11.8 - Volume stress

Volume stress: A stress that

acts on the entire surface of

an object, changing its

volume.

Tensile stress results in a change along a single

dimension of an object. A volume stress is one that

exposes the entire surface of an object to a force. The

force is assumed to be perpendicular to the surface

and uniform at all points.

One way to exert volume stress on an object is to

submerge it in a fluid (a liquid or a gas). For example,

submersible craft that visit the wreck of the Titanic

travel four kilometers below the surface, experiencing

a huge amount of volume stress on their hulls.

In all cases, stress is force per unit area, which is also the definition of pressure. With

volume stresses, the term pressure is used explicitly, since the pressure of fluids is a

commonly measured property.

Volume strain is measured as a fractional change in the volume of an object. The

modulus of elasticity that relates volume stress and strain is called the bulk modulus,

and is represented with the letter B.

The equation in Equation 1 states that the change in pressure equals the bulk modulus

times the strain. The negative sign means that an increase in pressure results in a

decrease in volume. Unlike the equation for tensile stress, this equation does not have

an explicit term for area, because the pressure term already takes this factor into

account. Notice that the equation is stated in terms of the change in pressure.

At the right is a table that lists values for the bulk modulus for some materials. To give

you a sense of the deformation, the increase in pressure at 100 meters depth of water,

as compared to the surface, is about 1.0×10^6 N/m^2. The volume of water will be

reduced by 0.043% at this depth; steel, only 0.00063%.

At a depth of 11 km, approximately the maximum depth of the Earth’s oceans, the

increased pressure is 1.1×10^8 N/m^2. At this depth, a steel ball with a radius of 1.0 meter

will compress to a radius of 0.997 m.

The effect of volume stress on a Styrofoam cup submerged 7875 feet underwater

(with an un-stressed cup also shown for comparison). The stress on the cup

exceeded its elastic limit: It is permanently deformed.

Volume stress

Pressure of fluids alters volume

Stress: pressure (force per unit area)

Strain: fractional change in volume

Bulk modulus

Relates stress, strain

(^212) Copyright 2000-2007 Kinetic Books Co. Chapter 11