsid iaimt shiration is h C Ptotal Sp At-Fi O-25 CLO0) (120) (0.1419) - 12 77 6 Bolts 5.87 NO OR