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This is the first of two volumes introducing structural and continuum mechanics in a comprehensive and consistent way. The current book, Volume 1: Equilibrium, presents all theoretical developments both in text and by means of an extensive set of figures. This same approach is used in the examples and problems, of which a generous amount have been provided to aid understanding and practice.
The book consists of distinct modules, each divided into sections which are conveniently sized to be used as lectures. Both formal and intuitive (engineering) arguments are used in parallel to derive the principles used, for instance in bending moment diagrams and shear force diagrams. A very important aspect of this book is the straightforward and consistent sign convention, based on the stress definitions of continuum mechanics.
This method has been tried and tested over a number of years, and has been used for introductory courses at Delft University of Technology in the faculties of Civil Engineering, Aeronautical Engineering, Industrial Design and Architectural Engineering.
Preface; Foreword; 1. Introduction: 1.1 Mechanics; 1.2 Quantities, units, dimensions; 1.3 Vectors; 1.4 Newton's Laws; 2. Statics of a Particle: 2.1 Coplanar forces; 2.2 Forces in space; 2.3 Equilibrium of a particle; 2.4 Problems; 3 Statics of a Rigid Body: 3.1 Coplanar forces and moments; 3.2 Equilibrium of a rigid body in a plane; 3.3 Forces and moments in space; 3.4 Equilibrium of a rigid body in space; 3.5 Problems; 4. Structures: 4.1 Structural elements; 4.2 Joints between structural elements; 4.3 Supports; 4.4 Planar structures; 4.5 Kinematic/static (in)determininate structures; 4.6 Problems; 5. Calculating Support Reactions and Interaction Forces: 5.1 Self contained structures; 5.2 Hinged beams; 5.3 Three-hinged frames; 5.4 Three-hinged frames with tie-rod; 5.5 Shored structures; 5.6 Trussed beams; 5.7 Strengthened beams; 5.8 Problems; 6. Loads: 6.1 Loads in mechanics; 6.2 Loads in regulations; 6.3 Working with distributed loads; 6.4 Modelling load flow; 6.5 Stress concept; normal stress and shear stress; 6.6 Problems; 7. Gas Pressure and Hydrostatic Pressure: 7.1 Pascal's law -- All-round pressure; 7.2 Working with gas pressures; 7.3 Working with hydrostatic pressures; 7.4 Summary; 7.5 Problems; 8. Earth Pressures: 8.1 Stresses in soil; 8.2 Vertical earth pressures; 8.3 Horizontal earth pressures; Appendix 8.1; Appendix 8.2; 8.4 Problems; 9. Trusses: 9.1 Plane Trusses; 9.2 Kinematically/statically (in)determinate trusses; 9.3 Determining member forces; 9.4 Problems; 10. Section Forces: 10.1 Force flow in a member; 10.2 Diagrams for the normal force, shear force and bending moment; 10.3 Deformation symbols for shear forces and bending moments; 10.4 Summary sign conventions for the N, V and M diagrams; 10.5 Problems; 11. Mathematical Description of the Relationship between Section Forces and Loading: 11.1 Differential equations for the equilibrium; 11.2 Mathematical elaboration of the relationship between N and qx(extention); 11.3 Mathematical elaboration of the relationship between M, V and qz (bending); 11. 4 Problems; 12. Bending Moment, Shear Force and Normal Force Diagrams: 12.1 Rules for drawing V and M diagrams more quickly; 12.2 Rules for drawing the N diagram more quickly; 12.3 Bent and compound bar type structures; 12.4 Principle of superposition; 12.5 Schematisations and reality; 12.6 Problems; 13. Calculating M, V and N Diagrams: 13.1 Self-contained structures; 13.2 Compound and associated structures; 13.3 Statically indeterminate structures; 13.4 Problems; 14. Cables, 14.2 Centre of force and line of force; 14.3 Relationship between cable, line of force and structural shape; 14.4 Problems; 15. Virtual work: 15.1 Work and strain energy; 15.2 Virtual work equation for a particle; 15.3 Virtual work equation for a rigid body; 15.4 Virtual work equation for mechanisms; 15.5 Calculating forces using virtual work; 15.6 Problems; 16. Influence Lines: 16.1 Influence lines using equilibrium equations; 16.2 Influence lines using virtual work; 16.3 Working with influence lines; 16.4 Problems.