Bones - Biomechanics of the Human Body - page 113

a b

T

T

A A

T

T

Fig. 7.1 A cylinder is subject to ( a ) tensile stress and to ( b ) compressive stress that cause
elongation and shortening, respectively. Note that the change in the shape is exaggerated

7.3.1 Tensile Stress and Compressive Stress

Let us introduce here other forces that have not been discussed in Chap. 1 . They are
tension and compression exerted on the objects, as shown in Fig. 7.1 . Both consist
of two forces T of equal magnitude but with opposite direction that maintain the
object at rest, and thus there is neither translation nor rotation, since the necessary
and sufficient conditions for a body to be in equilibrium are obeyed. Tension causes
an extension of the bodies and compression, on the other hand, compresses the
body, shortening it slightly. Simultaneously with the elongation or the shortening, a
small, in general not noticeable, narrowing or widening of the bodies occurs. If the
elongation or the shortening is relatively small which is, in general, the case, we do
not have to consider the modifications in its cross-sectional area.
The stress

is defined as the ratio of the applied force called tension, T , divided
by the cross-sectional area, A :

σ

T
A :

σ ¼ (7.1)

The tension, T , is the magnitude of the force, either tensile or compressive, that
causes the deformation.
Hence, the unit of stress is N/m 2 , the same unit as pressure, which has the special
name of pascal (Pa) in the International System of Units. Let us denote tensile
stress,

σ c , for the applied force either of tension or
compression, respectively. In these cases the force is always applied longitudinally,
i.e., perpendicularly to the area, A .
Conceptually, pressure and stress are physically equal, with pressure more used
for fluids and stress for solids, chiefly by engineers who perform tests of material
strength. The concept of pressure has already been presented in Chap. 1 and its use
is easier and more intuitive since it is a part of our daily life. The concept of stress is
more general, on the other hand, since it includes tensile stress.

σ t , or compressive stress,