## Introduction to mechanics of deformable solids |

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Page 231

The orientation of the principal planes is given by the angle a, tan 2a = 27 (11.2:

13) (Tx — <Ty The angle a between the x and the 1

counterclockwise angle 2a on the circle from the point corresponding to the plane

on which ...

The orientation of the principal planes is given by the angle a, tan 2a = 27 (11.2:

13) (Tx — <Ty The angle a between the x and the 1

**direction**is half thecounterclockwise angle 2a on the circle from the point corresponding to the plane

on which ...

Page 233

<?i — trz <ri — 0 t?i 0 — <7j — g3 |<ri| (a)rm« = — ^- or (6) — = -or (c) — - — - y

The

approximately by inspection. As illustrated by the square element of Fig. 11.15a,

if ax > ay, the ...

<?i — trz <ri — 0 t?i 0 — <7j — g3 |<ri| (a)rm« = — ^- or (6) — = -or (c) — - — - y

The

**direction**of ai and the plane on which it acts can be determinedapproximately by inspection. As illustrated by the square element of Fig. 11.15a,

if ax > ay, the ...

Page 240

Similarly, from summation of forces in the

and summation convention, Tn. = <Tijknlj. (11.4:11) where the s

inclined plane (Fig. 11.22). However, Eq. (11.4:11) applies to the component of ...

Similarly, from summation of forces in the

**direction**of rn,A, with the same notationand summation convention, Tn. = <Tijknlj. (11.4:11) where the s

**direction**is in theinclined plane (Fig. 11.22). However, Eq. (11.4:11) applies to the component of ...

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applied assemblage axial force beam behavior centroid circumferential column compatibility components of stress conditions of deformation constant creep cross section cylinder deflection diameter direction displacement elastic-perfectly plastic elongation equations of equilibrium factor of safety free-body sketch fully plastic 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 Poisson's ratio principal stresses Prob problem pure bending radial radius ratio rectangular residual stress rigid end plates rotation shaft shear strain shear stress shell simple shear solution statically statically determinate steel stress and strain stress-strain curve stress-strain relations Suppose surface symmetry temperature tensile stress thick-walled sphere thickness time-dependent torque torsion uniform unloading versus viscous yield curve yield stress zero