Question

Chapter 5, Reserve Problem 079 (Multistep) A cylindrical bronze sleeve (2) is held in compression against a rigid machine wall by a high-strength steel bolt (1), as shown in the figure. The steel [E = 204 GPa; a = 11.7 x 10-6/°C] bolt has a diameter of 24 mm. The bronze [E = 105 GPa; a = 22.0 x 10-6/°C] sleeve has an outside diameter of 72 mm, a wall thickness of 8 mm, and a length of L = 530 mm. The end of the sleeve is capped by a rigid washer with a thickness of t = 4 mm. At an initial temperature of T1 = 14°C, the nut is hand-tightened on the bolt until the bolt, washers, and sleeve are just snug, meaning that all slack has been removed from the assembly, but no stress has yet been induced. If the assembly is heated to T2 - 78°C, calculate (a) the normal stress (positive if tensile and negative if compressive) in the bronze sleeve. (b) the normal strain (positive if stretched and negative if compressed) in the bronze sleeve. Rigid Machine Wall Sleeve (2) Bolt (1) Answers: (a) 02 = MPa (b) 2 = με

Answer 1

Given that - L= 530 mm K- diameten of steel boklt ds- ramm Eg = 200 apa , & g = 11.7X106 loc - an outea diameter of bronze sleeve do= 72mm innen diameter of boronae sleeve diz do-2b = 72-(2) (8) = 56 mm Eb= 105 apa , 26=22x106 loc length of the bronze Sleeve L=530 mm -> initial temperature Ti=14c final temperature -> To = 786 ridb7as Cast) bronze P Steel P. S (loust) k > (SI) = (sl) = (SI)

Given that - L= 530 mm K- diameten of steel boklt ds- ramm Eg = 200 apa , & g = 11.7X106 loc - an outea diameter of bronze sleeve do= 72mm innen diameter of boronae sleeve diz do-2b = 72-(2) (8) = 56 mm Eb= 105 apa , 26=22x106 loc length of the bronze Sleeve L=530 mm -> initial temperature Ti=14c final temperature -> To = 786 ridb7as Cast) bronze P Steel P. S (loust) k > (SI) = (sl) = (SI)

from the Compatability condition (SI) = (58)= (80) - pose+ (past) SO + s (SANT) = (BX S AE b. -) Costa) + (QS AT) (Q6AT) - P AbEb up (T) Co² (200x103) + -11. Fx106 x (78-14). 2u (22x106) (78-14) - up (T) (72²56²) (105)) z) bed 1. 1062x10 8 (P) + 7.488x10-4 1.408 x163 5.9209 X6 a (P) z) 1-697 X10 e 6.592x104 P = 38.84 KN Normal stress in the bronze sleeve obz up π (do² di 2) (us Cå8.8u) (103) (a)(722-5692

5o = 24.15 MPa -> Compressive Stress Normal strain in the bronde sleeve eb 11 boyun 24-15 105x10 = 0.229x103 [en = 229.99 adx106