## Introduction to Mechanics of Deformable Solids |

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162 8 . 3 Independent Derivation for

Cross Sections 169 8 . 5 Torsion Problems 172 chapter 9 Thick - walled pressure

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2

**Solid**Bars and Thick - walled Tubes as Assemblages of Thin - walled Tubes162 8 . 3 Independent Derivation for

**Solid**Circular Shaft 167 8 . 4 NoncircularCross Sections 169 8 . 5 Torsion Problems 172 chapter 9 Thick - walled pressure

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Page 166

T = T [ 1 - 4600 ] - To Ti = T

shafts of elastic - perfectly plastic material . Comparison between

hollow shaft ri = r . / 3 . 30 ' is so for the hollow shaft . 8 3gY Unloading from the

limit ...

T = T [ 1 - 4600 ] - To Ti = T

**solid**T hollow Fig . 8 . 7 Torque - twist curves forshafts of elastic - perfectly plastic material . Comparison between

**solid**shaft andhollow shaft ri = r . / 3 . 30 ' is so for the hollow shaft . 8 3gY Unloading from the

limit ...

Page 167

8.3 / INDEPENDENT DERIVATION FOR

some advantage to beginning all over again and deriving the results for a

thick - walled circular shaft without the prior consideration of the assemblage of ...

8.3 / INDEPENDENT DERIVATION FOR

**SOLID**CIRCULAR SHAFT There issome advantage to beginning all over again and deriving the results for a

**solid**orthick - walled circular shaft without the prior consideration of the assemblage of ...

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actual addition angle answer applied assemblage axes axial axis beam behavior bending circle circular column combined compatibility components compression compressive stress Consider constant creep cross section curve cylinder deflection deformation determined diameter direction displacement effect elastic equal equation equilibrium example Figure Find force given gives homogeneous idealization increase initial interior isotropic length limit linear linear-elastic load material maximum Maxwell modulus moment needed nonlinear normal obtained outer plane plastic positive pressure principal Prob problem produced pure radius range ratio relation replaced requires residual response result rotation shaft shear stress shell shown shows simple sketch solid solution steel strain stress-strain relations structural Suppose surface symmetry temperature tensile tension thickness thin-walled torsion tube twisting uniform unloading versus viscous yield zero