NOTES

2.1 INTRODUCTION

Statics, as well as whole study of mechanics, is the study about the actions of forces and force systems on bodies and the effects of these actions.  An understanding of the characteristics of force systems and specific methods to analyse them, forms the basis to master the study of mechanics.
In this chapter, we will study the action of forces and force systems commonly encountered in engineering analyses.  To facilitate the study, the chapter is divided into three parts: Part A deals with forces, Part B deals with moments, and Part C deals with equivalent force systems.

A: FORCES

2.1 ACTIONS AND EFFECTS OF FORCES

A force is defined as the action of a body on another body.  A force is applied either through a direct contact or through a remote action.  Forces applied through a remote action are gravitational, electrical, and magnetic forces.  All other forces are applied through direct contacts.
A force acting on a body produces effects that can be divided into two types, namely external effect and internal effect.
As an illustration, consider teh structure portrayed in Figure 2.1.  Assume that the structure is of negligible mass.  The applied force F acting on the structure causes the reactive forces R1 and R2 which are applied by the support surfaces onto the structure so as to balance F.  The reactions R1 and R2 are effects external to the body which are caused by F.  Hence, external forces acting on a body are of two types, namely applied external forces (also called active forces) and reactive forces.
Beside causing the reactions R1 and R2, the applied force F also causes effects internal to the members of the structure.  These effects are in the forms of stresses and strains that appear in the material of the sturcture. The effects exist to balance the respective external actions and effects.
In the study of mechanics, only the external effects of a force are considered.  The internal effects are studied in disciplines of study specific to them, for example Mechanics Of Materials (also known as Strength Of Materials).

2.3 FORCE DISTRIBUTION

Any force applied to a body will act on a finite area of application.  The force is distributed over the area of application.  In many cases, the area of application is extremely small compared to the dimensions of the body being upon acted by the force.  In such cases, the dimension of the area of distribution can be neglected and the area of application can be considered as a point.  A force acting on such a point of action is called a concentrated force.  The tension of the cable of the crane in Figure 2. 2(a) is a concentrated force.
If the dimension of the area of application of a force cannot be neglected, we obtain a distributed force which acts either a line, an area, or a volume.  The push of the wind acting on the sign board in Figure 2.2(b) ia a distributed force.
The effect of a distributed force depends on the nature of distribution of the force.  This will be studied in more details in Section 2.18 and in Chapter 6.

2.4 FORCE AS A VECTOR QUANTITY
A concentrated force is a vector quantity.  This has been determined through experiments which shows that concentrated forces add-up according to the parallelogram law and when a concentrated is applied to a body, the effect depends on the magnitude, direction, and point of application of the force.  Hence, mathematical analyses of a concentrated force is based on the mathematical rules of vectors (see Appendix).

MAGNITUDE AND DIRECTION OF A FORCE.  The magnitude of a force is a scalar quantity.  In the SI system, it is measured in the unit newton (N).  A force acting on a body is illustrated graphically by a vector arrow at the point of application of the force, where the orientation of the arrow represents the direction of the line of action of the force whilst the arrow head represents the sense of the force, Figure 2.3.  A force is fully defined once its magnitude, direction, sense, and point of application is specified.
The magnitude, direction, and sense of a force F can be represented fully by a mathematical expression using a unit vector s which corresponds to line of action and sense of the force.  For example, the force F in Figure 2.4 has a magnitude F.  Its direction of action corresponds to that of the unit vector s.  Hence F can be written as F=Fs.