## Structural AnalysisThis main text encompasses both the principles of mechanics and basic structural concepts, and computer methods in structural analysis. In this edition, coverage of plane statistics and introductory vector analysis is increased; there is a greater design-based emphasis and more material on the principle of virtual work, and computer methods are referred to throughout. |

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### Contents

Definitions and introductory concepts | 1 |

13 Equilibrium of a body | 7 |

14 Displacements and rotations | 8 |

15 Stressesnotation and sign convention | 9 |

16 Strains | 13 |

17 Stressstrain relations | 17 |

Structural mechanics statically determinate plane frames | 21 |

22 Parallel forces in a plane | 25 |

719 Grillages | 277 |

720 Stiffness flexibility and equilibrium matrices single members | 278 |

721 Concluding remarks | 282 |

Problems | 283 |

Matrix flexibility method | 293 |

82 Relative merits of flexibility and stiffness methods | 300 |

Problems | 301 |

Instability of struts and frameworks | 304 |

23 The general case offerees in a plane | 29 |

supports and reactions | 32 |

25 Plane trusses | 35 |

26 Analysis of plane trusses | 41 |

27 Influence lines the effects of moving loads | 51 |

28 Shear forces and bending moments | 58 |

29 Influence lines for shear force and bending moment | 72 |

Problems | 75 |

Space statics and determinate space structures | 83 |

32 Constraint of space structures | 85 |

33 Determinate space structures | 87 |

34 Determinate space trusses | 90 |

35 Analysis of determinate space trusses | 92 |

Problems | 100 |

Basic structural concepts | 104 |

42 Displacements and corresponding displacements | 105 |

43 Dependent and independent actions and displacements | 108 |

44 Superposition of actions and displacementsinfluence coefficients | 109 |

45 Where superposition may not occur nonlinear behaviour | 111 |

46 Compatibility | 112 |

47 Work and complementary work | 115 |

48 Linearity of loaddeflection relationship | 116 |

49 Energystrain and complementary | 119 |

410 Superposition of strain energies | 120 |

411 Reciprocality of influence coefficients in elastic structures | 122 |

412 Generalized reciprocal theorem in an elastic structure Bettis theorem | 126 |

413 MuellerBreslaus principle Model analysis | 127 |

414 Principle of virtual work | 132 |

415 Applications of the principle of virtual work 1 | 134 |

416 Applications of the principle of virtual work 2 | 144 |

417 Energy methodsapplication in structural analysis | 168 |

418 Momentarea methods | 176 |

Problems | 181 |

Stiffness and flexibility | 190 |

52 Member stiffness and flexibility equations | 196 |

53 Transformation of axes | 199 |

54 Slopedeflection method | 208 |

Problems | 212 |

Moment distribution | 215 |

63 Application to continuous beams | 218 |

64 Twodimensional structures | 222 |

65 Pinned and overhanging ends | 223 |

66 Settlement of supports | 226 |

67 Frames in which sway occurs | 227 |

68 Use of the instantaneous centre of rotation and the principle of virtual work | 235 |

69 Frames with two or more modes of sway | 238 |

Problems | 242 |

Matrix stiffness method | 249 |

73 Assumptions | 251 |

75 Member stiffness | 252 |

76 Coordinate transformation | 253 |

77 Compatibility | 255 |

78 Equilibrium | 256 |

79 Structure stiffness matrix | 257 |

710 Restrained joints and symmetry | 259 |

711 Internal pins | 261 |

712 Worked example on a rigid frame | 263 |

713 Pinjointed structures | 267 |

714 Example on a pinjointed truss | 268 |

715 Loads between joints | 270 |

716 Temperature effects and lack of fit | 272 |

717 Continuous beams | 273 |

718 Threedimensional structures | 275 |

92 Other simple strut problems | 307 |

93 Real behaviour of struts | 311 |

94 The design of steel struts | 319 |

95 Complex struts | 323 |

96 Lateral torsional buckling of beams | 327 |

97 Solution of stability problems virtual work approach | 331 |

98 Posthuckling behaviour | 335 |

99 Stiffness of beamcolumns stability functions | 338 |

910 Influence of axial loads on end moments of fixedended beams | 344 |

911 Elastic instability of plane frames | 348 |

912 Calculation of critical loads of plane frames | 350 |

913 Buckling modes | 354 |

914 Ultimate load analysis of structures | 357 |

Problems | 358 |

Structural dynamics | 362 |

103 Free vibration with one degree of freedom | 364 |

104 Forced vibration with one degree of freedom | 370 |

106 Forced vibration with many degrees of freedom | 390 |

107 Vibrations with infinite number of degrees of freedom | 392 |

Elasticity problems and the finite difference method | 397 |

112 Specification of stress at a point | 400 |

113 Boundary conditions | 404 |

115 Principal stresses | 410 |

116 Compatibility conditions | 414 |

118 SaintVenants principle | 415 |

1110 Principle of superposition | 418 |

1111 Torsion of noncircular shafts | 419 |

1112 Plane stress and plane strain problems | 426 |

1113 Bending of thin plates | 428 |

1114 Finite difference method | 433 |

1115 Truncation errors and finite difference operators for uneven mesh intervals | 450 |

Problems | 454 |

The finite element method | 458 |

122 Elastic continua | 460 |

123 Triangular elements for plane stress | 463 |

124 Rectangular elements for plane stress | 472 |

125 Transformation matrix | 475 |

126 Assembling the structure stiffness matrix | 478 |

127 Rectangular elements in bending | 480 |

128 Various elements for two and threedimensional analyses | 485 |

129 Computer flow charts | 489 |

Problems | 498 |

Computer application | 501 |

132 Flow chartelastic critical loads of plane frames | 507 |

133 Solving large sets of linear equations | 509 |

134 Use of banded nature of stiffness matrix | 514 |

135 Eigenvalues and eigenvectors | 517 |

136 Reduction in order of stiffness matrix use of substructures | 522 |

Plastic theory of structures | 525 |

142 The elasticplastic stressstrain relation | 526 |

144 Effect of axial load on plastic moment | 532 |

145 Effect of shear force on plastic moment | 534 |

146 Collapse loads and collapse mechanisms | 535 |

147 Combination of mechanisms | 555 |

148 Distributed load | 564 |

149 The fundamental theorems of plastic collapse | 570 |

1410 Incremental collapse and shakedown | 575 |

588 | |

Appendix 1 | 593 |

Appendix 2 | 600 |

601 | |

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### Common terms and phrases

1n Fig analysis applied loads assumed axial forces axial load axis beam bending moment diagram biharmonic equation calculated coefficients collapse mechanism column compressive considered constant coordinate axes corresponding cross-section curvature curve defined deformation degrees of freedom direction displacement function displacement vector distributed load eigenvalues eigenvectors elastic encastre equal equations equilibrium Example flexural rigidity flow chart force in member given by Eqn Hence horizontal influence line joint length linear magnitude matrix stiffness method mechanism in Fig member forces member stiffness modulus nodal displacements nodal forces nodes normal occur pin-jointed pinned plastic hinge portal frame positive Problem represents result rotation satisfied shear force shear stresses shown in Fig shows sign convention Similarly SOLUT1ON solution space truss span SrEP statically determinate Step stiffness equation stiffness matrix strain energy structure stiffness matrix strut symmetrical truss vertical x-direction zero