## Engineering mechanics of materialsThis book provides the students of various engineering disciplines with a clear and understandable treatment of the concepts of Mechanics of Materials or Strength of Materials. This subject is concerned with the behavior of deformable bodies when subjected to axial, torsional and flexural loads as well as combinations thereof. It is a 3rd, updated edition of the popular undergraduate level textbook useful for students of mechanical, structural, civil, aeronautical and other engineering disciplines. The book is supplied with problems and a solution manual will be available from the authors. |

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Page 384

Fundamental concepts of the stability of

detail with the aid of a column model.

or neutral, depending upon whether the potential energy of the system is a ...

Fundamental concepts of the stability of

**equilibrium**are developed and studied indetail with the aid of a column model.

**Equilibrium**of a system is stable, unstable,or neutral, depending upon whether the potential energy of the system is a ...

Page 385

Stable

Relative minimum dU d6 de2' Relative maximum dO de2 <o U = constant 0 dU

de ' d2U J0: Minimum potential energy stable

energy ...

Stable

**equilibrium**77T -777- Unstable**equilibrium**(a) Neutral**equilibrium**0Relative minimum dU d6 de2' Relative maximum dO de2 <o U = constant 0 dU

de ' d2U J0: Minimum potential energy stable

**equilibrium**Maximum potentialenergy ...

Page 391

In order to investigate the stability of

of the potential energy V with respect to the angle 6. d2U de2 = - Wb + 2kc2

Factor 2kc2 on the right-hand side of the preceding equation : d2U d92 -<^' Since

...

In order to investigate the stability of

**equilibrium**, write out the second derivativeof the potential energy V with respect to the angle 6. d2U de2 = - Wb + 2kc2

Factor 2kc2 on the right-hand side of the preceding equation : d2U d92 -<^' Since

...

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### Contents

Stress Strain and Their Relationships | 60 |

Stresses and Strains in Axially Loaded Members | 121 |

Torsional Stresses Strains and Rotations | 159 |

Copyright | |

14 other sections not shown

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### Common terms and phrases

absolute maximum shear aluminum angle of twist applied Assume axial force axially loaded beam shown bending cantilever beam Castigliano's second theorem column compressive constant coordinate cross section cross-sectional area cylinder deflection deformation depicted in Fig elastic curve equal equation equilibrium Euler EXAMPLE factor of safety FIGURE flexural stress FORTRAN free-body diagram function given by Eq k-ft k-in kN-m lb/ft length longitudinal material maximum in-plane shear maximum shear stress modulus of elasticity Mohr's circle neutral axis normal stress obtained perpendicular plane stress condition plot positive principal centroidal axis principal strains principal stresses radius ratio reactions Refer to Fig respect rotation shear force shear strain shown in Fig simply supported beam slope SOLUTION Solve Problem statically indeterminate steel stress concentration stress element subjected torque torsional uniform load vertical yield strength yield stress zero