A collection of typical problems and solutions in strength of materials.

Translated from the Russian by Yuri Ermolyev

All credits to the original uploaders, this is an optimised pdf.

You can get the book here and here

Follow us on

Twitter https://x.com/MirTitles

Mastadon https://mastodon.social/@mirtitles

Bluesky https://bsky.app/profile/mirtitles.bsky.social

Tumblr https://www.tumblr.com/mirtitles

Internet Archive https://archive.org/details/mir-titles

Fork us on gitlab https://gitlab.com/mirtitles

CONTENTS

Notation 7

Units of Measurement 12

General Remarks on the Problems 13

Chapter 1. Tension and Compression
1.1. Axial Force 15
1.2. Normal Stresses, Total Elongation and Potential Energy 17
1.3. Lateral Deformation and Volume Change 19
1.4. Displacements of Points in Hinged-End Bar Systems 21
1.5. Strength and Stiffness 25
1.6. Taking the Dead Weight into Account 29
1.7. Statically Indeterminate Systems 32

Chapter 2. States of Stress and Strength Theories
2.1. Linear, Planar and Volumetric States of Stress 45
2.2. Strength Theories and Equivalent Stresses 51

Chapter 3. Thin-Walled Vessels 54

Chapter 4. Shear 61

Chapter 5. Design of Various Joints 63

Chapter 6. Geometrical Properties of Plane Figures
6.1. Static Moments of a Section 69
6.2. Moments of Inertia of the Area of a Section 71

Chapter 7. Torsion
7.1. Torque 80
7.2. Shearing Stresses, Angle of Twist and Elastic Strain Energy 82
7.3. Strength and Rigidity (Stiffness) 86
7.4. Statically Indeterminate Problems 91

Chapter 8. Transverse Bending
8.1. Transverse (Shearing) Force and Bending Moment 99
8.2. Normal Stresses and Selection of the Cross Section of Beams 118
8.3. Shearing Stresses, Shear Centre and Checking the Strength of Beams on the Basis of Shearing Stresses 127
8.4. Principal Stresses and Overall Checking of the Strength of Beams 136
8.5. Fundamentals of Limit Design for Beams 143
8.6. Displacements in Bending 146
8.7. Beams of Variable Cross Section 163
8.8. Statically Indeterminate Beams 172
8.9. Elastic Strain Energy in Bending 183

Chapter 9. Combined Strength of Straight Beams of High Rigidity
9.1. Oblique, or Unsymmetrical, Bending 206
9.2. Combined Tension or Compression and Bending 214
9.3. Combined Tension or Compression and Torsion 230
9.4. Combined Torsion and Bending 232
9.5. General Case of Combined Stress 244
9.6. Helical Extension or Compression Springs 252

Chapter 10. Lateral Deflection and Buckling of Columns
10.1. Critical Force and Critical Stress 258
10.2. Stability Calculations for Compressed Bars (Columns) 261
10.3. Bending Induced by Axial Loading 273

Chapter 11. Plane Curved Beams
11.1. Axial Force, Transverse (Shearing) Force and Bending Moment 279
11.2. Stresses 291
11.3. Strength Calculations 295

Chapter 12. Strain Energy Method of Designing Elastic Systems
12.1. Determining Elastic Generalized Displacements 299
12.2. Analysis of Statically Indeterminate Systems 317
12.3. Plane Thin-Walled Rings 332

Chapter 13. Thick-Walled Tubes
13.1. Cylindrical Tubes 357
13.2. Composite (Built-up) Cylindrical Tubes 363

Chapter 14. Dynamic Loads
14.1. Design of Moving Bodies (Systems) Taking Inertia into Account 370
14.2. Oscillations (Vibrations) of Elastic Bodies 379
14.3. Impact 401

Chapter 15. Alternating Stresses
15.1. Basic Factors Affecting the Fatigue Strength 420
15.2. Strength Analysis for a Uniaxial Stressed State and Pure Shear (Torsion) 424
15.3. Strength Analysis for a Complex Stressed State 430

Appendices 437

Answers to Problems 456