CONTENTS Introduction XV Notation Unsymmetrical Bending 1 Summary 1 Introduction 2 1.1 Product second moment of area 3 1.2 Principal second moments of area 1.3 Mohr's circle of second moments of area 6 1.4 Land's circle of second moments of area > 15 Rotation of axes:determination of moments of area in terms of the principal values 1.6 The ellipse of second moments of area 9 1.7 Momental ellipse 11 1.8 Stress determination 11 1.9 Alternative procedure for stress determination 11 1.10 Alternative procedure using the momental ellipse 13 1.11 Defections 15 Examples 16 Problems 24 Struts 28 Summary Introduction 2.1 Euler's theory 2301 2.2 Equivalent strut length 2.3 Comparison of Euler theory with experimental results 36 2.4 Euler "validity limit" 37 2.5 Rankine or Rankine-Gordon formula 2.6 Perry-Robertson formula 39 2.7 British Standard procedure (BS 449) 2.8 Struts with initial curvature 2.9 Struts with eccentric load 44126 2.10 Laterally loaded struts 2.11 Alternative procedure for any strut-loading condition 西CONTENTS Introduction xv Notation xvii 1 Unsymmetrical Bending 1 Summary Introduction I .1 1.2 1.3 1.4 1.5 I .6 1.7 Momenta1 ellipse 1.8 Stress determination 1.9 Alternative procedure for stress determination 1.10 Alternative procedure using the momenta1 ellipse 1.1 1 Dejections Examples Problems Product second moment of area Principal second moments of area Mohr’s circle of second moments of area Land’s circle of second moments of area Rotation of axes: determination of moments of area in terms of the principal values The ellipse of second moments of area 2 Struts Summary Introduction 2.1 Euler’s theory 2.2 Equivalent strut length 2.3 2.4 Euler “validity limit” 2.5 Rankine or Rankine-Gordon formula 2.6 Perry- Robertson formula 2.7 2.8 Struts with initial curvature 2.9 Struts with eccentric load 2.10 Laterally loaded struts 2.1 1 Comparison of Euler theory with experimental results British Standard procedure (BS 449) Alternative procedure for any strut-loading condition 8 9 11 11 11 13 15 16 24 28 28 30 31 35 36 37 38 39 41 41 42 46 48 V