Visualizing Stress

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Stress Defined

Stress is conventionally defined as a force acting on some area (Figure1).

Figure 1. Stress is defined as a force (F) acting on some area (A).

Figure 1 illustrates a force, F, acting on area A. In the form of an equation this becomes

(1)

where s is stress. Newton's first and second laws of motion provide key ingredients for an understanding of force, the principal parameter in Equation (1).

Law 1. An object continues in its initial state of rest or motion with uniform velocity unless it is acted on by an unbalanced, or net external, force. The net force acting on an object, also called the resultant force, is the vector sum of all the forces acting on it (Tipler, 1976).

Mathematically, Law 1 can be expressed as

(2)

where Fnet represents the net force, and SF represents the vector sum of all of the forces acting on a given object.

Law 2. The acceleration of an object is inversely proportional to its mass and directly proportional to the net force acting on it (Tipler, 1976).

Mathematically, Law 2 can be expressed as

(3)

or, upon rearranging and isolating Fnet on the left-hand side, as

(4)

where a = acceleration and m = the mass of the object upon which the force is acting. Physicists define mass as an intrinsic property of an object that is a measure of its resistance to acceleration while acceleration is simply the change in velocity over a change in time (i.e. a=Dv/Dt) (Tipler, 1976). Thus, force is that which changes, or tends to change, the state of rest or the state of motion of a body or object.

Two of the more common units of force are the dyne (d) and Newton (N). The units of a Newton are kgm/s2 while those for a dyne are gcm/s2. A Newton then, is the force required to impart an acceleration of one meter per second per second to a body of one kilogram mass. In similar terms, a dyne is the force required to impart an acceleration of one centimeter per second per second to a body whose mass is one gram (Davis and Reynolds, 1996). The units of stress are simply N/m2 or d/cm2, or, as it turns outseveral other more complicated but equivalent terms. For example, shown in Table 1 are ten common units geologists use to describe the units of stress and the conversion factors that can be used to switch from one to another.

Units
MPa Equivalent
Megapascal (MPa)
1.000
Gigapascal (GPa)
0.001
Pascal (Pa)
1,000,000.000
N/m2
1,000,000.000
kg/cm2
10.197
d/cm2
100,000,000.000
Bar (b)
10.000
Kilobar (kb)
0.010
Pounds per square inch (psi)
145.030
Atmosphere (atm)
9.869

Table 1. Ten common units geologists use to describe stress equivalent to 1.000 Megapascal (MPa).

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