Contents vii 4.9 "Middle-quarter"and "middle-third"rules 76 4.10 Shear stresses owing to bending 77 4.11 Strain energy in bending 78 4.12 Limitations of the simple bending theory 78 Examples 79 Problems 88 5 Slope and Deflection of Beams 92 Summary Introduction 9 5.1 Relationship between loading,S.F.,B.M.,slope and deflection 94 5.2 Direct integration method 97 5.3 Macaulay's method 102 5.4 Macaulay's method for u.d.I's 105 5.5 Macaulay's method for beams with u.d.1.applied over part of the beam 106 5.6 Macaulay's method for couple applied at a point 106 5.7 Mohr's "area-moment"method 108 5.8 Principle of superposition 112 5.9 Energy method 112 5.10 Maxwell's theorem of reciprocal displacements 112 5.11 Continuous beams-Clapeyron's "three-moment"equation 115 5.12 Finite difference method 118 5.13 Deflections due to temperature effects 119 Examples 123 Problems 138 6 Built-in Beams 140 Summary 140 Introduction 141 6.1 Built-in beam carrying central concentrated load 141 6.2 Built-in beam carrying uniformly distributed load across the span 142 6.3 Built-in beam carrying concentrated load offset from the centre 143 6.4 Built-in beam carrying a non-uniform distributed load 145 6.5 Advantages and disadvantages of built-in beams 146 6.6 Effect of movement of supports 146 Examples 147 Problems 152Contents vii 4.9 4.10 Shear stresses owing to bending 4.1 1 Strain energy in bending 4.12 Limitations of the simple bending theory “Middle-quarter ” and “middle-third ” rules Examples Problems 5 Slope and Deflection of Beams Summary Introduction 5.1 5.2 Direct integration method 5.3 MacaulayS method 5.4 Macaulay’s method for u.d.ls 5.5 Macaulay’s method for beams with u.d.1. applied over part of the beam 5.6 Macaulay’s method for couple applied at a point 5.7 Mohr’s “area-moment” method 5.8 Principle of superposition 5.9 Energy method 5.10 Maxwell’s theorem of reciprocal displacements 5.1 1 Continuous beams - CIapeyron’s “three-moment ” equation 5.12 Finite difference method 5.13 Defections due to temperature effects Relationship between loading, S.F., B.M., slope and akfection Examples Problems 6 Built-in Beams Summary Introduction 6.1 Built-in beam carrying central concentrated load 6.2 Built-in beam carrying uniformly distributed load across the span 6.3 Built-in beam carrying concentrated load offset from the centre 6.4 Built-in beam carrying a non-uniform distributed load 6.5 Advantages and disadvantages of built-in beams 6.6 Effect of movement of supports Examples Problems 76 77 78 78 79 88 92 92 94 94 97 102 105 106 106 108 112 112 112 115 118 119 123 138 140 140 141 141 142 143 145 146 146 147 152