A Treatise on the Mathematical Theory of Elasticity, المجلد 2University Press, 1893 An indispensable reference work for engineers, mathematicians, and physicists, this book is the most complete and authoritative treatment of classical elasticity in a single volume. Beginning with elementary notions of extension, simple shear and homogeneous strain, the analysis rapidly undertakes a development of types of strain, displacements corresponding to a given strain, cubical dilatation, composition of strains and a general theory of strains. A detailed analysis of stress including the stress quadric and uniformly varying stress leads into an exposition of the elasticity of solid bodies. Based upon the work-energy concept, experimental results are examined and the significance of elastic constants in general theory considered. Hooke's Law, elastic constants, methods of determining stress, thermo-elastic equations, and other topics are carefully discussed. --Back cover. |
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الصفحة viii
... TWISTING OF RODS OR WIRES IN THREE DIMENSIONS . Arts . 232-248 . Kinematics . Twist . General equations . Stress - couples . Kirchhoff's Kinetic Analogue . Case of terminal couples . Wire of equal flexi- bility in all planes through its ...
... TWISTING OF RODS OR WIRES IN THREE DIMENSIONS . Arts . 232-248 . Kinematics . Twist . General equations . Stress - couples . Kirchhoff's Kinetic Analogue . Case of terminal couples . Wire of equal flexi- bility in all planes through its ...
الصفحة ix
... twist . Equations of equilibrium and small motion . Equilibrium of circular wire bent in its plane . Circular wire bent perpendicularly to its plane . Vibrations of circular wire . Flexural vibrations in plane of wire . Flexural ...
... twist . Equations of equilibrium and small motion . Equilibrium of circular wire bent in its plane . Circular wire bent perpendicularly to its plane . Vibrations of circular wire . Flexural vibrations in plane of wire . Flexural ...
الصفحة xi
... Twisted shaft . Shaft under thrust and twisting couple . Ring under pressure . Rectangular plate under edge - thrust . Circular plate . Infinite strip of finite breadth . Stability and strength of boilers and boiler - flues . Infinite ...
... Twisted shaft . Shaft under thrust and twisting couple . Ring under pressure . Rectangular plate under edge - thrust . Circular plate . Infinite strip of finite breadth . Stability and strength of boilers and boiler - flues . Infinite ...
الصفحة xii
... twist ' . line 9 99 , for ( B - C ) read C. Additional Corrigenda in Vol . I. p . 74 , scheme of transformation , insert z ' in lowest left - hand compartment . p . 131 , line 10 from bottom , for 40 and 40 read 。 and 。. line 11 99 99 ...
... twist ' . line 9 99 , for ( B - C ) read C. Additional Corrigenda in Vol . I. p . 74 , scheme of transformation , insert z ' in lowest left - hand compartment . p . 131 , line 10 from bottom , for 40 and 40 read 。 and 。. line 11 99 99 ...
الصفحة 4
... twist or angular displacement of the sections of the rod about the tangent . The simple fact that the equation of moments of the Bernoulli - Eulerian theory only applies to flexure in a principal plane appears to have been first noticed ...
... twist or angular displacement of the sections of the rod about the tangent . The simple fact that the equation of moments of the Bernoulli - Eulerian theory only applies to flexure in a principal plane appears to have been first noticed ...
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angle approximation axis bending body boundary-conditions centre of inertia circular coefficients components compression const curve cylinder deflexion deformation differential equations direction-cosines displacements edge-line elastic central-line elastica element equations of equilibrium expression Ət² finite flexural couple flexural rigidity forces and couples formulæ functions G₁ G₂ given impact K₁ K₂ kinetic Kirchhoff's line-elements lines of curvature middle-surface modes N₁ normal section obtained order of approximation osculating plane P₁ P₂ parallel plane plate potential energy principal axes principal curvatures prism quantities radius referred shell shew shewn sin po small motion solution strained elastic central-line stress-couples stress-resultants stresses suppose surface tangent terminal theory thin rod twist U₁ U₂ unit length unstrained V₁ V₂ values vanish velocity wire Young's modulus θα ав дв дг ди ду дх მყ