Contents Preface v 1. Slope Deflection Method 1 1.1Introduction 1 1.2Assumptions 1 1.3Sign conventions 2 1.4Derivation of slope deflection equation 3 1.5Application of slope deflection equations 6 Continuous beams 6 Analysis of frames without sway 22 Analysis of frames with sway 31 Exercises 43 2. Moment Distribution Method 47 2.1 Introduction 47 2.2 Terminology 48 2.3 Sign Conventions 49 2.4 Expressions for carryover factor and stiffness 49 2.5 Expression for distribution factor 51 2.6 Application of moment distribution method to continuous beams with fixed ends 52 2.7 Continuous beams with simply supported ends 58 2.8 Continuous beams with sinking supports 66 2.9 Analysis of frames without sway 70 2.10 Analysis of frames with sway 79 2.11 Analysis of skew frames 93 Exercises 96 3. Kani's Method of Rotation Contribution 97 3.1 Introduction 97 3.2 Analysis of structures without relative displacement at ends 97 Application of Kani's method to continuous beams with fixed ends 100 Application to continous beams with simply supported and overhanging ends 105 3.3 Analysis of frames without lateral sway 115 3.4 Analysis of symmetric frames taking advantage of symmetry 119 Analysis of symmetric frames when line of symmetry passes through columns 120 Analy si s of symmetric frames when line of symmetry passes through mid span of beams 122 3.5 Analysis of structures with relative displacement at ends 126 Analysis of frames with sway when all columns in a storey have same height 126 Analysis of frames with sway when all columns in a storey have different height 138 Exercises 142 4. Column Analogy Method 147 4.1 Introduction 147 4.2 The column analogy 147 4.3 Sign convention 149 4.4 Stresses in a column 150 4.5 Application to beams 152 4.6 Application to symmetric frames 163 4.7 Application to closed frames 171 4.8 Application to unsymmetric frames 173 4.9 Stiffness and carry over factors of beams with variable cross-section 177 Exercises 183 5 Influence Line Diagrams for Statically Indeterminate Beams 187 5.1 Introduction 187 5.2 Muller-Breslau Principle 187 5.3 Usefulness of Muller-Breslau principle 190 Exercises 205 6. Analysis of Multistorey frames by Approximate Methods 207 6.1 Introduction 207 6.2 Substitute frame method 207 6.3 Analysis of multystorey frames for horizontal forces 214 Portal method 214 Cantilever method 216 Factor method 219 6.4 Comments on approximate methods for horizontal loads 223 Exercise 227 7. Two-hinged Arches 225 7.1 Introduction 225 7.2 Two-hinged arches 225 First theorem of Castigliano 226 Unit load method 226 7.3 Analysis of two-hinged circular arches 228 7.4Analysis of parabolic arches 241 7.5 Effect of yielding of supports 254 7.6Effect of shortening of rib 255 7.7Effect of temperature changes 257 7.8Tied arch 261 7.9Linear arch 264 7.10 Influence lines 266 ILD for horizontal thrust 266 ILD for bending moment at D 267 ILD for radial shear Q at D 268 ILD for normal thrust at D 268 Exercises 269 8. Fixed Arches 271 8.1 Introduction 271 8.2 Consistent deformation method 271 8.3 Elastic centre method 274 Symmetrically fixed arches 275 Unsymmetrically fixed arches 277 8.4Column analogy method 278 8.5Analysis of symmetric parabolic arches 279 8.6Analysis of unsymmetric parabolic arches 288 Exercises 294 9. Beams Curved in Plan 295 9.1 Introduction 295 9.2 Forces developed at a section in a curved beam 295 9.3 Torsion factor 296 9.4 Analysis of beams curved in plan 297 9.5 Circular arc cantilever 298 9.6 Semicircular beams fixed at two ends and subjected to central concentrated load W 302 9.7 Semicircular beam subject to UDL and simply supported by three columns spaced equality 306 9.8 Circular ring beams 309 Exercises 312 10 Unsymmetric Bending and Shear Centre 313 10.1 Introduction 313 10.2 Principal moment of inertia 314 10.3 Stresses in beams due to unsymmetric bending 322 10.4 Shear centre 329 10.5 Method of locating shear centre 330 Exercises 339 11 Matrix Method of Structural Analysis 343 11.1 Introduction 343 Different approaches to matrix method 344 11.2 Degree of static and kinematic in determinancy 344 11.3 Generalised co-ordinate systems 346 11.4 Flexibility matrix 347 11.5 Stiffness matrix 347 11.6 Relationship between flexibility and stiffness matrices 348 11.7 Flexibility matrix method 348 11.8 Stiffness matrix method 370 11.9 Analysis of pin-jointed frames by direct stiffness matrix method 389 Exercises 394 12 Introduction to Plastic Analysis 397 12.1 Introduction 397 12.2 Definitions of plastic hinge and plastic moment capacity 399 12.3 Assumptions 399 12.4 Shape factor 400 12.5 Shape factor for general sections 406 12.6 Collapse load 410 12.7 Basic theorems for finding collapse loads 411 12.8 Methods of plastic analysis 412 12.9 Statical method 412 12.10 Kinematic method 417 12.11 Kinematic method applied to beams 417 12.12 Kinematic method applied to frames 432 Beam mechanism 433 Sway mechanism 433 Combined mechanism 434 Exercises 447 Index 451