List of Figures

• 1.1. Rigid body displacements and rotation
• 1.2. Sign Convention
• 1.3. Right-handed and left-handed coordinates
• 1.4. Moment diagrams for unit force Q and unit moment M
• 1.5. Beam element deformations
• 1.6. Moment diagrams for force Q and moment M
• 1.7. Shear force diagrams for force Q and unit force q
• 1.8. Bending of a frame element (Sign Convention 2)
• 1.9. A differential frame element
• 1.10. External reactions and restraints on displacements
• 1.11. Frame element (Sign Convention 2)
• 1.12. Internal reactions (contact forces) and displacements of joints
• 1.13. Structure of the system of boundary value problem equations
• 1.14. Angles between the vector and the coordinate axes
• 2.1. Transitivity
• 2.2. Compatibility at rigid joint A3
• 2.3. Compatibility at hinged joint A2
• 2.4. Compatibility at rigid joint B3
• 2.5. Compatibility at rigid & pin joint B32
• 2.6. Compatibility at pin joint B2
• 2.7. Compatibility at rigid joint T2
• 2.8. Compatibility at pin joint T1
• 2.9. Equilibrium of joint A3
• 2.10. Equilibrium of joint A2
• 2.11. Equilibrium of joint B3
• 2.12. Equilibrium of joint B2
• 2.13. Equilibrium of joint B32
• 2.14. Equilibrium of support node A3s
• 2.15. Equilibrium of support node A2v
• 2.16. Equilibrium of support node A2p
• 2.17. Equilibrium of joint T2s
• 2.18. Equilibrium of joint T1s
• 2.19. Cross-sectional directions
• 2.20. Truss element
• 3.1. The two-span frame
• 3.2. Numeration of displacements at frame element ends
• 3.3. Numeration of forces at frame element ends
• 3.4. Bending moment diagram of the two-span frame
• 3.5. Diagrams of the axial force N and shear force Q of the two-span frame
• 3.6. Boundary forces of the two-span frame
• 3.7. Elements of the two-span frame
• 3.8. Sparsity pattern of matrix spA of the two-span frame
• 3.9. Two-span frame EST93
• 3.10. Numeration of displacements and forces of the two-span frame EST93
• 3.11. Internal forces diagrams of the two-span frame EST93
• 3.12. Boundary forces of the two-span frame EST93
• 3.13. Elements of the two-span frame EST93
• 3.14. Sparsity pattern of matrix spA of the two-span frame EST93
• 3.15. The frame EST77
• 3.16. Numeration of displacements and forces of the frame EST77
• 3.17. Internal forces diagrams of the frame EST77
• 3.18. Boundary forces of the frame EST77
• 3.19. Elements of the frame EST77
• 3.20. Sparsity pattern of matrix spA of the frame EST77
• 3.21. The continuous beam EST
• 3.22. Numeration of displacements and forces of the continuous beam EST
• 3.23. Internal forces diagrams of the continuous beam (1st loading)
• 3.24. Internal forces diagrams of the continuous beam (2nd loading)
• 3.25. Internal forces diagrams of the continuous beam (3rd loading)
• 3.26. The continuous beam minimum-maximum bending moments
• 3.27. Elements of the continuous beam EST
• 3.28. Sparsity pattern of matrix spA of the continuous beam EST
• 3.29. The truss EST
• 3.30. A free-body diagram of the truss with joint numbers
• 3.31. Numeration of displacements and forces of the truss EST
• 3.32. Support reactions of the truss EST
• 3.33. Elements of the truss EST
• 3.34. Sparsity pattern of matrix spA of the truss
• 4.1. The three-hinged frame EST1
• 4.2. Numeration of displacements and forces of the frame EST1
• 4.3. Support reactions of the frame EST1
• 4.4. Internal forces diagrams of the three-hinged frame EST1
• 4.5. Elements of the three-hinged frame EST1
• 4.6. Sparsity pattern of matrix spA of the three-hinged frame EST1
• 4.7. The three-span Gerber beam EST
• 4.8. Numeration of displacements and forces of the Gerber beam
• 4.9. Internal forces diagrams of the Gerber beam EST
• 4.10. Elements of the Gerber beam EST
• 4.11. Sparsity pattern of matrix spA of the Gerber beam EST
• 4.12. A polygonal eight-panel truss
• 4.13. Influence line for member 9
• 4.14. Sparsity pattern of matrix spA of the polygonal truss
• 5.1. Normal, shear, axial and transverse shear forces
• 5.2. Deformed beam elements with the axial and normal forces
• 5.3. Components of the normal force
• 5.4. Bending moments of a beam-column
• 5.5. Axial and normal forces
• 6.1. The frame EST1
• 6.2. Numeration of displacements and forces of the frame EST1
• 6.3. Internal forces diagrams of the frame EST1
• 6.4. Boundary forces of the frame EST1
• 6.5. Elements of the frame EST1
• 6.6. Sparsity pattern of matrix spA of the frame EST1
• 6.7. The two-span frame EST2
• 6.8. Displacement and force numbers of the two-span frame EST2
• 6.9. Horizontal displacements diagram of the frame EST2
• 6.10. Internal forces diagrams of the two-span frame EST2
• 6.11. Boundary forces of the two-span frame EST2
• 6.12. Elements of the frame EST2
• 6.13. Sparsity pattern of matrix spA of the frame EST2
• 7.1. Stress-strain curve
• 7.2. Rectangular cross section
• 7.3. Shape factor for different sections
• 7.4. Cross section and stresses
• 7.5. Work done in a plastic hinge
• 7.6. Upper and lower bound values
• 8.1. The frame ESTsn3
• 8.2. Bending moment diagrams of an n = 3 times indeterminate frame
• 8.3. Bending moment diagrams of an n = 2 times indeterminate frame
• 8.4. Bending moment diagrams of an n = 1 times indeterminate frame
• 8.5. Bending moment diagrams of a statically determined frame (n = 0)
• 8.6. Load-deflection relation for the frame ESTsn3
• 8.7. Load cases of the n = 3 times indeterminate frame ESTsn3
• 8.8. Numeration of displacements and forces of the frame ESTsn3
• 8.9. Load cases of the n = 2 times indeterminate frame ESTsn2
• 8.10. Load cases of the n = 1 times indeterminate frame ESTsn1
• 8.11. Load cases of the n = 0 times indeterminate frame ESTsn0
• A.1. Sparsity pattern of matrix spA
• A.2. Assembly sequence of a Gerber beam
• A.3. Coordinate transformation
• A.4. Direction cosines of an element
• B.1. Bar member a-b