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Series : SOLID MECHANICS AND ITS APPLICATIONS

Plates and FEM, Ed. 1

Surprises and Pitfalls

¥ 8,402 (tax included)

Description

The book aims to be the bridge between commercially available FEM packages and consulting structural engineers. Elastic plate analysis results must be translated to economic cross-section dimensions and reinforcement ratios, which raises difficulties. This is becoming increasingly more important since easy-to-use powerful programs are offered, for which the average structural engineer is not well-equipped. To be clear, the book is not a text on Finite Element Method, but it supports structural engineers in handling output of such software.

Contents

Part 1 Theory of Plates;

1 Plate Membrane Theory ; 1.1 Introduction: Special Case of a Plate, the Truss; 1.2 Membrane Plate Problem Statement ; 1.2.1 Kinematic Equations ; 1.2.2 Constitutive Equations ; 1.2.3 Equilibrium Equations ; 1.2.4 The Displacement Method ; 1.3 Boundary Conditions ; 1.4 Message of the Chapter ;

2 Applications of the Plate Membrane Theory ; 2.1 Trial Solutions in the Form of Polynomials ; 2.1.1 Homogeneous Stress States ; 2.1.2 Constant BendingMoment in Beam; 2.1.3 Constant Shear Force in Beam; 2.2 Solution for aWall ; 2.2.1 Beam Intermezzo ; 2.2.2 Solution for theWall ; 2.2.3 Practical Application2.3 Stresses, Transformations and Principal Stresses ; 2.4 Other Applications ; 2.5 Message of the Chapter ;

3 Thick Plates in Bending and Shear ; 3.1 Introduction - Beam as Special Case ; 3.1.1 Illustration ; 3.1.2 Simplification for Slender Beam; 3.1.3 Suppositions of Timoshenko Beam in Hindsight ; 3.2 Outline of Thick Plates ; 3.2.1 Suppositions ; 3.3 Basic Equations ; 3.3.1 Kinematic Equations; 3.3.2 Constitutive Equations ; 3.3.3 Equilibrium Equations ; 3.4 Differential Equations for Thick Plates ; 3.5 Orthotropic Plate ; 3.6 Twisted Plate Strip ; 3.7 Message of the Chapter ;

4 Thin Plates in Bending ; 4.1 Theory for Thin Plates ; 4.2 Transformation Rules and PrincipalMoments; 4.3 Principal Shear Force ; 4.4 Boundary Conditions for Thin Plates ; 4.4.1 Clamped Edge ; 4.4.2 Simply-Supported Edge ; 4.4.3 Free Edge ; 4.4.4 Discontinuity in Thickness; 4.5 Message of the Chapter ;

5 Rectangular Plate Examples ; 5.1 Basic Bending Cases ; 5.1.1 Cylindrical Deflection; 5.1.2 Cylindrical Deflection of Arbitrary Shape ; 5.1.3 Omni-Directional Bending; 5.2 Torsion Panel ; 5.3 Two-Way Sine Load on Square Plate ; 5.3.1 Displacement ; 5.3.2 Moments and Shear Forces ; 5.3.3 Support Reactions ; 5.3.4 Stiff Edge Beams ; 5.4 Twist-Less Plate ; 5.5 Edge Load on Viaduct ; 5.6 Message of the Chapter ;

6 Circular Membrane Plates ; 6.1 Axisymmetric Circular Membrane Problems ; 6.1.1 Thick-Walled Tube ; 6.1.2 Circular Hole in a Homogeneous Stress State ; 6.1.3 Curved Beam Subjected to ConstantMoment ; 6.2 Non-Axisymmetric Circular Membrane Problems; 6.2.1 Point Load on a Half Plane ; 6.2.2 Brazilian Splitting Test ; 6.2.3 Hole in Plates with Shear and Uniaxial Stress ; 6.3 Message of the Chapter ;

7 Circular Thin Plates in Bending; 7.1 Derivation of the Differential Equation ; 7.2 Simply-Supported Circular Plate with Edge Moment ; 7.3 Clamped Circular Plate with Distributed Load ; 7.4 Simply-Supported Circular Plate with Distributed Load ; 7.5 Clamped Circular Plate with Point Load ; 7.6 Simply-Supported Circular Plate with Point Load ; 7.7 Circular Plate Part on Top of Column; 7.8 Message of the Chapter;

Part 2 Didactical Discrete Models;

8 Discrete Model for Membrane Analysis ; 8.1 TrussModel ; 8.2 Membrane PlateModel ; 8.2.1 Example. Deep Beam Subjected to OwnWeight ; 8.3 Message of the Chapter;

9 Discrete Model for Plate Bending ; 9.1 BeamModel ; 9.1.1 Example. Cantilever Beam ; 9.2 Plate BendingModel ; 9.2.1 Example 1. Rectangular Simply-Supported Plate ; 9.2.2 Example 2. Lift-Slab in Office Building ; 9.3 Didactical Model for Simply-Supported Plate ; 9.4 DiscreteModel for Plate on Flexible Edge Beams ; 9.5 Message of the Chapter ;

Part 3 FE-Based Design in Daily Practice

10 FEM Essentials ; 10.1 Elements and Degrees of Freedom ; 10.2 Stiffness Matrix and Constraints ; 10.3 Model Input ; 10.4 Output Selection ; 10.5 Message of the Chapter ;

11 Handling Membrane FEMResults; 11.1 Surprising Stresses ; 11.1.1 Effect of Poisson's Ratio ; 11.1.2 Effect of Kink in Beam Flange ; 11.2 Stress Singularities in FEM ; 11.3 FEM-Supported Strut-and-Tie Modeling ; 11.4 Re-entrant Corner ; 11.5 TallWall with Openings; 11.5.1 Modeling withMembrane Elements; 11.5.2 Modeling as Frame ; 11.6 Checking and Detailing ; 11.6.1 Steel ; 11.6.2 Reinforced Concrete ; 11.7 Message of the Chapter ;

12 Understanding FEMPlate Bending ; 12.1 Intended Goal and Chosen Structure ; 12.2 Bending Moments and Equilibrium ; 12.2.1 Discussion ofMoment Diagrams; 12.2.2 Equilibrium Check for Moments ; 12.3 Shear Forces, Support Reactions and Equilibrium ; 12.3.1 Discussion of Shear Force Diagrams ; 12.3.2 Equilibrium Check for Shear Forces ; 12.4 Message of the Chapter;

13 FE Analysis for Different Supports ; 13.1 Simply-Supported Plat; 13.1.1 Distributed Load ; 13.1.2 Point Load ; 13.2 Corner Supports ; 13.2.1 Distributed Load; 13.2.2 Point Load ; 13.3 Edge Beams; 13.3.1 Rigid Beams ;13.3.2 Flexible Beams ; 13.4 Pressure-Only Support ; 13.5 Message of the Chapter ;

14 Handling Peak Moments ; 14.1 Peaks at Columns ; 14.2 Column Reaction Distribution ; 14.3 Application; 14.4 Cast-Connected Column ; 14.5 Dependence on Program ; 14.5.1 Review of FEMResults ; 14.5.2 Program Comparison ; 14.6 Dependence on User ; 14.7 Impact of Support Flexibility and Concrete Cracking ; 14.7.1 Application of Finite Element Program ; 14.8 Message of the Chapter ;

15 Sense and Nonsense of Mindlin; 15.1 Result Dependence on Analyst and Program; 15.1.1 Invitation ; 15.1.2 Submitted Results ; 15.2 Explanation of the Differences ; 15.3 Supporting Side Study ; 15.3.1 Thin Plate Results ; 15.3.2 Thick Plate Results ; 15.4 Comparison in Hindsight ; 15.5 Message of the Chapter ; 15.5.1 Lessons for Thin Plates ; 15.5.2 Lessons for Thick Plates;

16 Reinforcement Design Using Linear Analysis ; 16.1 Design ofMembrane States ; 16.2 Design of Slabs- Normal Moment Yield Criterion ; 16.3 Slab and Shell Elements - BasicModel ; 16.3.1 Basic Model - No Cracking Due to Transverse Shear ; 16.3.2 BasicModel - Cracking Due to Transverse Shear ; 16.3.3 Evaluation ; 16.4 Formulation of the Advanced Three-layer Model; 16.5 Applications on Element Level ; 16.5.1 Element with Membrane Force and Bending Moment ; 16.5.2 Slab Element with TwistingMoment ; 16.6 Applications on Structural Level ; 16.6.1 Deep Beam ; 16.6.2 Slab; 16.7 Message of the Chapter ;

17 Special Slab Systems ; 17.1 Wide-Slab Floor ; 17.2 Reinforced Floor Unit ; 17.2.1 Serviceability Limit State ; 17.2.2 Ultimate Limit State ; 17.3 Pre-stressed Floor Unit without Lateral Reinforcement ; 17.3.1 Serviceability Limit State ; 17.3.2 Ultimate Limit State; 17.4 Pre-stressed Floor Unit with Lateral Reinforcement; 17.4.1 Serviceability Limit State ; 17.4.2 Ultimate Limit State ; 17.5 Strengthened Strip Floor ; 17.6 Message of the Chapter ; 17.6.1 Wide-slab Floor; 17.6.2 Strengthened Strip Floor ;

18 Special Topics and Trends; 18.1 Stringer-Panel Method; 18.1.1 Beam with Dapped Ends ; 18.1.2 ShearWall with Opening ; 18.2 Membrane Plates with Concrete Pressure Only ; 18.2.1 ShearWall with Opening ; 18.3 Advanced Orthotropy ; 18.3.1 Bridge with Point Load ; 18.4 Plates on Soil Foundation; 18.4.1 Two Close Slabs ; 18.5 Message of this Chapter ;

19 Case History of Cable-Stayed Wide-Box Bridge ; 19.1 Introduction ; 19.2 Calculation of a Construction Phase ; 19.2.1 Problem Definition and Finite Element Mesh ; 19.2.2 Results of the FE Analysis and the Model Test ; 19.3 Interpretation of the Results; 19.3.1 Stress sxx in Span Direction ; 19.3.2 Stress syy in Transverse Direction;19.3.3 Shear Stress sxy ; 19.3.4 Deflection Diagram; 19.3.5 Evaluation ; 19.4 Message of the Chapter;

Part 4 Shape Orthotropy;

20 Shape-Orthotropic Membrane Rigidities ; 20.1 Problem Statement ; 20.2 Occasion of the Chapter ; 20.3 Membrane Plate with Stiffeners ; 20.4 Plate Strips of Different Thickness ; 20.4.1 Extensional Rigidity ; 20.4.2 Shear Rigidity the y-Direction; 20.5 Plate with Hat Stiffeners ; 20.5.1 Extensional Rigidity ; 20.5.2 Shear Rigidity; 20.6 Message of the Chapter;

21 Orthotropic Plates in Bending and Shear; 21.1 Problem Statement; 21.2 Plate with I-Sections; 21.2.1 Flexural Rigidity ; 21.2.2 Torsional Rigidity ; 21.2.3 Shear Rigidity; 21.3 Multi-Cell Bridge ; 21.3.1 Flexural Rigidity ; 21.3.2 Torsion Rigidity; 21.3.3 Shear Rigidity ; 21.3.4 Combination of Shear Force and Twisting Moment ; 21.4 Plate with Separate Boxes ; 21.4.1 Flexural Rigidity ; 21.4.2 Torsional Rigidity ; 21.4.3 Shear Rigidity ; 21.5 Message of the Chapter ; References ; Index