Preface |
|
xi | |
|
1 Revisionary mathematics |
|
|
1 | (20) |
|
|
2 | (1) |
|
|
2 | (1) |
|
1.3 Measurement of angles |
|
|
2 | (1) |
|
1.4 Trigonometry revision |
|
|
3 | (3) |
|
|
6 | (1) |
|
|
7 | (2) |
|
|
9 | (2) |
|
|
11 | (2) |
|
1.9 Simultaneous equations |
|
|
13 | (8) |
|
Revision Test 1 Revisionary mathematics |
|
|
17 | (2) |
|
Multiple-Choice Questions Test 1 |
|
|
19 | (2) |
|
2 Further revisionary mathematics |
|
|
21 | (32) |
|
2.1 Units, prefixes and engineering notation |
|
|
22 | (4) |
|
2.2 Metric-US/Imperial conversions |
|
|
26 | (4) |
|
|
30 | (2) |
|
2.4 Gradients, intercepts and equation of a graph |
|
|
32 | (3) |
|
2.5 Practical straight line graphs |
|
|
35 | (1) |
|
2.6 Introduction to calculus |
|
|
36 | (1) |
|
2.7 Basic differentiation revision |
|
|
36 | (2) |
|
2.8 Revision of integration |
|
|
38 | (2) |
|
|
40 | (2) |
|
2.10 Simple vector analysis |
|
|
42 | (11) |
|
Revision Test 2 Further revisionary mathematics |
|
|
45 | (2) |
|
Multiple-Choice Questions Test 2 |
|
|
47 | (2) |
|
Mathematics help -- some references |
|
|
49 | (2) |
|
Notation used in Mechanics of Solids |
|
|
51 | (2) |
|
|
53 | (36) |
|
3.1 Plane pin-jointed trusses |
|
|
54 | (1) |
|
3.2 Criterion for sufficiency of bracing |
|
|
55 | (1) |
|
3.3 Mathematics used in statics |
|
|
55 | (1) |
|
3.4 Equilibrium considerations |
|
|
56 | (11) |
|
3.5 Bending moment and shearing force |
|
|
67 | (1) |
|
|
68 | (1) |
|
|
69 | (1) |
|
3.8 Bending moment and shearing force diagrams |
|
|
70 | (4) |
|
3.9 Point of contraflexure |
|
|
74 | (4) |
|
3.10 Relationship between bending moment (M), shearing force (F) and intensity of load (w) |
|
|
78 | (3) |
|
|
81 | (6) |
|
|
87 | (2) |
|
|
89 | (22) |
|
|
90 | (1) |
|
|
91 | (1) |
|
4.3 Load-extension relationships |
|
|
91 | (2) |
|
|
93 | (1) |
|
|
93 | (3) |
|
4.6 Shear stress and shear strain |
|
|
96 | (2) |
|
|
98 | (1) |
|
|
98 | (1) |
|
4.9 Relationship between the material constants E, G, K and v |
|
|
99 | (1) |
|
4.10 Three-dimensional stress |
|
|
99 | (1) |
|
|
100 | (2) |
|
|
102 | (1) |
|
|
103 | (6) |
|
|
109 | (1) |
|
4.15 Failure due to creep |
|
|
110 | (1) |
|
5 Geometrical properties of symmetrical sections |
|
|
111 | (22) |
|
|
112 | (1) |
|
|
112 | (1) |
|
5.3 Second moment of area |
|
|
112 | (1) |
|
5.4 Polar second moment of area |
|
|
113 | (1) |
|
5.5 Parallel axis theorem |
|
|
113 | (1) |
|
5.6 Perpendicular axis theorem |
|
|
113 | (10) |
|
5.7 Calculation of I through numerical integration |
|
|
123 | (6) |
|
5.8 Computer program for calculating y and IXX |
|
|
129 | (1) |
|
5.9 Use of EXCEL spreadsheet in calculating geometrical properties of beams |
|
|
130 | (3) |
|
6 Bending stresses in beams |
|
|
133 | (18) |
|
|
134 | (1) |
|
6.2 Proof of σ/y = M/I=E/R |
|
|
134 | (2) |
|
6.3 Sectional modulus (Z) |
|
|
136 | (2) |
|
6.4 Anticlastic curvature |
|
|
138 | (1) |
|
|
139 | (3) |
|
|
142 | (3) |
|
6.7 Composite ship structures |
|
|
145 | (2) |
|
|
147 | (1) |
|
6.9 Combined bending and direct stress |
|
|
147 | (4) |
|
7 Beam deflections due to bending |
|
|
151 | (18) |
|
|
152 | (1) |
|
7.2 Repeated integration method |
|
|
152 | (5) |
|
|
157 | (4) |
|
7.4 Statically indeterminate beams |
|
|
161 | (4) |
|
|
165 | (1) |
|
7.6 Slope-deflection equations |
|
|
166 | (3) |
|
|
169 | (32) |
|
|
170 | (1) |
|
|
170 | (1) |
|
8.3 Assumptions made in circular shaft theory |
|
|
170 | (1) |
|
8.4 Proof of τ/r =T/J = Gθ/1 |
|
|
170 | (3) |
|
|
173 | (2) |
|
|
175 | (1) |
|
|
176 | (4) |
|
|
180 | (1) |
|
8.9 Close-coiled helical springs |
|
|
180 | (1) |
|
8.10 Torsion of thin-walled non-circular sections |
|
|
181 | (1) |
|
8.11 Torsion of thin-walled rectangular sections |
|
|
182 | (1) |
|
8.12 Torsion of thin-walled open sections |
|
|
183 | (1) |
|
8.13 Elastic-plastic torsion of circular-section shafts |
|
|
184 | (17) |
|
Multiple-Choice Questions Test 3 |
|
|
191 | (4) |
|
Revision Test 3 Specimen examination questions for Chapters 3 to 8 |
|
|
195 | (2) |
|
Multiple-Choice Questions Test 4 |
|
|
197 | (4) |
|
9 Complex stress and strain |
|
|
201 | (30) |
|
|
202 | (1) |
|
9.2 To obtain σθ in terms of the co-ordinate stresses |
|
|
202 | (1) |
|
9.3 Principal stresses (σ1 and σ2) |
|
|
203 | (2) |
|
|
205 | (3) |
|
9.5 Combined bending and torsion |
|
|
208 | (3) |
|
9.6 Two-dimensional strain systems |
|
|
211 | (2) |
|
9.7 Principal strains (ε, and ε2) |
|
|
213 | (2) |
|
9.8 Mohr's circle of strain |
|
|
215 | (1) |
|
9.9 Stress-strain relationships for plane stress |
|
|
215 | (1) |
|
9.10 Stress-strain relationships for plane strain |
|
|
216 | (1) |
|
|
216 | (4) |
|
|
220 | (7) |
|
9.13 Computer program for principal stresses and strains |
|
|
227 | (1) |
|
9.14 The constitutive laws for a lamina of a composite in global co-ordinates |
|
|
228 | (3) |
|
10 Membrane theory for thin-walled circular cylinders and spheres |
|
|
231 | (12) |
|
|
232 | (1) |
|
10.2 Is it possible for humans to inhabit the moon? |
|
|
232 | (1) |
|
10.3 Circular cylindrical shells under uniform internal pressure |
|
|
233 | (2) |
|
10.4 Thin-walled spherical shells under uniform internal pressure |
|
|
235 | (5) |
|
10.5 Bending stresses in circular cylinders under uniform pressure |
|
|
240 | (1) |
|
10.6 Circular cylindrical shell with hemispherical ends |
|
|
241 | (2) |
|
|
243 | (40) |
|
|
244 | (1) |
|
11.2 The method of minimum potential (Rayleigh-Ritz) |
|
|
244 | (1) |
|
11.3 The principle of virtual work |
|
|
244 | (1) |
|
11.4 The principle of complementary virtual work |
|
|
245 | (1) |
|
11.5 Castigliano's first theorem |
|
|
245 | (1) |
|
11.6 Castigliano's second theorem |
|
|
245 | (1) |
|
11.7 Strain energy stored in a rod under axial loading |
|
|
246 | (1) |
|
11.8 Strain energy stored in a beam subjected to couples of magnitude Matits ends |
|
|
247 | (1) |
|
11.9 Strain energy due to a torque T stored in a uniform circular-section shaft |
|
|
247 | (4) |
|
11.10 Deflection of thin curved beams |
|
|
251 | (10) |
|
|
261 | (7) |
|
11.12 Suddenly applied and impact loads |
|
|
268 | (1) |
|
|
269 | (5) |
|
11.14 Plastic collapse of beams |
|
|
274 | (4) |
|
11.15 Residual stresses in beams |
|
|
278 | (5) |
|
12 Theories of elastic failure |
|
|
283 | (12) |
|
|
284 | (1) |
|
12.2 Maximum principal stress theory (Rankine) |
|
|
284 | (1) |
|
12.3 Maximum principal strain theory (St Venant) |
|
|
284 | (1) |
|
12.4 Total strain energy theory (Beltrami and Haigh) |
|
|
285 | (1) |
|
12.5 Maximum shear stress theory (Tresca) |
|
|
286 | (1) |
|
12.6 Maximum shear strain energy theory (Hencky and von Mises) |
|
|
286 | (2) |
|
|
288 | (5) |
|
|
293 | (2) |
|
13 Thick cylinders and spheres |
|
|
295 | (24) |
|
|
296 | (1) |
|
13.2 Derivation of the hoop and radial stress equations for a thick-walled cylinder |
|
|
296 | (2) |
|
|
298 | (4) |
|
|
302 | (5) |
|
13.5 Plastic yielding of thick tubes |
|
|
307 | (4) |
|
13.6 Thick spherical shells |
|
|
311 | (2) |
|
|
313 | (2) |
|
13.8 Plastic collapse of discs |
|
|
315 | (1) |
|
|
316 | (1) |
|
13.10 Design of the `Trieste' to conquer the Mariana Trench |
|
|
316 | (3) |
|
14 The buckling of struts |
|
|
319 | (18) |
|
|
320 | (1) |
|
14.2 Axially loaded struts |
|
|
320 | (1) |
|
14.3 Elastic instability of very long slender struts |
|
|
320 | (3) |
|
14.4 Struts with various boundary conditions |
|
|
323 | (1) |
|
14.5 Limit of application of Euler theory |
|
|
324 | (1) |
|
14.6 Rankine-Gordon formula for struts buckling inelastically |
|
|
324 | (2) |
|
14.7 Effects of geometrical imperfections |
|
|
326 | (1) |
|
14.8 Eccentrically loaded struts |
|
|
327 | (4) |
|
14.9 Struts with initial curvature |
|
|
331 | (2) |
|
14.10 Perry-Robertson formula |
|
|
333 | (2) |
|
14.11 Dynamic instability |
|
|
335 | (2) |
|
15 Asymmetrical bending of beams |
|
|
337 | (16) |
|
|
338 | (1) |
|
15.2 Symmetrical-section beams loaded asymmetrically |
|
|
338 | (1) |
|
15.3 Asymmetrical sections |
|
|
339 | (1) |
|
|
340 | (1) |
|
15.5 Principal axes of bending |
|
|
341 | (2) |
|
15.6 Mohr's circle of inertia |
|
|
343 | (5) |
|
15.7 Stresses in beams of asymmetrical section |
|
|
348 | (5) |
|
16 Shear stresses in bending and shear deflections |
|
|
353 | (20) |
|
|
354 | (1) |
|
16.2 Vertical shearing stresses |
|
|
354 | (1) |
|
16.3 Horizontal shearing stresses |
|
|
355 | (8) |
|
|
363 | (4) |
|
16.5 Shear centre positions for closed thin-walled tubes |
|
|
367 | (2) |
|
|
369 | (3) |
|
|
372 | (1) |
|
17 Experimental strain analysis |
|
|
373 | (16) |
|
|
374 | (1) |
|
17.2 Electrical resistance strain gauges |
|
|
374 | (1) |
|
17.3 Types of electrical resistance strain gauge |
|
|
375 | (1) |
|
|
376 | (1) |
|
|
376 | (1) |
|
|
377 | (1) |
|
|
378 | (1) |
|
|
378 | (2) |
|
|
380 | (2) |
|
|
382 | (1) |
|
17.11 Brittle lacquer techniques |
|
|
383 | (1) |
|
17.12 Semiconductor strain gauges |
|
|
383 | (1) |
|
|
383 | (6) |
|
Revision Test 4 Specimen examination questions for Chapters 9 to 17 |
|
|
385 | (4) |
|
18 An introduction to matrix algebra |
|
|
389 | (10) |
|
|
390 | (1) |
|
18.2 Elementary matrix algebra |
|
|
390 | (1) |
|
18.3 Addition and subtraction of matrices |
|
|
391 | (1) |
|
18.4 Matrix multiplication |
|
|
391 | (2) |
|
18.5 Two by two determinants |
|
|
393 | (1) |
|
18.6 Three by three determinants |
|
|
394 | (5) |
|
Multiple-Choice Questions Test 5 |
|
|
397 | (2) |
|
|
399 | (16) |
|
19.1 A comparison of mechanical properties of materials |
|
|
400 | (1) |
|
19.2 Matrix equations for composites |
|
|
400 | (1) |
|
19.3 Derivation of the stiffness matrix (Q) and (S)-1 for isotropic materials |
|
|
401 | (2) |
|
19.4 Compliance matrix (S) for an orthotropic ply or sheet or layer |
|
|
403 | (4) |
|
19.5 Derivation of the stiffness matrix (Q) for orthotropic materials |
|
|
407 | (1) |
|
19.6 An orthotropic ply with off-axis loading |
|
|
407 | (2) |
|
19.7 A laminate or ply based on orthotropic plies with off-axis loading |
|
|
409 | (1) |
|
19.8 Failure criteria for composite materials |
|
|
410 | (5) |
|
20 The matrix displacement method |
|
|
415 | (20) |
|
|
416 | (1) |
|
20.2 The matrix displacement method |
|
|
416 | (1) |
|
20.3 The structural stiffness matrix (K) |
|
|
417 | (1) |
|
20.4 Elemental stiffness matrix for a plane rod |
|
|
418 | (3) |
|
|
421 | (6) |
|
20.6 Analysis of pin-jointed trusses on SmartPhones, tablets and Microsoft computers |
|
|
427 | (2) |
|
20.7 Analysis of continuous beams on SmartPhones, tablets and Microsoft computers |
|
|
429 | (3) |
|
20.8 Analysis of rigid-jointed plane frames on SmartPhones, tablets and Microsoft computers |
|
|
432 | (3) |
|
21 The finite element method |
|
|
435 | (12) |
|
|
436 | (1) |
|
21.2 Stiffness matrix for the in-plane triangular element |
|
|
436 | (4) |
|
21.3 Stiffness matrix for a three node rod element |
|
|
440 | (7) |
|
Revision Test 5 Specimen examination questions for Chapters 19 to 21 |
|
|
443 | (4) |
|
22 An introduction to linear elastic fracture mechanics |
|
|
447 | (20) |
|
|
448 | (1) |
|
22.2 Basis of fracture mechanics theory |
|
|
448 | (1) |
|
22.3 Strain energy release and crack propagation |
|
|
448 | (3) |
|
22.4 Energy balance approach |
|
|
451 | (3) |
|
22.5 The stress intensity approach |
|
|
454 | (1) |
|
22.6 Plane stress and plane strain |
|
|
455 | (1) |
|
22.7 Plane stress and plain strain behaviour |
|
|
455 | (1) |
|
22.8 Allowance for small scale yielding at crack tip |
|
|
456 | (1) |
|
22.9 Fracture toughness crack tip opening displacement (CTOD) |
|
|
457 | (3) |
|
22.10 Application of fracture mechanics to fatigue crack growth |
|
|
460 | (2) |
|
|
462 | (2) |
|
22.12 Crack extension resistance curves (R-curves) |
|
|
464 | (3) |
|
23 Material property considerations |
|
|
467 | (22) |
|
|
468 | (1) |
|
23.2 Fatigue and the effects of cyclic loading |
|
|
468 | (2) |
|
23.3 Design against fatigue |
|
|
470 | (2) |
|
23.4 Mean stress and fatigue |
|
|
472 | (2) |
|
23.5 Further applications of Goodman diagrams |
|
|
474 | (1) |
|
23.6 Varying stress amplitudes and fatigue |
|
|
475 | (2) |
|
23.7 The effects of surface treatment and surface finish on fatigue |
|
|
477 | (1) |
|
23.8 Corrosion and fatigue |
|
|
477 | (1) |
|
23.9 Creep -- the effects of high temperature |
|
|
477 | (1) |
|
|
478 | (1) |
|
23.11 Extrapolation of creep data |
|
|
479 | (6) |
|
23.12 Effect of restraint -- creep relaxation |
|
|
485 | (4) |
A revisionary list of formulae for Mechanics of Solids |
|
489 | (7) |
Answers to multiple-choice questions |
|
496 | (1) |
References |
|
497 | (2) |
Index |
|
499 | |