Mechanics of Optimal Structural Design

David Rees, Brunel University, UK, is a senior lecturer in the School of Engineering and Design at Brunel University. He has published four books on solid mechanics and structures Basic Engineering Plasticity (Elsevier, 2006); Mechanics of Solids and Structures (World Scientific I.C. Press, 2000); and Basic Solid Mechanics (Macmillan, 1997) as well as over 100 journal papers in the fields of plasticity, creep, fatigue, fracture and engineering design. His research covers the fields of multi-axial plasticity and creep, cyclic deformation and interactions between creep and fatigue, autofrettage and buckling of cylinders and discs and sheet metal formability.

"The usual formulation is strength-to-weight ratio, but Rees (engineering and design, Brunel U.) points out that the goal is to reduce weight without reducing strength, not vice versa, so a better expression would be the weight-to-strength ratio, and that is what he explores." (Book News, December 2009)

• Preface xiGlossary of Terms xvKey Symbols xixChapter 1 Compression of Slender Struts 11.1 Introduction 11.2 Failure Criteria 11.3 Solid Cross-Sections 31.4 Thin-Walled, Tubular Sections 61.5 Thin-Walled, Open Sections 131.6 Summary of Results 24References 25Exercises 25Chapter 2 Compression of Wide Struts 292.1 Introduction 292.2 Failure Criteria 292.3 Cellular Sections 312.4 Open Sections 372.5 Corrugated Sandwich Panel 572.6 Summary of Results 60References 61Exercise 61Chapter 3 Bending of Slender Beams 653.1 Introduction 653.2 Solid Cross-Sections 663.3 Thin-Walled, Tubular Sections 693.4 Open Sections 763.5 Summary of Results 88References 89Exercises 89Chapter 4 Torsion of Bars and Tubes 914.1 Introduction 914.2 Solid Cross-Sections 924.3 Thin-Walled, Open Sections 994.4 Thin-Walled, Closed Tubes 1094.5 Multi-Cell Tubes 121References 130Exercises 130Chapter 5 Shear of Solid Bars, Tubes and Thin Sections 1355.1 Introduction 1355.2 Bars of Solid Section 1365.3 Thin-Walled Open Sections 1435.4 Thin-Walled, Closed Tubes 1595.5 Concluding Remarks 170References 171Exercise 171Chapter 6 Combined Shear and Torsion in Thin-Walled Sections 1736.1 Introduction 1736.2 Thin-Walled, Open Sections 1736.3 Thin-Walled, Closed Tubes 1776.4 Concluding Remarks 189References 190Exercises 190Chapter 7 Combined Shear and Bending in Idealised Sections 1937.1 Introduction 1937.2 Idealised Beam Sections 1937.3 Idealised Open Sections 2017.4 Idealised Closed Tubes 210References 221Exercises 221Chapter 8 Shear in Stiffened Webs 2238.1 Introduction 2238.2 Castellations in Shear 2238.3 Corrugated Web 2268.4 Flat Web with Stiffeners 231References 237Exercises 237Chapter 9 Frame Assemblies 2399.1 Introduction 2399.2 Double-Strut Assembly 2399.3 Multiple-Strut Assembly 2449.4 Cantilevered Framework 2479.5 Tetrahedron Framework 2539.6 Cantilever Frame with Two Struts 2569.7 Cantilever Frame with One Strut 259References 264Exercises 264Chapter 10 Simply Supported Beams and Cantilevers 26510.1 Introduction 26510.2 Variable Bending Moments 26510.3 Cantilever with End-Load 27110.4 Cantilever with Distributed Loading 28110.5 Simply Supported Beam with Central Load 29210.6 Simply Supported Beam with Uniformly Distributed Load 30310.7 Additional Failure Criteria 316References 322Exercises 323Chapter 11 Optimum Cross-Sections for Beams 32511.1 Introduction 32511.2 Approaching Optimum Sections 32611.3 Generalised Optimum Sections 32811.4 Optimum Section, Combined Bending and Shear 33011.5 Solid, Axisymmetric Sections 33111.6 Fully Optimised Section 34111.7 Fully Optimised Weight 34511.8 Summary 355References 356Exercises 356Chapter 12 Structures under Combined Loading 35712.1 Introduction 35712.2 Combined Bending and Torsion 35712.3 Cranked Cantilever 35912.4 Cranked Strut with End-Load 36212.5 Cranked Bracket with End-Load 36512.6 Portal Frame with Central Load 36812.7 Cantilever with End and Distributed Loading 37112.8 Centrally Propped Cantilever with End-Load 37712.9 End-Propped Cantilever with Distributed Load 38512.10 Simply Supported Beam with Central-Concentrated and Distributed Loadings 39012.11 Centrally Propped, Simply Supported Beam with Distributed Load 395References 400Exercises 400Chapter 13 Encastré Beams 40313.1 Introduction 40313.2 Central-Concentrated Load 40313.3 Uniformly Distributed Load 41813.4 Combined Loads 437References 463Exercises 463Chapter 14 Plastic Collapse of Beams and Frames 46514.1 Introduction 46514.2 Plane Frames 46614.3 Beam Plasticity 46814.4 Collapse of Simple Beams 47414.5 Encastré Beams 47814.6 Continuous Beams 48114.7 Portal Frames 48614.8 Effect of Axial Loading upon Collapse 49714.9 Effect of Shear Force upon Collapse 50014.10 Effect of Hardening upon Collapse 505References 507Exercises 507Chapter 15 Dynamic Programming 51115.1 Introduction 51115.2 Single-Span Beam 51115.3 Two-Span Beam 51315.4 Three-Span Beam 51515.5 Design Space 517Reference 520Exercises 520Appendix A Mechanical Properties 521A. 1 Non-Metals 521A. 2 Metals and Alloys 522References 524Appendix B Plate Buckling Under Uniaxial Compression 525B. 1 Wide and Slender Struts 525B. 2 Plates with Supported Sides 527B. 3 Inelastic Buckling 530B. 4 Post-Buckling 533References 534Appendix C Plate Buckling Under Biaxial Compression and Shear 537C. 1 Biaxial Compression 537C. 2 Pure Shear 539C.3 Inelastic Shear Buckling 541References 541Appendix D Secondary Buckling 543D. 1 Buckling Modes 543D. 2 Local Compressive Buckling 544D. 3 Global Buckling 545D. 4 Local Shear Buckling 547References 547Bibliography 549Index 553