# Engineering Mechanics Vol 1

Engineering Mechanics Volume 1 Equilibrium by C. Hartsuijker, J.W. Wellemen

**Contents of Engineering Mechanics Volume 1**

1 Introduction 1

1.1 Mechanics 1

1.2 Quantities, units, dimensions 8

1.3 Vectors 11

1.4 Newton’s Laws 18

2 Statics of a Particle 23

2.1 Coplanar forces 23

2.2 Forces in space 30

2.3 Equilibrium of a particle 35

2.4 Problems 39

3 Statics of a Rigid Body 51

3.1 Coplanar forces and moments 52

3.2 Equilibrium of a rigid body in a plane 71

3.3 Forces and moments in space 80

3.4 Equilibrium of a rigid body in space 93

3.5 Problems 99

4 Structures 111

4.1 Structural elements 113

4.2 Joints between structural elements 116

4.3 Supports 120

4.4 Planar structures 126

4.5 Kinematic/static (in)determinate structures 130

4.6 Problems 145

5 Calculating Support Reactions and Interaction Forces 153

5.1 Self-contained structures 154

5.2 Hinged beams 162

5.3 168

5.4 Three-hinged frames with tie-rod 173

5.5 Shored strucures 176

5.6 Trussed beams 184

5.7 Strengthened beams 186

5.8 Problems 190

6 Loads 205

6.1 Loads in mechanics 206

6.2 Loads in regulations 210

6.3 Working with distributed loads 219

6.4 Modelling load flow 231

6.5 Stress concept; normal stress and shear stress 233

6.6 Problems 236

7 Gas Pressure and Hydrostatic Pressure 245

7.1 Pascal’s law – All-round pressure 246

7.2 Working with gas pressures 248

7.3 Working with hydrostatic pressures 255

7.4 Summary 269

7.5 Problems 271

8 Earth Pressures 285

8.1 Stresses in soil 286

8.2 Vertical earth pressures 288

8.3 Horizontal earth pressures 292

Appendix 8.1 307

Appendix 8.2 308

8.4 Problems 309

9 Trusses 319

9.1 Plane trusses 321

9.2 Kinematically/statically (in)determinate trusses 328

9.3 Determining member forces 337

9.4 Problems 370

10 Section Forces 387

10.1 Force flow in a member 388

10.2 Diagrams for the normal force, shear force and

bending moment 401

10.3 Deformation symbols for shear forces and bending moments 416

10.4 Summary sign conventions for the N, V and M diagrams 420

10.5 Problems 421

11 Mathematical Description of the Relationship between

Section Forces and Loading 431

11.1 Differential equations for the equilibrium 432

11.2 Mathematical elaboration of the relationship between N

and qx (extension) 436

11.3 Mathematical elaboration of the relationship between M,

V and qz (bending) 441

11.4 Problems 456

12 Bending Moment, Shear Force and Normal Force

Diagrams 461

12.1 Rules for drawing V and M diagrams more quickly 462

12.2 Rules for drawing the N diagram more quickly 493

12.3 Bent and compound bar type structures 495

12.4 Principle of superposition 505

12.5 Schematisations and reality 508

12.6 Problems 517

13 Calculating M, V and N Diagrams 545

13.1 Self-contained structures 545

13.2 Compound and associated structures 586

13.3 Statically indeterminate structures 596

13.4 Problems 608

14 Cables, Lines of Force and Structural Shapes 631

14.1 Cables 632

14.2 Centre of force and line of force 674

14.3 Relationship between cable, line of force and structural shape 679

14.4 Problems 694

15 Virtual Work 709

15.1 Work and strain energy 710

ENGINEERING MECHANICS. VOLUME 1: EQUILIBRIUM

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Table of Contents vii

15.2 Virtual work equation for a particle 713

15.3 Virtual work equation for a rigid body 719

15.4 Virtual work equation for mechanisms 725

15.5 Calculating forces using virtual work 729

15.6 Problems 739

16 Influence Lines 743

16.1 Influence lines using equilibrium equations 744

16.2 Influence lines using virtual work 748

16.3 Working with influence lines 755

16.4 Problems

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