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E-raamat: Limit Analysis and Concrete Plasticity

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(Technical University of Denmark, Bygning), (University of Southern Denmark, Odense)
  • Formaat: 816 pages
  • Ilmumisaeg: 19-Apr-2016
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781040055540
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Limit Analysis and Concrete PlasticitySuurem pilt
  • Formaat: 816 pages
  • Ilmumisaeg: 19-Apr-2016
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781040055540
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First published in 1984, Limit Analysis and Concrete Plasticity explains for advanced design engineers the principles of plasticity theory and its application to the design of reinforced and prestressed concrete structures, providing a thorough understanding of the subject, rather than simply applying current design formulas.

Updated and revised throughout, Limit Analysis and Concrete Plasticity, Third Edition adds











Reinforcement design formulas for three-dimensional stress fields that enable design of solid structures (also suitable for implementation in computer-based lower bound optimizations) Improved explanations of the crack sliding theory and new solutions for beams with arbitrary curved shear cracks, continuous beams, lightly shear reinforced beams and beams with large axial compression More accurate treatment of and solutions for beams with circular cross-section Applications of crack sliding theory to punching shear problems New solutions that illustrate the implication of initial cracking on load-carrying capacity of disks Yield condition for the limiting case of isotropically cracked disk

The authors also devote an entirely new chapter to a recently developed theory of rigid-plastic dynamics for seismic design of concrete structures. In comparison with time-history analyses, the new theory is simpler to use and leads to large material savings. With this chapter, plasticity design methods for both statical and dynamical loads are now covered by the book.
Preface to 3rd Edition xi
Preface to 2nd Edition xiii
Preface to 1st Edition xv
Introduction xvii
1 The Theory of Plasticity
1(16)
1.1 Constitutive Equations
1(7)
1.1.1 Von Mises's Flow Rule
1(7)
1.2 Extremum Principles for Rigid-Plastic Materials
8(3)
1.2.1 The Lower Bound Theorem
8(1)
1.2.2 The Upper Bound Theorem
9(1)
1.2.3 The Uniqueness Theorem
10(1)
1.3 The Solution of Plasticity Problems
11(2)
1.4 Reinforced Concrete Structures
13(4)
2 Yield Conditions
17(118)
2.1 Concrete
17(35)
2.1.1 Failure Criteria
17(1)
2.1.2 Failure Criteria for Coulomb Materials and Modified Coulomb Materials
18(7)
2.1.3 Failure Criteria for Concrete
25(14)
2.1.4 Structural Concrete Strength
39(13)
2.2 Yield Conditions for Reinforced Disks
52(22)
2.2.1 Assumptions
52(4)
2.2.2 Orthogonal Reinforcement
56(1)
2.2.2.1 The Reinforcement Degree
56(1)
2.2.2.2 Tension and Compression
57(1)
2.2.2.3 Pure Shear
57(2)
2.2.2.4 The Yield Condition in the Isotropic Case
59(6)
2.2.2.5 The Yield Condition in the Orthotropic Case
65(2)
2.2.3 Skew Reinforcement
67(3)
2.2.4 Uniaxial Stress and Strain
70(4)
2.2.5 Experimental Verification
74(1)
2.3 Yield Conditions for Slabs
74(18)
2.3.1 Assumptions
74(1)
2.3.2 Orthogonal Reinforcement
74(1)
2.3.2.1 Pure Bending
74(2)
2.3.2.2 Pure Torsion
76(3)
2.3.2.3 Combined Bending and Torsion
79(9)
2.3.2.4 Analytical Expressions for the Yield Conditions
88(1)
2.3.2.5 Effectiveness Factors
89(1)
2.3.3 An Alternative Derivation of the Yield Conditions for Slabs
90(1)
2.3.4 Arbitrarily Reinforced Slabs
91(1)
2.3.5 Experimental Verification
91(1)
2.3.6 Yield Conditions for Shells
92(1)
2.4 Reinforcement Design
92(43)
2.4.1 Disks with Orthogonal Reinforcement
92(6)
2.4.2 Examples
98(1)
2.4.2.1 Pure Tension
98(3)
2.4.2.2 Shear
101(1)
2.4.3 Disks with Skew Reinforcement
102(2)
2.4.4 Slabs
104(2)
2.4.5 Shells
106(1)
2.4.6 Three-Dimensional Stress Fields
106(1)
2.4.6.1 Preliminaries
106(4)
2.4.6.2 Statement of Problem: Notation
110(2)
2.4.6.3 Case 1: All Shear Stresses Are Positive
112(3)
2.4.6.4 Intermission: Reinforcement Given in One Direction
115(1)
2.4.6.5 Case 1 (cont.): All Shear Stresses Are Positive
116(2)
2.4.6.6 Case 2: Three Negative Shear Stresses
118(4)
2.4.6.7 Summary of Formulas
122(3)
2.4.6.8 Examples
125(4)
2.4.6.9 Concluding Remarks Regarding Three-Dimensional Stress Fields
129(1)
2.4.7 Reinforcement Design According to the Elastic Theory
130(1)
2.4.8 Stiffness in the Cracked State
131(1)
2.4.9 Concluding Remarks
132(3)
3 The Theory of Plain Concrete
135(76)
3.1 Statical Conditions
135(1)
3.2 Geometrical Conditions
136(1)
3.3 Virtual Work
136(1)
3.4 Constitutive Equations
137(19)
3.4.1 Plastic Strains in Coulomb Materials
137(3)
3.4.2 Dissipation Formulas for Coulomb Materials
140(4)
3.4.3 Plastic Strains in Modified Coulomb Materials
144(3)
3.4.4 Dissipation Formulas for Modified Coulomb Materials
147(3)
3.4.5 Planes and Lines of Discontinuity
150(1)
3.4.5.1 Strains in a Plane of Discontinuity
150(1)
3.4.5.2 Plane Strain
151(3)
3.4.5.3 Plane Stress
154(2)
3.5 The Theory of Plane Strain for Coulomb Materials
156(16)
3.5.1 Introduction
156(1)
3.5.2 The Stress Field
156(7)
3.5.3 Simple, Statically Admissible Failure Zones
163(2)
3.5.4 The Strain Field
165(2)
3.5.5 Simple, Geometrically Admissible Strain Fields
167(5)
3.6 Applications
172(39)
3.6.1 Pure Compression of a Prismatic Body
172(2)
3.6.2 Pure Compression of a Rectangular Disk
174(1)
3.6.3 A Semi-Infinite Body
175(3)
3.6.4 A Slope with Uniform Load
178(2)
3.6.5 Strip Load on a Concrete Block
180(1)
3.6.5.1 Loading Far from the Edge
180(3)
3.6.5.2 Loading Near the Edge
183(3)
3.6.6 Point Load on a Cylinder or Prism
186(3)
3.6.7 Design Formulas for Concentrated Loading
189(1)
3.6.7.1 Approximate Formulas
189(4)
3.6.7.2 Semi-Empirical Formulas
193(5)
3.6.7.3 Comparison with Tests
198(5)
3.6.7.4 Conclusion
203(1)
3.6.7.5 Effect of Reinforcement
204(1)
3.6.7.6 Edge and Corner Loads
205(2)
3.6.7.7 Group Action
207(1)
3.6.7.8 Size Effects
208(3)
4 Disks
211(108)
4.1 Statical Conditions
211(1)
4.2 Geometrical Conditions
212(1)
4.3 Virtual Work
213(1)
4.4 Constitutive Equations
214(4)
4.4.1 Plastic Strains in Disks
214(2)
4.4.2 Dissipation Formulas
216(2)
4.5 Exact Solutions for Isotropic Disks
218(12)
4.5.1 Various Types of Yield Zones
218(1)
4.5.2 A Survey of Known Solutions
219(3)
4.5.3 Illustrative Examples
222(1)
4.5.3.1 Circular Disk with a Hole
222(3)
4.5.3.2 Rectangular Disk with Uniform Load
225(4)
4.5.4 Comparison with the Elastic Theory
229(1)
4.6 The Effective Compressive Strength of Reinforced Disks
230(26)
4.6.1 Strength Reduction due to Internal Cracking
230(9)
4.6.2 Strength Reduction due to Sliding in Initial Cracks
239(3)
4.6.3 Implications of Initial Crack Sliding on Design
242(2)
4.6.4 Plastic Solutions Taking into Account Initial Crack Sliding
244(1)
4.6.4.1 Additional Reinforcement to Avoid Crack Sliding
245(3)
4.6.4.2 Yield Condition for Isotropically Cracked Disks
248(2)
4.6.4.3 Shear Strength of Isotropically Cracked Disk
250(2)
4.6.4.4 Shear Strength of Orthotropic Disk with Initial Cracks
252(3)
4.6.5 Concluding Remarks
255(1)
4.7 General Theory of Lower Bound Solutions
256(17)
4.7.1 Statically Admissible Stress Fields
256(3)
4.7.2 A Theorem of Affinity
259(2)
4.7.3 The Stringer Method
261(7)
4.7.4 Shear Zone Solutions for Rectangular Disks
268(1)
4.7.4.1 Distributed Load on the Top Face
268(3)
4.7.4.2 Distributed Load at the Bottom Face
271(1)
4.7.4.3 Distributed Load along a Horizontal Line
271(1)
4.7.4.4 Arbitrary Loads
272(1)
4.7.4.5 Effectiveness Factors
272(1)
4.8 Strut and Tie Models
273(17)
4.8.1 Introduction
273(1)
4.8.2 The Single Strut
273(3)
4.8.3 Strut and Tie Systems
276(7)
4.8.4 Effectiveness Factors
283(3)
4.8.5 More Refined Models
286(4)
4.9 Shear Walls
290(18)
4.9.1 Introduction
290(1)
4.9.2 Strut Solution Combined with Web Reinforcement
290(6)
4.9.3 Diagonal Compression Field Solution
296(5)
4.9.4 Effectiveness Factors
301(1)
4.9.5 Test Results
302(6)
4.10 Homogeneous Reinforcement Solutions
308(6)
4.10.1 Loads at the Top Face
308(2)
4.10.2 Loads at the Bottom Face
310(1)
4.10.3 A Combination of Homogeneous and Concentrated Reinforcement
311(1)
4.10.4 Very Deep Disks
312(2)
4.11 Design According to the Elastic Theory
314(5)
5 Beams
319(104)
5.1 Beams in Bending
319(6)
5.1.1 Load-Carrying Capacity
319(2)
5.1.2 Effectiveness Factors
321(4)
5.2 Beams in Shear
325(82)
5.2.1 Maximum Shear Capacity, Transverse Shear Reinforcement
325(1)
5.2.1.1 Lower Bound Solutions
325(7)
5.2.1.2 Upper Bound Solutions
332(3)
5.2.2 Maximum Shear Capacity, Inclined Shear Reinforcement
335(1)
5.2.2.1 Lower Bound Solutions
335(3)
5.2.2.2 Upper Bound Solutions
338(1)
5.2.3 Maximum Shear Capacity, Beams without Shear Reinforcement
339(1)
5.2.3.1 Lower Bound Solutions
339(1)
5.2.3.2 Upper Bound Solutions
340(1)
5.2.4 The Influence of Longitudinal Reinforcement on Shear Capacity
341(1)
5.2.4.1 Beams with Shear Reinforcement
341(2)
5.2.4.2 Beams without Shear Reinforcement
343(1)
5.2.5 Effective Concrete Compressive Strength for Beams in Shear
344(1)
5.2.5.1 Beams with Shear Reinforcement
344(3)
5.2.5.2 Beams without Shear Reinforcement
347(1)
5.2.6 Crack Sliding Theory
348(1)
5.2.6.1 Beams without Shear Reinforcement
348(24)
5.2.6.2 Lightly Shear Reinforced Beams
372(5)
5.2.6.3 Beams with Circular Cross Section
377(4)
5.2.7 Design of Shear Reinforcement in Beams
381(1)
5.2.7.1 Beams with Constant Depth and Arbitrary Transverse Loading
381(5)
5.2.7.2 Beams with Normal Forces
386(6)
5.2.7.3 Beams with Variable Depth
392(1)
5.2.7.4 Beams with Bent-Up Bars or Inclined Prestressing Reinforcement
392(1)
5.2.7.5 Variable θ Solutions
393(5)
5.2.7.6 Lightly Reinforced Beams
398(1)
5.2.7.7 Beams with Strong Flanges
398(1)
5.2.7.8 Beams with Arbitrary Cross Section
399(1)
5.2.8 Maximum Shear Capacity, Confined Circular Beams
400(1)
5.2.8.1 Lower Bound Solution
400(5)
5.2.8.2 Upper Bound Solution
405(2)
5.3 Beams in Torsion
407(11)
5.3.1 Reinforcement Design
407(4)
5.3.1.1 Corner Problems
411(1)
5.3.1.2 Torsion Capacity of Rectangular Sections
412(6)
5.3.1.3 Effectiveness Factors
418(1)
5.4 Combined Bending, Shear, and Torsion
418(5)
6 Slabs
423(156)
6.1 Statical Conditions
423(3)
6.1.1 Internal Forces in Slabs
423(1)
6.1.2 Equilibrium Conditions
423(3)
6.1.3 Lines of Discontinuity
426(1)
6.2 Geometrical Conditions
426(3)
6.2.1 Strain Tensor in a Slab
426(2)
6.2.2 Conditions of Compatibility
428(1)
6.2.3 Lines of Discontinuity, Yield Lines
428(1)
6.3 Virtual Work, Boundary Conditions
429(6)
6.3.1 Virtual Work
429(2)
6.3.2 Boundary Conditions
431(4)
6.4 Constitutive Equations
435(5)
6.4.1 Plastic Strains in Slabs
435(2)
6.4.2 Dissipation Formulas
437(3)
6.5 Exact Solutions for Isotropic Slabs
440(29)
6.5.1 Various Types of Yield Zones
440(1)
6.5.1.1 Yield Zone of Type 1
440(1)
6.5.1.2 Yield Zone of Type 2
441(2)
6.5.1.3 Yield Zone of Type 3
443(1)
6.5.1.4 Yield Lines
444(1)
6.5.1.5 The Circular Fan
445(1)
6.5.2 Boundary Conditions
446(1)
6.5.2.1 Boundary Conditions for Yield Lines
446(2)
6.5.2.2 Boundary Conditions for Yield Zones
448(1)
6.5.3 A Survey of Exact Solutions
449(2)
6.5.4 Illustrative Examples
451(1)
6.5.4.1 Simple Statically Admissible Moment Fields
451(5)
6.5.4.2 Simply Supported Circular Slab Subjected to Uniform Load
456(1)
6.5.4.3 Simply Supported Circular Slab with Circular Line Load
457(2)
6.5.4.4 Semicircular Slab Subjected to a Line Load
459(1)
6.5.4.5 Rectangular Slab Subjected to Two Line Loads
460(2)
6.5.4.6 Hexagonal Slab Subjected to Uniform Load
462(1)
6.5.4.7 Concentrated Force at a Corner
463(2)
6.5.4.8 Ring-Shaped Slab under Torsion
465(1)
6.5.4.9 Rectangular Slab Subjected to Uniform Load
466(3)
6.6 Upper Bound Solutions for Isotropic Slabs
469(38)
6.6.1 The Work Equation Method and the Equilibrium Method
469(1)
6.6.2 The Relationship between the Work Equation Method and the Equilibrium Method
469(1)
6.6.2.1 Bending and Torsional Moments in the Neighborhood of Yield Lines
469(4)
6.6.3 Nodal Forces
473(1)
6.6.3.1 Nodal Forces of Type 1
473(1)
6.6.3.2 Nodal Forces of Type 2
474(5)
6.6.4 Calculations by the Equilibrium Method
479(2)
6.6.5 Geometrical Conditions
481(1)
6.6.6 The Work Equation
481(2)
6.6.7 Examples
483(1)
6.6.7.1 Square Slab Supported on Two Adjacent Edges
483(3)
6.6.7.2 Rectangular Slab Supported along All Edges
486(4)
6.6.7.3 Triangular Slab with Uniform Load
490(1)
6.6.7.4 Line Load on a Free Edge
491(1)
6.6.7.5 Concentrated Load
492(1)
6.6.7.6 Simply Supported Square Slab with a Concentrated Load
493(2)
6.6.8 Practical Use of Upper Bound Solutions
495(10)
6.6.8.1 Example 6.6.1
505(2)
6.7 Lower Bound Solutions
507(38)
6.7.1 Introduction
507(1)
6.7.2 Rectangular Slabs with Various Support Conditions
508(2)
6.7.2.1 A Slab Supported on Four Edges
510(3)
6.7.2.2 A Slab Supported on Three Edges
513(3)
6.7.2.3 A Slab Supported on Two Adjacent Edges
516(3)
6.7.2.4 A Slab Supported along One Edge and on Two Columns
519(2)
6.7.2.5 A Slab Supported on Two Edges and on a Column
521(1)
6.7.2.6 Other Solutions
522(1)
6.7.3 The Strip Method
522(1)
6.7.3.1 Square Slab with Uniform Load
523(1)
6.7.3.2 One-Way Slab with a Hole
524(2)
6.7.3.3 Triangular Slab with a Free Edge
526(1)
6.7.3.4 Angular Slab
527(1)
6.7.3.5 Line Load on a Free Edge
528(4)
6.7.3.6 Slabs Supported on a Column
532(4)
6.7.3.7 Concentrated Force on Simply Supported Slab
536(1)
6.7.3.8 Flat Slab
537(3)
6.7.4 Some Remarks Concerning the Reinforcement Design
540(1)
6.7.5 Stiffness in the Cracked State
540(5)
6.8 Orthotropic Slabs
545(11)
6.8.1 The Affinity Theorem
545(6)
6.8.2 Upper Bound Solutions
551(3)
6.8.2.1 Example 6.8.1
554(2)
6.9 Analytical Optimum Reinforcement Solutions
556(2)
6.10 Numerical Methods
558(2)
6.11 Membrane Action
560(19)
6.11.1 Membrane Effects in Slabs
560(4)
6.11.2 Unreinforced One-Way Slabs
564(2)
6.11.3 Work Equation
566(3)
6.11.4 Unreinforced Square Slabs
569(3)
6.11.5 Unreinforced Rectangular Slabs
572(1)
6.11.6 The Effect of Reinforcement
573(1)
6.11.7 Comparison with Tests
574(1)
6.11.8 Conclusion
575(1)
6.11.8.1 Example 6.11.1
576(3)
7 Punching Shear of Slabs
579(50)
7.1 Introduction
579(1)
7.2 Internal Loads
579(25)
7.2.1 Concentric Loading, Upper Bound Solution
579(1)
7.2.1.1 The Failure Mechanism
579(2)
7.2.1.2 Upper Bound Solution
581(4)
7.2.1.3 Analytical Results
585(3)
7.2.2 Experimental Verification, Effectiveness Factors
588(1)
7.2.2.1 Failure Surface
588(1)
7.2.2.2 Ultimate Load
589(2)
7.2.3 Practical Applications
591(2)
7.2.4 Eccentric Loading
593(6)
7.2.5 The Effect of Counterpressure and Shear Reinforcement
599(5)
7.3 Edge and Corner Loads
604(18)
7.3.1 Introduction
604(2)
7.3.2 Corner Load
606(5)
7.3.3 Edge Load
611(2)
7.3.4 General Case of Edge and Corner Loads
613(5)
7.3.5 Eccentric Loading
618(4)
7.4 Punching Shear Analysis by the Crack Sliding Theory
622(5)
7.5 Concluding Remarks
627(2)
8 Shear in Joints
629(40)
8.1 Introduction
629(1)
8.2 Analysis of Joints by Plastic Theory
629(16)
8.2.1 General
629(1)
8.2.2 Monolithic Concrete
630(3)
8.2.3 Joints
633(1)
8.2.4 Statical Interpretation
634(1)
8.2.5 Axial Forces
635(1)
8.2.6 Effectiveness Factors
635(3)
8.2.7 Skew Reinforcement
638(4)
8.2.8 Compressive Strength of Specimens with Joints
642(3)
8.3 Strength of Different Types of Joints
645(24)
8.3.1 General
645(1)
8.3.2 The Crack as a Joint
645(6)
8.3.3 Construction Joints
651(8)
8.3.4 Butt Joints
659(3)
8.3.5 Keyed Joints
662(7)
9 The Bond Strength of Reinforcing Bars
669(66)
9.1 Introduction
669(1)
9.2 The Local Failure Mechanism
669(6)
9.3 Failure Mechanisms
675(7)
9.3.1 Review of Mechanisms
675(1)
9.3.2 Splice Strength vs. Anchor Strength
676(1)
9.3.3 The Most Important Mechanisms
677(1)
9.3.4 Lap Length Effect
678(1)
9.3.5 Development Length
678(1)
9.3.6 Example 9.3.1
679(3)
9.4 Analysis of Failure Mechanisms
682(15)
9.4.1 General
682(1)
9.4.2 Corner Failure
682(5)
9.4.3 V-Notch Failure
687(6)
9.4.4 Face Splitting Failure
693(1)
9.4.5 Concluding Remarks
694(3)
9.5 Assessment of Anchor and Splice Strength
697(9)
9.5.1 Example 9.5.1
698(6)
9.5.2 Example 9.5.2
704(2)
9.6 Effect of Transverse Pressure and Support Reaction
706(12)
9.7 Effect of Transverse Reinforcement
718(15)
9.7.1 General
718(2)
9.7.2 Transverse Reinforcement Does Not Yield
720(6)
9.7.3 Transverse Reinforcement Yields
726(5)
9.7.3.1 Example 9.7.1
731(2)
9.8 Concluding Remarks
733(2)
10 Seismic Design by Rigid-Plastic Dynamics
735(28)
10.1 Introduction
735(1)
10.2 Constitutive Properties
735(4)
10.3 Rotation Capacity
739(3)
10.4 Rigid-Plastic Dynamics
742(5)
10.4.1 Introductory Remarks
742(1)
10.4.2 Single-Degree-of-Freedom System
742(3)
10.4.3 Multi-Degree-of-Freedom Systems
745(2)
10.5 Rigid-Plastic Spectra
747(3)
10.6 Seismic Design by Plastic Theory
750(1)
10.7 P-Δ Effects
751(1)
10.8 Examples
752(9)
10.8.1 Four-Story Plane Frame
752(6)
10.8.2 Twelve-Story Space Frame
758(3)
10.9 Conclusions
761(2)
References 763(26)
Index 789
M.P. Nielsen Technical University of Denmark, Bygning, L.C. Hoang
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