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Advanced mechanics of materials (1993-John Willey) Episode 9

Tham khảo tài liệu 'advanced mechanics of materials (1993-john willey) episode 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 462 11 THE THICK-WALL CYLINDER SF p1 are - SF P1 -l-80pi b2 a2 . 402 202 Sf P1 ê5 L8 402 _202 3.000p b 0.6000 The actual stresses at the inner radius are obtained by adding the residual stresses given by Eq. a to those given by Eqs. b . Thus ơrr l.SOpi ơee 3.0000pi 220.4 c a 0.6000 - 110.2 The octahedral shear-stress yield condition requires that 2 Y 1 __ -y- I Wee - ffrr 2 crr - T-J2 - ee 2 d Substituting the values for the stress components given by Eq. c into Eq. d we find that Pi 154.2 MPa is the working internal pressure for the cylinder that was preloaded to the fully plastic pressure. Substituting the values for the stress components given by Eq. b into Eq. d we obtain the working internal pressure for the cylinder without residual stresses Pi 108.3 MPa Hence the working pressure for the cylinder that is preloaded to the fully plastic pressure is 42.4 greater than the working pressure for the elastic cylinder without residual stresses. 11.6 CYLINDER SOLUTION FOR TEMPERATURE CHANGE ONLY Consider the stress distribution in a thick-wall cylinder subjected to uniform internal and external pressures Pi and p2 axial load p and temperature change AT that depends on the radial coordinate r only. The stress distribution may be ob 11.6 SOLUTION FOR TEMPERATURE CHANGE ONLY 463 tained from Eqs. 11.8 11.9 11.10 11.11 and 11.16 . The special case of constant uniform temperature was considered in Sec. 11.3. In this section the case of a cylinder subjected to a temperature change AT T r in the absence of pressures and axial load is treated. If internal and external pressures and temperature changes occur simultaneously the resulting stresses may be obtained by superposition of the results of this section and Sec. 11.3. As in Sec. 11.3 the results of this section are restricted to the static steady-state problem. Accordingly the steadystate temperature change AT T r is required input to the problem. Steady-Steady Temperature Change .