Introduction 173

1. Basic concepts and principles 175

1.2. Types of loads and deformations 177

1.3. Determining the internal forces by the method of sections. Stresses 177

2. Tension and compression of a bar 181

2.1. Stresses and a longitudinal deformation in tension and compression 181

2.2. Hooke^,s law in tension and compression 183

2.3. The transverse deformation in tension and compression 184

2.4. The tension diagram of the lowcarbon steel 184

2.5. The potential deformation energy in tension 187

2.6. Strength calculation in tension and compression 188

2.7. Statically indeterminate problems 189

2.8. Stresses at inclined sections under tension (compression) in one direction 193

2.9. Law of the shearing stresses couple 194

2.10. Determination of stresses at the inclined sections in tension (compression) in two directions 195

2.11. Determining the principal stresses and the principal planes position 197

2.12. The relation between the deformations and the stresses for the plane and general stresses (a general form of Hook^’s law) 198

2.13. The work of the external and internal forces in tension (compression). Strain energy 200

3. Geometric characteristics of cross sections 202

3.1. First moment of an area 202

3.2. Polar moment of inertia 204

3.3. Axial moment of inertia 205

3.4. The moment of inertia at parallel displacement of axis 206

3.5. Principal axes and principal moment of inertia 207

4. Torsion 208

4.1. Determining the twisting moment 208

4.2. Determining the stresses in the round section bar 211

4.3. The deformations and displacements in the shaft torsion 214

4.4. Internal strain energy in torsion 215

5. Bending of bars 216

5.1. Types of the beam support 216

5.2. Determining the support reactions 217

5.3. Determining the internal stresses in bending 218

5.4. The sign rule for the bending moments and the shearing forces 219

5.5. The differential relationships in bending 220

5.6. Drawing bending moment and shearing force diagrams 222

5.7. Determining the normal stress 223

5.8. Strength conditions with normal stresses 227

5.9. Strain energy in bending 229

5.10. Betty^’s reciprocal theorem. Reciprocal displacement theorem 229

5.11. Determining displacements by Mohr^’s method 232

6. strengtn theory 234

6.1. The purpose of strength hypotheses 234

6.2. The first strength hypothesis 236

6.3. The second and third strength hypotheses 236

6.4. The energy hypotheses of strength 237

7. Combined stress 238

7.1. Bending in two planes (non-uniplanar bending) 238

7.2. Combined axial tension (compression) and bending 242

7.3. Eceentrical tension (compression) 244

7.4. Combined torsion and bending 246

7.5. Combined torsion and compression 248

7.6. Example of the shaft calculation in bending with torsion 249

8. Calculation of the thin-walled vessels 251

9. stability analysis of the bars in compression (buckling) 255

9.1. Stable and unstable equilibrium forms 255

9.2. Euler^’s formula for the critical force 257

9.3. Influence of bar end conditions on the critical force 259

9.4. Applicability limits of of Euler^’s formula 261

9.5. Empirical formula for determining the critical stresses 262

9.6. The practical formula for the stability analysis 263

10. Dynamic load action 265

10.1. Dynamic load 265

10.2. Calculating stresses under the uniformly accelerated motion 266

10.3. Determining displacements and stresses under the impact 268

11. Stress analysis under the stresses changing cyclically in time 271

11.1. Basic definitions 271

11.2. Fatigue (Wohler^’s) curve under the symmetrical cycle. Fatigue strength 275

11.3. The limit stress diagram and the cycle amplitude 277

11.4. Factors influencing on the fatigue strength 280

11.5. Determining the factor of safety under the symmetrical cycle 284

11.6. Determining the factor of safety under the asymmetrical stress cycle 284

11.7. Practical measures to increase the fatigue strength 287

Practicum 290

Laboratory work № 1 290

Laboratory work № 2 304

Laboratory work № 3 314

Англо-русский терминологический словарь 321

Алфавитный указатель 400