vi Contents 2.2 Compound bars-"equivalent"or "combined"modulus 29 2.3 Compound bars subjected to temperature change 30 2.4 Compound bar (tube and rod) 32 2.5 Compound bars subjected to external load and temperature effects 34 2.6 Compound thick cylinders subjected to temperature changes 34 Examples 4 Problems 3 Shearing Force and Bending Moment Diagrams 41 Summary 41 3.1 Shearing force and bending moment 41 3.1.1 Shearing force (S.F.)sign convention 42 3.1.2 Bending moment (B.M.)sign convention 42 3.2 S.F.and B.M.diagrams for beams carrying concentrated loads only 43 3.3 S.F.and B.M.diagrams for uniformly distributed loads 46 3.4 S.F.and B.M.diagrams for combined concentrated and uniformly distributed loads 47 3.5 Points of contraflexure 48 3.6 Relationship between S.F.O,B.M.M,and intensity of loading w 49 3.7 S.F.and B.M.diagrams for an applied couple or moment 50 3.8 S.F.and B.M.diagrams for inclined loads 52 3.9 Graphical construction of S.F.and B.M.diagrams 54 3.10 S.F.and B.M.diagrams for beams carrying distributed loads of increasing value 55 3.11 S.F.at points of application of concentrated loads 55 Examples 56 Problems 59 4 Bending 62 Summary 62 Introduction 63 4.1 Simple bending theory 64 4.2 Neutral axis 66 4.3 Section modulus 68 4.4 Second moment of area 68 4.5 Bending of composite or flitched beams 70 4.6 Reinforced concrete beams-simple tension reinforcement 71 4.7 Skew loading 73 4.8 Combined bending and direct stress-eccentric loading 74vi Contents 2.2 Compound bars - ‘<equivalent ” or “combined” modulus 2.3 Compound bars subjected to temperature change 2.4 Compound bar (tube and rod) 2.5 Compound bars subjected to external load and temperature effects 2.6 Compound thick cylinders subjected to temperature changes Examples Problems 3 Shearing Force and Bending Moment Diagrams Summary 3.1 Shearing force and bending moment 3.1.1 Shearing force (S.F.) sign convention 3.1.2 Bending moment (B.M.) sign convention 3.2 S.F. and B.M. diagrams for beams carrying concentrated loads only 3.3 S.F. and B.M. diagrams for uniformly distributed loads 3.4 S.F. and B.M. diagrams for combined concentrated and uniformly distributed loads 3.5 Points of contrafexure 3.6 Relationship between S.F. Q, B.M. M, and intensity of loading w 3.1 S.F. and B.M. diagrams for an applied couple or moment 3.8 S.F. and B.M. diagrams for inclined loa& 3.9 Graphical construction of S.F. and B.M. diagrams 3.10 S.F. and B.M. diagrams for beams carrying distributed loads of increasing value 3.1 1 S.F. at points of application of concentrated loads Examples Problems 4 Bending Summary Introduction 4.1 Simple bending theory 4.2 Neutral axis 4.3 Section modulus 4.4 Second moment of area 4.5 4.6 4.1 Skew loading 4.8 Bending of composite or fitched beams Reinforced concrete beams -simple tension reinforcement Combined bending and direct stress -eccentric loading 29 30 32 34 34 34 39 41 41 41 42 42 43 46 47 48 49 50 52 54 55 55 56 59 62 62 63 64 66 68 68 70 71 73 74