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Mechanics of Materials - Problems - Solution Manual Part 4

Tham khảo tài liệu 'mechanics of materials - problems - solution manual part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | PROBLEM 3.105 3.105 A hollow steel shaft is 0.9 m long and has the cross section shown. The steel is assumed to be elastoplastic with rr 180 MPa and G 77 GPa. Determine a the angle of twist at which the section first becomes fully plastic Ố the corresponding magnitude of the applied torque. SOLUTION c ỳd O.OiiT cx TJ - 0.035 n ơA For- otnscF op -Polly p-PasF c yieJJin J C lị - r G -- 7 d I4O-26 7Õ r 4 5.0 Ool Tị 2Ĩ1 7irp if - llTtr -ệ- C1 - 3 - 1- c c s - iSox o aoS 3 - O.O -S - . x o3 H - 14.84 l N-M PROBLEM 3.106 3 106 A shaft of mild steel is machined to the shape shown and then twisted by torques ofmagnitude 45 kip-in. Assuming the steel to be elastoplastic with rr 21 ksi determine a the thickness of the plastic zone in portion CD of the shaft b the length of the portion BE which remains fully elastic. SOLUTION dl Zn ỊDô ílOM CD c - p 1.00 TY- - fc rr - i l.0o 3 a 32.W k-p-m 4 - ậĩ . - 2 - - 0.3C62Ô Tr 3X.787 -ệ-r 0.7IẰ83 Dr Co.7l23 i.ooV 0 7 3 ty - C-Ạ - 0-287 Qa For- TCr _ 1 Ly TTCe3 E Ỵ - lị J c - ce J I - io k-p 3 -2Z SMtà I I - _3 E -i- Áíi X - l.ai2G in n Us r p fc t coions Ặv-Ù Fine 1.25 - Ị.OựH _ _2Ị_ 1.85 - 1-00 tị X 2.44 3. ỉ 07 The magnitude ofthe torque T applied to the tapered shaft ofProb. 3.106 is slowly increased. Determine a the largest torque which may be applied to the shaft Z the length of portion BE which remains fully elastic. SOLUTION The Xfcrjesl ioiT ue may be. cư pỉìej Wie. In porẠỉơM Ct c - L ờó H Ị i.oo 3 ai . 32.387 k.p.itt. To rlvy y pJLs-h c sk íst pf o T Tr Í - ậ s 32.987 3. g4 k.p.ụ ft W.Qkfin - k ị Ỵ - Ey c- Cfj T- 3. 3 Ắf 5 ỉn. Cg- - OỠÔ in k-X-J -J r - s - .33333 V TTĨr IT Rlj Đsìn pA p0 4 10 1 s 4 ke slteJ cJri 1-00 V X - 2 3 M PROBLEM 3.108 SOLUTION 3.108 Considering the partially plastic shaft of Fig. 3.38c derive Eq. 3.32 by recalling that the integral in Eq. 3.26 represents the second moment about the raxis of the area under the T-p curve. JI .