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Table of Contents

Cover

Preface

1 Introduction to Statically Indeterminate Structural Analysis

1.1. Introduction
1.2. External static indeterminacy
1.3. Internal static indeterminacy
1.4. Kinematic static indeterminacy
1.5. Statically indeterminate structural analysis methods
1.6. Superposition principle
1.7. Advantages and disadvantages of statically indeterminate structures
1.8. Conclusion
1.9. Problems

2 Method of Three Moments

2.1. Simple beams
2.2. Continuous beam
2.3. Applying Clapeyron's theorem
2.4. Focus method
2.5. Conclusion
2.6. Problems

3 Method of Forces

3.1. Beam with one degree of static indeterminacy
3.2. Beam with many degrees of static indeterminacy
3.3. Continuous beam with support settlements
3.4. Analysis of a beam with two degrees of static indeterminacy
3.5. Analysis of a beam subjected to a moment
3.6. Analysis of frames
3.7. Analysis of truss
3.8. Conclusion
3.9. Problems

4 Slope-Deflection Method

4.1. Relationship between deflections and transmitted moments
4.2. Fixed-end moments
4.3 Rigidity factor and transmission coefficient
4.4. Beam analysis
4.5. Analysis of frames
4.6. Conclusion
4.7. Problems

5 Moment-Distribution Method

5.1. Hypotheses of the moment-distribution method
5.2. Presentation of the moment-distribution method
5.3. Continuous beam analysis
5.4. Analysis of frames
5.5. Conclusion
5.6. Problems

6 Influence Lines of Statically Indeterminate Structures

6.1. Introduction
6.2. Influence lines of beams
6.3. Influence lines of frames
6.4. Influence lines of trusses
6.5. Conclusion
6.6. Problems

7 Statically Indeterminate Arch Analysis

7.1. Introduction
7.2. Classification of arches
7.3. Semicircular arch under concentrated load
7.4. Parabolic arch under concentrated load
7.5. Semicircular arch under distributed load
7.6. Parabolic arch under distributed load
7.7. Semicircular arch fixed under concentrated load
7.8. Statically indeterminate tied arch
7.9. Arch with many degrees of freedom
7.10. Influence lines of statically indeterminate arch
7.11. Conclusion
7.12. Problems

Appendix

A.1. Standard structural deflections
A.2. Fixed-end moments

Bibliography

Index

End User License Agreement

List of Tables

3 Method of Forces

Table 3.1. Degree of static indeterminacy (Figure 3.47)
Table 3.2. Nature of static indeterminacy
Table 3.3. Forces on the bars of the fundamental system
Table 3.4. Forces on the bars of the unit system and displacement along the diagonal (AC)
Table 3.5. Forces on the bars of the given structure
Table 3.6. Forces on the bars of the given structure for F = F₁ = F₂
Table 3.7. Horizontal displacement of joint D
Table 3.8. Internal forces on the bars of the given system
Table 3.9. Internal forces on the bars

5 Moment-Distribution Method

Table 5.1. Equilibrium and transmission of moments. For a color version of this table, see www.iste.co.uk/khalfallah/analysis 2.zip
Table 5.2. Moments at joints
Table 5.3. Comparison between the slope-deflection and moment-distribution methods
Table 5.4. Moments at joints after three iterations
Table 5.5. Comparison between the slope-deflection and moment-distribution methods . For a color version of this table, see www.iste.co.uk/khalfallah/analysis 2.zip
Table 5.6. Moments at joints of a cantilever beam
Table 5.7. Convergence rate and moment-distribution method (qL²)
Table 5.8. Distribution of shore moment
Table 5.9. Comparison between the slope-deflection and moment-distribution methods
Table 5.10. Frame analysis using the moment-distribution method
Table 5.11. Analysis of frame without sidesway. For a color version of this table, see www.iste.co.uk/khalfallah/analysis 2.zip
Table 5.12. Analysis of frame with support settlement. For a color version of this table, see www.iste.co.uk/khalfallah/analysis 2.zip
Table 5.13. Comparison between the slope-deflection and moment-distribution methods . For a color version of this table, see www.iste.co.uk/khalfallah/analysis 2.zip
Table 5.14. Frame without sidesway. For a color version of this table, see www.iste.co.uk/khalfallah/analysis 2.zip
Table 5.15. Frame with sidesway
Table 5.16. Moments at joints of frame
Table 5.17. Moments of a frame with sidesway
Table 5.18. Moments of a frame with sidesway
Table 5.19. Moments of a frame without sidesway
Table 5.20. Moments of a frame with sidesway
Table 5.21. Moments at joints of given frame
Table 5.22. Moments of a frame without sidesway
Table 5.23. Moments of a frame with sidesway
Table 5.24. Moments of given frame
Table 5.25. Moments of fixed frame. For a color version of this table, see www.iste.co.uk/khalfallah/analysis 2.zip
Table 5.26. Moments of a frame with sidesway. For a color version of this table, see www.iste.co.uk/khalfallah/analysis 2.zip

6 Influence Lines of Statically Indeterminate Structures

Table 6.1. Moments at the ends of bars
Table 6.2. Degrees of static indeterminacy
Table 6.3. Different static indeterminacy
Table 6.4. Internal forces on the bars of the fundamental system
Table 6.5. Internal forces on the bars of the fundamental system
Table 6.6. Internal forces on the bars of the unit system due to a unit action applied along the axis (AC)

List of Illustrations

1 Introduction to Statically Indeterminate Structural Analysis

Figure 1.1. Statically indeterminate externally of plane structures
Figure 1.2. Statically indeterminate externally of space structures
Figure 1.3. Externally statically indeterminate plane structures
Figure 1.4. Statically indeterminate space truss
Figure 1.5. Given truss
Figure 1.6. Space truss
Figure 1.7. Space truss
Figure 1.8. Static indeterminacy of frames and beams
Figure 1.9. Static indeterminacy of space beams and frames
Figure 1.10. Crossbeams
Figure 1.11. Crossbeam layer
Figure 1.12. Deflection of beam (AC)
Figure 1.13. Given structures
Figure 1.14. Plane truss
Figure 1.15. Free-body structure
Figure 1.16. Space truss
Figure 1.17. Free-body structure
Figure 1.18. Superposition of displacements and forces
Figure 1.19. Maximum displacements
Figure 1.20. Maximum bending moment
Figure 1.21. Destruction of the interior support
Figure 1.22. Support settlement
Figure 1.23. Temperature effect

2 Method of Three Moments

Figure 2.1. Single span beam
Figure 2.2. Statically determinate structure
Figure 2.3. Unit moment at joint A
Figure 2.4. Unit moment at joint B
Figure 2.5. Effect of fixing moment M_A
Figure 2.6. Effect of fixing moment M_B
Figure 2.7. Support settlement effect
Figure 2.8. Studied beam
Figure 2.9. Basic statically determinate beam
Figure 2.10. Diagrams a) of bending moment and b) of shear force
Figure 2.11. Beam with several spans
Figure 2.12. Continuous statically determinate beam
Figure 2.13. (i – 1)th span
Figure 2.14. ith span
Figure 2.15. Effect of left moment M′_i-1
Figure 2.16. Effect of left moment M″i.
Figure 2.17. Effect of moments M′i
Figure 2.18. Effect of moments M″_i+1
Figure 2.19. Beam with two spans
Figure 2.20. Beam with two spans
Figure 2.21. Beam with two spans
Figure 2.22. Bending moment diagram *(P.L)
Figure 2.23. Shear force diagram *(P)
Figure 2.24. Continuous beam with support settlement
Figure 2.25. Bending moment diagram
Figure 2.26. Shear force diagram
Figure 2.27. Beam with cantilever
Figure 2.28. Bending moment diagram
Figure 2.29. Shear force diagram *()
Figure 2.30. Continuous beam under M_n+1
Figure 2.31. Bending moment diagram
Figure 2.32. Shear force diagram
Figure 2.33. Continuous beam under M_s
Figure 2.34. Bending moment diagram
Figure 2.35. Shear force diagram
Figure 2.36. Continuous beam with loaded bays
Figure 2.37. Study of the ith span
Figure 2.38. Bending moment diagram
Figure 2.39. Shear force diagram
Figure 2.40. Given beam
Figure 2.41. Bending moment diagram
Figure 2.42. Shear force diagram (KN)

3 Method of Forces

Figure 3.1. Equivalent beam
Figure 3.2. Fundamental system
Figure 3.3. Unit system
Figure 3.4. Equivalent beam
Figure 3.5. Fundamental beam
Figure 3.6. Deflection and diagram of the fundamental moment *(qL²)
Figure 3.7. Deflection and bending moment of the first unit system
Figure 3.8. Deflection and bending moment of the second unit system
Figure 3.9. Deflection and bending moment of the third unit system
Figure 3.10. Deflections of unit systems
Figure 3.11. Equivalent beam
Figure 3.12. Determinate beam
Figure 3.13. First unit system
Figure 3.14. Second unit system
Figure 3.15. Equivalent beam
Figure 3.16. Basic beam
Figure 3.17. First unit system
Figure 3.18. Second unit system
Figure 3.19. Given frame
Figure 3.20. Equivalent frame
Figure 3.21. Statically determinate system
Figure 3.22. Bending moment diagram of the fundamental system
Figure 3.23. Unit systems
Figure 3.24. Bending moment diagram
Figure 3.25. Shear force diagram
Figure 3.26. Frame with cantilever
Figure 3.27. Equivalent frame
Figure 3.28. Fundamental system
Figure 3.29. Bending moment diagram of the fundamental system
Figure 3.30. Unit systems
Figure 3.31. Bending moment diagram
Figure 3.32. Shear force diagram
Figure 3.33. Given frame
Figure 3.34. Equivalent frame
Figure 3.35. Statically determinate system
Figure 3.36. Bending moment diagram of the fundamental system
Figure 3.37. Unit systems
Figure 3.38. Bending moment diagram
Figure 3.39. Shear force diagram
Figure 3.40. Given frame
Figure 3.41. Equivalent frame
Figure 3.42. Statically determinate system
Figure 3.43. Bending moment diagram of the fundamental system
Figure 3.44. Unit systems
Figure 3.45. Bending moment diagram *(qa²)
Figure 3.46. Shear force diagram *(qa)
Figure 3.47. Different types of truss structures
Figure 3.48. Given truss structure
Figure 3.49. Equivalent truss system
Figure 3.50. Basic truss system
Figure 3.51. Unit truss system
Figure 3.52. Normal force diagram *(F)
Figure 3.53. Given truss structure
Figure 3.54. Equivalent truss structure
Figure 3.55. Fundamental structure
Figure 3.56. Unit truss structure
Figure 3.57. Normal force diagram *(F)
Figure 3.58. Given truss structure
Figure 3.59. Equivalent structure
Figure 3.60. Fundamental structure
Figure 3.61. Trusses under unit loads
Figure 3.62. Internal force diagram * (F)

4 Slope-Deflection Method

Figure 4.1. Statically indeterminate beam
Figure 4.2. The moments at the ends of the studied beam
Figure 4.3. Deflection due to support settlement
Figure 4.4. Fixed-end moment
Figure 4.5. Bi-hinged beam
Figure 4.6. Simply supported beam
Figure 4.7. Beam subjected to couple M_AB
Figure 4.8. Beam subjected to M_AB
Figure 4.9. Beam fixed in B
Figure 4.10. Simply supported beam in B
Figure 4.11. Deformed beam
Figure 4.12. Support settlement
Figure 4.13. Support reaction and moment
Figure 4.14. Deformed beam
Figure 4.15. Deflection of the beam and support reaction
Figure 4.16. Support reactions: load and moment
Figure 4.17. Support actions: reactions and moments
Figure 4.18. Beam extension
Figure 4.19. The moments at the ends of each beam
Figure 4.20. Deflection of the beam and support reaction
Figure 4.21. The Column (AB)
Figure 4.22. The bar (BC)
Figure 4.23. Deflection of the beam, support reaction and moment
Figure 4.24. Symmetrical frame
Figure 4.25. Bending moment diagram
Figure 4.26. The Column (AB)
Figure 4.27. Shear force diagram
Figure 4.28. Bar (FB)
Figure 4.29. Deflection of the beam and support reactions
Figure 4.30. Frame under support settlement
Figure 4.31. Bending moment diagram
Figure 4.32. Bar (AB)
Figure 4.33. Shear force diagram
Figure 4.34. Bar (CB)
Figure 4.35. Bar (BD)
Figure 4.36. Deflection, fixed moments and support reactions of frame and support reactions
Figure 4.37. Frame with sidesway
Figure 4.38. Bar (AB)
Figure 4.39. Bar (DC)
Figure 4.40. Bar (AB)
Figure 4.41. Bar (DC)
Figure 4.42. Deflection of frame, fixing moment *(qL²) and support reactions *(qL)
Figure 4.43. Deformed frame
Figure 4.44
Figure 4.45. Bar (DC)
Figure 4.46. Bar (AB)
Figure 4.47. Deflection of frame, fixed moments *(qL²) and support reactions *(qL)
Figure 4.48. Deformed frame
Figure 4.49. Bar (AB)
Figure 4.50. Bar (DC)
Figure 4.51. Beam (BC)
Figure 4.52. Deflection of frame, fixed moments *(qa²) and support reactions *(qa)
Figure 4.53. Multistory frame
Figure 4.54. Deformed frame
Figure 4.55. Column (AB)
Figure 4.56. Bending moment diagram *(qL²)
Figure 4.57. Shear force diagram *(qL)
Figure 4.58. Deflection and support reactions

5 Moment-Distribution Method

Figure 5.1. Distribution of nodal moment M_A
Figure 5.2. Loading or support settlement
Figure 5.3. Frame without sidesway
Figure 5.4. Column (CB)
Figure 5.5. Column (CD)
Figure 5.6. Frame with sidesway – direct method
Figure 5.7. Frame with sidesway – indirect method
Figure 5.8. Frame without sidesway
Figure 5.9. Frame with sidesway
Figure 5.10. Frame without sidesway
Figure 5.11. Column (AB)
Figure 5.12. Column (DC)
Figure 5.13. Horizontal bar (BC)
Figure 5.14. Frame with sidesway
Figure 5.15. Shear forces of the bar (BC)
Figure 5.16. Multistory frame
Figure 5.17. Frame without sidesway
Figure 5.18. Frame with sidesway due to displacement Δ

6 Influence Lines of Statically Indeterminate Structures

Figure 6.1. Continuous beam with one degree of static indeterminacy
Figure 6.2. Equivalent beam
Figure 6.3. Fundamental beam
Figure 6.4. Deflection of the fundamental beam
Figure 6.5. Deflected unit system
Figure 6.6. Bending moment at point D
Figure 6.7. Beam with cantilever
Figure 6.8. Unit force on cantilever (AB)
Figure 6.9. Unit force on span (BC)
Figure 6.10. Influence line of reaction RB
Figure 6.11. Influence line of shear force TD
Figure 6.12. Influence line of bending moment MC*(a)
Figure 6.13. Beam with two degrees of static indeterminacy
Figure 6.14. Equivalent beam
Figure 6.15. Fundamental beam
Figure 6.16. First unit system
Figure 6.17. Diagram of moment m1(x)
Figure 6.18. Second unit system
Figure 6.19. Diagram of moment m₂(x)
Figure 6.20. Displacements at points B and C
Figure 6.21. Influence lines of reactions R_B and R_C
Figure 6.22. Influence line of moment M_A
Figure 6.23. a) Given frame and b) frame without sidesway
Figure 6.24. Influence line of bending moment
Figure 6.25. Influence line of shear force
Figure 6.26. Statically indeterminate truss structures. a) Internally statically indeterminate; b) externally statically indeterminate; c) externally and internally statically indeterminate
Figure 6.27. Given system
Figure 6.28. Equivalent system
Figure 6.29. Basic system
Figure 6.30. Equilibrium of node C
Figure 6.31. Equilibrium of joint B
Figure 6.32. Equilibrium of joint A
Figure 6.33. Equilibrium of joint C
Figure 6.34. Equilibrium of joint B
Figure 6.35. Unit system
Figure 6.36. Influence line and normal force on bar
Figure 6.37. Given truss
Figure 6.38. Equivalent structure
Figure 6.39. Fundamental structure
Figure 6.40. Unit force at joint N
Figure 6.41. Force on the bars due to a unit force applied at joint N*(1/24)
Figure 6.42. Force on the bars due to a unit force applied at joint M*(1/24)
Figure 6.43. Force on the bars due to a unit force applied at joint L (1/24)
Figure 6.44. Force on the bars due to a unit force applied at joint K (1/24)
Figure 6.45. Force on the bars due to a unit force applied at joint J*(1/24)
Figure 6.46. Influence lines of support reactions R_L and R_I
Figure 6.47. Influence line and internal force on bar (DE)

7 Statically Indeterminate Arch Analysis

Figure 7.1. Statically indeterminate arches
Figure 7.2. Classes of arch
Figure 7.3. Semicircular arch under concentrated load
Figure 7.4. (a) Equivalent system and (b) fundamental system
Figure 7.5. Arch under a unit action
Figure 7.6. Section 0 ≤ x ≤ a
Figure 7.7. Section θ₁ ≤ θ ≤ π
Figure 7.8. Section 0 ≤ x ≤ a
Figure 7.9. Section θ₁ ≤ θ ≤ π
Figure 7.10. Bending moment diagram (*PR)
Figure 7.11. Shear force diagram *(P)
Figure 7.12. Normal force diagram *(-P)
Figure 7.13. Parabolic arch
Figure 7.14. Fundamental and unit arches
Figure 7.15. Bending moment diagram *(PL)
Figure 7.16. Shear force diagram *(P)
Figure 7.17. Section 0 ≤ x ≤ a
Figure 7.18. Shear force diagram
Figure 7.19. Semicircular arch under uniform load
Figure 7.20. Deflected fundamental system
Figure 7.21. Deflected unit system
Figure 7.22. Bending moment diagram *(qR²)
Figure 7.23. Shear force
Figure 7.24. Shear force diagram *(qR²)
Figure 7.25. Normal force
Figure 7.26. Shear force diagram *(qR)
Figure 7.27. Parabolic arch under uniform load
Figure 7.28. Basic structure
Figure 7.29. Unit structure
Figure 7.30. Bending moment diagram
Figure 7.31. Shear force diagram
Figure 7.32. Normal force
Figure 7.33. Normal force
Figure 7.34. Normal force diagram
Figure 7.35. Arch fixed at an end
Figure 7.36. Unit system
Figure 7.37. Bending moment diagram (*PR)
Figure 7.38. Fundamental arch
Figure 7.39. Unit system
Figure 7.40. Bending moment diagram (*PR)
Figure 7.41. Section
Figure 7.42. Section
Figure 7.43. Shear force diagram *(P)
Figure 7.44. Normal force diagram *(P)
Figure 7.45. Tied arch
Figure 7.46. Fundamental system
Figure 7.47. Unit system
Figure 7.48. Bending moment diagram
Figure 7.49. Shear force diagram
Figure 7.50. Bi-fixed arch
Figure 7.51. Deflected fundamental arch
Figure 7.52. Arch under unit actions
Figure 7.53. Section 0 ≤ θ ≤ π
Figure 7.54. Bending moment diagram *(qR²)
Figure 7.55. Shear force diagram *(qR)
Figure 7.56. Normal force diagram *(qR)
Figure 7.57. Bi-hinged arch under concentrated load
Figure 7.58. Concentrated force α ≤ x
Figure 7.59. Concentrated force α ≤ x
Figure 7.60. Influence line of reaction H_A
Figure 7.61. Influence line of support reaction V_B
Figure 7.62. Influence line of a bending moment *(R) in relation to
Figure 7.63. Influence line of a shear force in relation to
Figure 7.64. Influence line of a normal force in relation to
Figure 7.65. Arch fixed at an end
Figure 7.66. Fundamental system
Figure 7.67. Unit system
Figure 7.68. Influence line of reaction V_A
Figure 7.69. Influence line of fixed-end moment M_B*(R)
Figure 7.70. Influence line of a bending moment in relation to

First published 2018 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

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The rights of Salah Khalfallah to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2018946933

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ISBN 978-1-78630-339-4