Biomechanics: Concepts and Computation
Using a quantitative biomechanics approach, this book integrates both general and specific topics, theoretical background and biomedical engineering applications, as well as analytical and numerical approaches.
TABLE OF CONTENTS Biomechanics: Concepts and Computation
Chapter 3: Static Equilibrium
3.1 Introduction
According to Newton s law the acceleration of the centroid of a body multiplied by its mass equals the total force applied to the body and there will be a spin around the centroid, when there is a resulting moment with respect to the centroid. But in many cases bodies do not move at all when forces are applied to them. In that case the bodies are in static equilibrium. A simple example is given in Fig. 3.1. In Fig. 3.1(a) a body is loaded by two forces of equal size but with an opposite direction. The lines-of-action of the two forces coincide and clearly the body is in equilibrium. If the lines-of-action do not coincide, as in Fig. 3.1(b), the forces have a resulting moment and the body will rotate. To enforce static equilibrium a counteracting moment should be applied to prevent the body rotating, as indicated in Fig. 3.1(c).
Figure 3.1: Examples of satisfaction and violation of static equilibrium.
3.2 Static Equilibrium Conditions
If a body moves monotonously (no acceleration of the centroid, no rate of rotation around the centroid), the body is in static equilibrium. If the velocities are zero as well, the body is at rest. In both cases the sum of all forces and the sum of all moments (with respect to any point) acting on the body are zero. Suppose that n forces 
( i = 1, 2, , n) are applied to the body. Each of...
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