Engineering Mechanics

Preface; Foreword; 1 Material Behaviour; 1.1 Tensile test; 1.2 Stress-strain diagrams; 1.3 Hooke's Law; 2 Bar Subject to Extension; 2.1 The fibre model; 2.2 The three basic relationships; 2.3 Strain diagram and normal stress diagram; 2.4 Normal centre and bar axis; 2.5 Mathematical description of the extension problem; 2.6 Examples relating to change in length and displacement; 2.7 Examples relating to the differential equation for extension; 2.8 Formal approach and engineering practice; 2.9 Problems; 3 Cross-Sectional Properties; 3.1 First moments of area; centroid and normal centre; 3.2 Second moments of area; 3.3 Thin-walled cross-sections; 3.4 Formal approach and engineering practice; 3.5 Problems; 4 Members Subject to Bending and Extension; 4.1 The fibre model; 4.2 Strain diagram and neutral axis; 4.3 The three basic relationships; 4.4 Stress formula and stress diagram; 4.5 Examples relating to the stress formula for bending with extension; 4.6 Section modulus; 4.7 Examples of the stress formula related to bending without extension; 4.8 General stress formula related to the principal directions; 4.9 Core of the cross-section; 4.10 Applications related to the core of the cross-section; 4.11 Mathematical description of the problem of bending with extension; 4.12 Thermal effects; 4.13 Notes for the fibre model and summary of the formulas; 4.14 Problems; 5 Shear Forces and Shear Stresses Due to Bending; 5.1 Shear forces and shear stresses in longitudinal direction; 5.2 Examples relating to shear forces and shear stresses in the longitudinal direction; 5.3 Shear stresses on a cross-sectional plane; 5.4 Examples relating to the shear stress distribution in a cross-section; 5.5 Shear centre; 5.6 Other cases of shear; 5.7 Summary of the formulas and rules; 5.8 Problems; 6 Bar Subject to Torsion; 6.1 Material behaviour in shear; 6.2 Torsion of bars with circular cross-section; 6.3 Torsion of thin-walled cross-sections; 6.4 Numerical examples; 6.5 Summary of theformulas; 6.6 Problems; 7 Deformation of Trusses; 7.1 The behaviour of a single truss member; 7.2 Williot diagram; 7.3 Williot diagram with rigid-body rotation; 7.4 Williot-Mohr diagram; 7.5 Problems; 8 Deformation Due to Bending; 8.1 Direct determination from the moment distribution; 8.2 Differential equation for bending; 8.3 Forget-me-nots; 8.4 Moment area theorems; 8.5 Simply supported beams and the M/EI diagram; 8.6 Problems; 9 Unsymmetrical and Inhomogeneous Cross-Sections; 9.1 Sketch of the problems and required assumptions; 9.2 Kinematic relationships; 9.3 Curvature and neutral axis; 9.4 Normal force and bending moments - centre of force; 9.5 Constitutive relationships for unsymmetrical and/or inhomogeneous cross-sections; 9.6 Plane of loading and plane of curvature - neutral axis; 9.7 The normal centre NC for inhomogeneous cross-sections; 9.8 Stresses due to extension and bending - a straightforward method; 9.9 Applications of the straightforward method; 9.10 Stresses in the principal coordinate method - alternative method; 9.11 Transformation formulae for the bending stiffness tensor; 9.12 Application of the alternative method based on the principal directions; 9.13 Displacements due to bending; 9.14 Maxwell's reciprocal theorem; 9.15 Core of a cross-section; 9.16 Thermal effects; 9.17 Shear flow and shear stresses in arbitrary cross-sections; 9.18 Problems; Index.