I. Stress. When forces are applied to a body they tend in a greater or less degree to break it. Preventing or tending to prevent the rupture, there arise, generally, forces between every two adjacent parts of the body. Thus, when a load is suspended by means of an iron rod, the rod is subjected to a downward pull at its lower end and to an upward pull at its upper end, and these two forces tend to pull it apart. At any cross-section of the rod the iron on either side "holds fast" to that on the other, and these forces which the parts of the rod exert upon each other prevent the tearing of the rod. For example, in Fig. 1, let a represent the rod and its suspended load, 1,000 pounds; then the pull on the lower end equals 1,000 pounds. If we neglect the weight of the rod, the pull on the upper end is also 1,000 pounds, as shown in Fig. 1 (b); and the upper part A exerts on the lower part B an upward pull Q equal to 1,000 pounds, while the lower part exerts on the upper a force P also equal to 1,000 pounds. These two forces, P and Q, prevent rupture of the rod at the "section" C; at any other section there are two forces like P and Q preventing rupture at that section.

By stress at a section of a body is meant the force which the part of the body on either side of the section exerts on the other. Thus, the stress at the section C (Fig. 1) is P (or Q), and it equals 1,000 pounds.

a. Stresses are usually expressed (in America) in pounds, sometimes in tons. Thus the stress P in the preceding article is

Strength Of Materials Simple Stress 03006

Fig. 1.

1.000 pounds, or ton. Notice that this value has nothing to do with the size of the cross-section on which the stress acts.

3. Kinds of Stress, (a) When the forces acting on a body (as a rope or rod) are such that they tend to tear it, the stress at any cross-section is called a tension or a tensile stress. The stresses P and Q, of Fig. 1, are tensile stresses. Stretched ropes, loaded "tie rods" of roofs and bridges, etc., are under tensile stress. (b.) "When the forces acting on a body (as a short post, brick, etc.) are such that they tend to crush it, the stress at any section at right angles to the direction of the crushing forces is called a pressure or a compres-sive stress. Fig. 2 (a) represents a loaded post, and Fig. 2 (b) the upper and lower parts. The upper part presses down on B, and the lower part presses up on A, as shown. P or Q is the compressive stress in the post at section C. Loaded posts, or struts, piers, etc., are under compressive stress.

(c.) When the forces acting on a body (as a rivet in a bridge joint) are such that they tend to cut or "shear" it across, the stress at a section along which there is a tendency to cut is called a shear or a shearing stress. This kind of stress takes its name from the act of cutting with a pair of shears. In a material which is being cut in this way, the stresses that are being "overcome" are shearing stresses. Fig. 3 (a) represents a riveted joint, and Fig. 3 (b) two parts of the rivet. The forces applied to the joint are such that A tends to slide to the left, and B to the right; then B exerts on A a force P toward the right, and A on B a force Q toward the left as shown. P or Q is the shearing stress in the rivet.

Tensions, Compressions and Shears are called simple stresses. "Forces may act upon a body so as to produce a combination of simple stresses on some section; such a combination is called a complex stress. The stresses in beams are usually complex. There are other terms used to describe stress; they will be defined farther on.

Strength Of Materials Simple Stress 03007

Fig. 2.

4. Unit=Stress. It is often necessary to specify not merely the amount of the entire stress which acts on an area, but also the amount which acts on each unit of area (square inch for example). By unit-stress is meant stress per unit area.

To find the value of a unit-stress: Divide the whole stress by the whole area of the section on which it acts, or over which it is distributed. Thus, let

P denote the value of the whole stress,

A the area on which it acts, and

S the value of the unit-stress; then

S = P/A, also P = AS.

(I)

Strictly these formulas apply only when the stress P is uniform, that is, when it is uniformly distributed over the area, each square inch for example sustaining the same amount of stress. When the stress is not uniform, that is, when the stresses on different square inches are not equal, then PA equals the average value of the unit-stress.

Strength Of Materials Simple Stress 03008

Fig. 3.

5. Unit-stresses are usually expressed (in America) in pounds per square inch, sometimes in tons per square inch. If P and A in equation 1 are expressed in pounds and square inches respectively, then S will be in pounds per square inch; and if P and A are expressed in tons and square inches, S will be in tons per square inch.

Examples. 1. Suppose that the rod sustaining the load in Fig. 1 is 2 square inches in cross-section, and that the load weighs l000 pounds. What is the value of the unit-stress ?

Here P = 1,000 pounds, A= 2 square inches; hence.

S = 1,000/ 2 = 500 pounds per square inch.

2. Suppose that the rod is one-half square inch in cross-section. What is the value of the unit-stress?

A = square inch, and, as before, P = 1,000 pounds; hence S = 1,000 = 2,000 pounds per square inch.

Notice that one must always divide the whole stress by the area to get the unit-stress, whether the area is greater or less than one.

6. Deformation. "Whenever forces are applied to a body it changes in size, and usually in shape also. This change of size and shape is called deformation. Deformations are usually measured in inches; thus, if a rod is stretched 2 inches, the "elongation" = 2 inches.

7. Unit-Deformation. It is sometimes necessary to specify not merely the value of a total deformation but its amount per unit length of the deformed body. Deformation per unit length of the deformed body is called unit-deformation.