Items related to Intermediate Mechanics of Materials
Synopsis
Introduction.- 1.1 The Engineering design process;1.2 Design optimization;1.2.1 Predicting the behaviour of the component.- 1.2.2 Approximate solutions.- 1.3 Relative magnitude of different effects.- 1.4 Formulating and solving problems.- 1.4.1 Use of procedures.- 1.4.2 Inverse problems.- 1.4.3 Physical uniqueness and existence arguments.- 1.5 Review of elementary mechanics of materials.- 1.5.1 Definition of stress components.- 1.5.2 Transformation of stress components.- 1.5.3 Displacement and strain.- 1.5.4 Hooke's law.- 1.5.5 Bending of beams.- 1.5.6 Torsion of circular bars.- 1.6 Summary.- Problems.- 2 Material Behaviour and Failure.- 2.1 Transformation of stresses.- 2.1.1 Review of two-dimensional results.- 2.1.2 Principal stresses in three dimensions.- 2.2 Failure theories for isotropic materials.- 2.2.1 The failure surface.- 2.2.2 The shape of the failure envelope.- 2.2.3 Ductile failure (yielding).- 2.2.4 Brittle failure.- 2.3 Cyclic loading and fatigue.- 2.3.1 Experimental data.- 2.3.2 Statistics and the size effect.- 2.3.3 Factors influencing the design stress.- 2.3.4 Effect of combined stresses.- 2.3.5 Effect of a superposed mean stress.- 2.3.6 Summary of the design process.- 2.4 Summary.- Problems.- 3 Energy Methods.- 3.1 Work done on loading and unloading.- 3.2 Strain energy.- 3.3 Load-displacement relations.- 3.3.1 Beams with continuously varying bending moments.- 3.3.2 Axial loading and torsion.- 3.3.3 Combined loading.- 3.3.4 More general expressions for strain energy.- 3.3.5 Strain energy associated with shear forces in beams.- 3.4 Potential energy.- 3.5 The principle of stationary potential energy.- 3.5.1 Potential energy due to an external force.- 3.5.2 Problems with several degrees of freedom.- 3.5.3 Non-linear problems.- 3.6 The Rayleigh-Ritz method.- 3.6.1 Improving the accuracy.- 3.6.2 Improving the back of the envelope approximation.- 3.7 Castigliano's first theorem.- 3.8 Linear elastic systems.- 3.8.1 Strain energy.- 3.8.2 Bounds on the coefficients.- 3.8.3 Use of the reciprocal theorem.- 3.9 The stiffness matrix.- 3.9.1 Structures consisting of beams.- 3.9.2 Assembly of the stiffness matrix.- 3.10 Castigliano's second theorem.- 3.10.1 Use of the theorem.- 3.10.2 Dummy loads.- 3.10.3 Unit load method.- 3.10.4 Formal procedure for using Castigliano's second theorem.- 3.10.5 Statically indeterminate problems.- 3.10.6 Three-dimensional problems.- 3.11 Summary.- Problems.- 4 Unsymmetrical Bending.- 4.1 Stress distribution in bending.- 4.1.1 Bending about the x-axis only.- 4.1.2 Bending about the y-axis only.- 4.1.3 Generalized bending.- 4.1.4 Force resultants.- 4.1.5 Uncoupled problems.- 4.1.6 Coupled problems.- 4.2 Displacements of the beam.- 4.3 Second moments of area.- 4.3.1 Finding the centroid.- 4.3.2 The parallel axis theorem.- 4.3.3 Thin-walled sections.- 4.4 Further properties of second moments.- 4.4.1 Coordinate transformation.- 4.4.2 Mohr's circle of second moments.- 4.4.3 Solution of unsymmetrical bending problems in principal coordinates.- 4.4.4 Design estimates for the behaviour of unsymmetrical sections.- 4.4.5 Errors due to misalignment.- 4.5 Summary.- Problems.- 5 Non-linear and Elastic-Plastic Bending.- 5.1 Kinematics of bending.- 5.2 Elastic-plastic constitutive behaviour.- 5.2.1 Unloading and reloading.- 5.2.2 Yield during reversed loading.- 5.2.3 Elastic-perfectly plastic material.- 5.3 Stress fields in non-linear and inelastic bending.- 5.3.1 Force and moment resultants.- 5.4 Pure bending about an axis of symmetry.- 5.4.1 Symmetric problems for elastic-perfectly plastic materials.- 5.4.2 Fully plastic moment and shape factor.- 5.5 Bending of a symmetric section about an orthogonal axis.- 5.5.1 The fully plastic case.- 5.5.2 Non-zero axial force.- 5.5.3 The partially plastic solution.- 5.6 Unsymmetrical plastic bending.- 5.7 Unloading, springback and residual stress.- 5.7.1 Springback and residual curvature.- 5.7.2 Reloading and s
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