Fundamentals of Statics

Abstract

In this chapter, we give some fundamental knowledge on Statics. We will introduce three aspects: concept of force, axioms in Statics, and moment of a force. This is the beginning of Statics and the whole course.

Exercises

• 2.1 The figure is shown in Fig. 2.14. Determine the moment of the force F

  Fig. 2.14

  

  Moment of a force

  • (1) about point C

  • (2) about axis x

• 2.2 Determine the moments of the force about the following axes (as shown in Fig. 2.15):

  Fig. 2.15

  

  Moment of a force

  • (1) AB (2) CD (3) CG (4) CH (5) EG

• 2.3 Determine the total moments of all forces about point A (as shown in Fig. 2.16).

  Fig. 2.16

  

  Planar moment of a force

• 2.4 As shown in the Cartesian coordinate system in Fig. 2.17, there is a cuboid with the side length 1 cm. There is a force F = –4i + 5k (unit: N) applied at one corner. Please give the expressions of the moment of the force to z-axis, and the moment of the force to point O.

  Fig. 2.17

  

  A cuboid with one force

Answers

• 2.1 $(1)\;557.09\varvec{j} + 742.78\varvec{k}\,{\text{N}}\cdot{\text{m}}\;(2)\;1114.17\varvec{i}\,{\text{N}}\cdot{\text{m}}$

• 2.2 $(1)\;36\,{\text{kN}}\cdot{\text{m}}\;(2)\;36\,{\text{kN}}\cdot{\text{m}}\;(3)\;24\,{\text{kN}}\cdot{\text{m}}\;(4)\;0\,{\text{kN}}\cdot{\text{m}}\;(5)\;0\,{\text{kN}}\,{\text{m}}$

• 2.3 $M_{A} = 493.18\,{\text{kN}}\,{\text{m}}$

• 2.4 $M_{z} = 0,\;M_{O} = {-}0.09\varvec{j}\,{\text{N}}\cdot{\text{m}}$.