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 A hollow steel shaft is 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 cx TJ - n ơA For- otnscF op -Polly p-PasF c yieJJin J C lị - r G -- 7 d I4O-26 7Õ r 4 Ool Tị 2Ĩ1 7irp if - llTtr -ệ- C1 - 3 - 1- c c s - iSox o aoS 3 - -S - . x o3 H - l N-M PROBLEM 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 TY- - fc rr - i 3 a k-p-m 4 - ậĩ . - 2 - - Tr -ệ-r Dr 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 - in n Us r p fc t coions Ặv-Ù Fine - _ _2Ị_ - 1-00 tị X 3. ỉ 07 The magnitude ofthe torque T applied to the tapered shaft ofProb. 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 3 ai . . To rlvy y pJLs-h c sk íst pf o T Tr Í - ậ s 3. g4 ft - 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 SOLUTION Considering the partially plastic shaft of Fig. derive Eq. by recalling that the integral in Eq. represents the second moment about the raxis of the area under the T-p curve. JI .