Part 1 Statics and strength of materials 1 1 The effects of forces on materials 1 1.1 Introduction 1 1.2 Tensile force 2 1.3 Compressive force 2 1.4 Shear force 2 1.5 Stress 2 1.6 Strain 3 1.7 Elasticity, limit of proportionality and elastic limit 6 1.8 Hooke’s law 7 1.9 Ductility, brittleness and malleability 11 1.10 Modulus of rigidity 12 1.11 Thermal strain 12 1.12 Compound bars 13 2 Tensile testing 18 2.1 The tensile test 18 2.2 Worked problems on tensile testing 19 2.3 Further worked problems on tensile testing 21 3 Forces acting at a point 25 3.1 Scalar and vector quantities 25 3.2 Centre of gravity and equilibrium 25 3.3 Forces 26 3.4 The resultant of two coplanar forces 27 3.5 Triangle of forces method 28 3.6 The parallelogram of forces method 29 3.7 Resultant of coplanar forces by calculation 29 3.8 Resultant of more than two coplanar forces 30 3.9 Coplanar forces in equilibrium 32 3.10 Resolution of forces 34 3.11 Summary 37 4 Forces in structures 40 4.1 Introduction 40 4.2 Worked problems on mechanisms and pin-jointed trusses 41 4.3 Graphical method 42 4.4 Method of joints (a mathematical method) 46 4.5 The method of sections (a mathematical method) 52 Assignment 1 55 5 Simply supported beams 57 5.1 The moment of a force 57 5.2 Equilibrium and the principle of moments 58 5.3 Simply supported beams having point loads 61 5.4 Simply supported beams with couples 64 6 Bending moment and shear force diagrams 69 6.1 Introduction 69 6.2 Bending moment (M) 69 6.3 Shearing force (F) 69 6.4 Worked problems on bending moment and shearing force diagrams 70 6.5 Uniformly distributed loads 78 7 First and second moment of areas 84 7.1 Centroids 84 7.2 The first moment of area 84 7.3 Centroid of area between a curve and the x-axis 84 7.4 Centroid of area between a curve and the y-axis 85 7.5 Worked problems on centroids of simple shapes 86