## Introduction to mechanics of deformable solids |

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Page 177

The equations of equilibrium, the conditions of deformation or

the stress-strain relations must be written down and used simultaneously in

general. Equilibrium has been considered already (9.1:3, 4) so that

...

The equations of equilibrium, the conditions of deformation or

**compatibility**, andthe stress-strain relations must be written down and used simultaneously in

general. Equilibrium has been considered already (9.1:3, 4) so that

**compatibility**...

Page 179

... gives the equation of equilibrium, (avg<r6)2irr Ar = (<t> + Ao>)ir(r + Ar)2 — <r,

irr2 = A(arirr2) or, in the limit as Ar — > 0, 4- (<rrrJ) = 2«,r (9.1:13) or This relation,

of course, is Eq. (9.1 :4) with the substitution of <rr for —p.

...

... gives the equation of equilibrium, (avg<r6)2irr Ar = (<t> + Ao>)ir(r + Ar)2 — <r,

irr2 = A(arirr2) or, in the limit as Ar — > 0, 4- (<rrrJ) = 2«,r (9.1:13) or This relation,

of course, is Eq. (9.1 :4) with the substitution of <rr for —p.

**Compatibility**of strains...

Page 202

Suppose that a particular set of values e', de' /dt, a', da' /dt, M', dM' /dt, . . . satisfies

equilibrium,

loading of a body and that another solution for the same body under a different ...

Suppose that a particular set of values e', de' /dt, a', da' /dt, M', dM' /dt, . . . satisfies

equilibrium,

**compatibility**, and the stress-strain relations everywhere for oneloading of a body and that another solution for the same body under a different ...

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angle applied assemblage axial force beam behavior cantilever centroid circumferential column compatibility components of stress constant creep cross section cylinder dashpot deflection diameter direction displacement elastic-perfectly plastic elongation equation of virtual equations of equilibrium factor of safety free-body sketch homogeneous idealization increase inelastic initial interior pressure isotropic Kelvin Kelvin material limit linear Maxwell linear-elastic response linear-viscoelastic linear-viscous load maximum Maxwell material modulus Mohr's circle neutral axis nonlinear nonlinear-viscous normal stress outer perfectly plastic perpendicular plane plastic deformation plastic-limit principal stresses Prob problem pure bending radial radius ratio rotation shaft shear center shear strain shear stress shell shown in Fig simple shear solution statically statically determinate steel strain rate stress and strain stress-strain curve stress-strain relations Suppose surface symmetry temperature tensile stress thick-walled thickness time-dependent torsion twisting uniform unloading versus viscous yield curve yield stress zero