... of a body

By applying equilibrium to the free-body diagram of a body you can find unknown forces and moments which prevent motion (translation and rotation). The concept of equilibrium of a body is treated in chapter 3.1.1 of the book Engineering Mechanics Volume 1 Hartsuijker & Welleman, 2006. At maximum three unknown forces (of which maximum one couple) can be solved in a planar problem and six forces in a threedimensional problem. The steps involved are:

1. Draw a free body diagram of the body
2. Split the forces in convenient directions by applying resolution of forces
3. Solve the forces and moments using $\sum F = 0$ in two nonparallel convenient directions and ${\left. {\sum T } \right|_x} = 0$ for any arbitrary points $x$ as treated in chapter 3.1.5 of the book Engineering Mechanics Volume 1 Hartsuijker & Welleman, 2006. For threedimensional problem, moments are taken around a line as treated in chapter 3.3.2. The full procedure for planar problems is shown in chapter 3.2 and for threedimensional problems in chapter 3.4.

Exercises¶

• If you’re a TU Delft student, you can practise with the following exercises on planar problems
• Exercises in chapter 3.5 of the book Engineering Mechanics Volume 1 Hartsuijker & Welleman, 2006, answers are available on this website:
  • Moment of a force around a point: 3.6 - 3.8b
  • Equilibrium for planar problems 3.19, 3.20, 3.32 - 3.46