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6. Lawrance, A., Modern Inertial Technology-Navigation, Guidance, and Control, Springer-Verlag, New
York, 1993.
7. McConnell, K. G., Vibration Testing: Theory and Practice, New York: Wiley, 1995.
8. Machine Vibration: Dynamics and Control, London: Springler, 1992–1996.
9. Measuring Vibration, Bruel & Kjaer, 1982.
10. Sydenham, P. H., Hancock, N. H., and Thorn, R., Introduction to Measurement Science and Engi-
neering, New York: Wiley, 1989.
11. Tompkins, W. J. and Webster, J. G., Interfacing Sensors to the IBM PC, Englewood Cliffs, NJ: Prentice-
Hall, 1988.

19.3 Force Measurement

M. A. Elbestawi

Force, which is a vector quantity, can be defined as an action that will cause an acceleration or a certain
reaction of a body. This chapter will outline the methods that can be employed to determine the magnitude
of these forces.

General Considerations
The determination or measurement of forces must yield to the following considerations: if the forces
acting on a body do not produce any acceleration, they must form a system of forces in equilibrium. The
system is then considered to be in static equilibrium. The forces experienced by a body can be classified
into two categories: internal, where the individual particles of a body act on each other, and external
otherwise. If a body is supported by other bodies while subject to the action of forces, deformations
and/or displacements will be produced at the points of support or contact. The internal forces will be
distributed throughout the body until equilibrium is established, and then the body is said to be in a
state of tension, compression, or shear. In considering a body at a definite section, it is evident that all
the internal forces act in pairs, the two forces being equal and opposite, whereas the external forces act
singly.

Hooke’s Law
The basis for force measurement results from the physical behavior of a body under external forces.
Therefore, it is useful to review briefly the mechanical behavior of materials. When a metal is loaded in
uniaxial tension, uniaxial compression, or simple shear (Fig. 19.29), it will behave elastically until a critical
value of normal stress (S) or shear stress (τ) is reached, and then it will deform plastically [1]. In the

p p

F

p p
F
(a) (b) (c)

FIGURE 19.29 When a metal is loaded in uniaxial tension (a), uniaxial compression (b), or simple shear(c), it will
behave elastically until a critical value of normal stress or shear stress is reached.

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