gas, the volume is decreased, that is, its molecules are forced more closely together. If the pressure is reduced the volume is increased, i. e., the molecules move further apart than before. With gases, a slight pressure causes considerable change of volume, while in liquids and solids, the pressure must be very great in order to produce a perceptible change. If a bar of iron is fixed firmly at its upper end and a heavy weight is hung from the lower, the bar lengthens. If a weight is placed on the top of a block of wood or metal the block is shortened. In the above examples, the weight or force tends to change the shape or volume or both, and the forces within the body that tend to resist the change are called stresses. The word "stress" is also used as a name for the force. Engineers say that a body is strained or stressed when a load is placed upon it.

The weights or forces which act externally are also called stresses. Stresses, like forces, are measured in pounds, tons, grams, kilograms, etc. For example, if a weight of fifteen hundred pounds is suspended by a rope, the stress in the rope is fifteen hundred pounds. If a block of iron has a weight or force of forty tons on its top, the stress is forty tons. If the force tends to pull the particles of the body apart, it is called tensile stress, if it tends to crush the body, it is called compressive stress. The stress that resists two forces which tend to cut a body between them is called a shearing stress. There are other stresses; transverse, seen in the bending of beams, and torsional, a force that resists twisting, the propeller shaft of a marine engine, for instance. Of these stresses, Tensile, Compressive, and Shearing are called the simple stresses and are the only ones that will be considered here.

A Unit Stress, or unit strain, is the amount of stress on a unit area of section and is expressed as pounds per square inch, tons per square inch or per square foot, kilograms per square centimeter, etc. For example, if a block of cast iron has an area of three square inches and a stress of 15,000 pounds is applied to the upper surface, the stress per square inch will be 15.000 = 5,000 pounds per square inch. Let A equal the area in square inches, P the total stress in pounds, then the unit stress will be If S equals unit stress, we have the formulas,

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Α

Suppose a brick in a testing machine to crush at a stress of ten tons, the section of the brick being 2 X 4 inches. The unit compressive strain is

If a rope supports a weight of 314.16 pounds, the unit tensile strain being 400 pounds per square inch, what is the diameter of the rope?

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A = =
S

314.16
400

.7854 square inches.

Since the area is .7854 square inches, the diameter is one inch.

When a force or weight is applied to a bar or block, there is a change of form or volume. If the stress is tensile, the body lengthens, if it is compressive, the body shortens. This change of shape is called deformation and is measured in inches, centimeters, etc. This change of shape is also called strain. Strain is, however, an ambiguous term, being used by some as stress and by others as deformation. If we use the term strain, explanation will be given as to the meaning intended, by use of the terms stress or deformation. Unit deformation is the amount of lengthening or shortening per unit of length. Let L equal length in feet, b the elongation or shortening per unit of length, and B the total deformation, then evidently L X 6 B, or B = bL. If a bar of iron ten feet long lengthens .1 of an inch under a load of 20,000 pounds, the elongation per foot will be

If a small load is placed on a body, a slight change of shape will take place; if the load is removed the body will regain its original shape. This quality or property of returning to original shape on release of load is called elasticity.

Experiment shows that deformation is approximately proportional to the load, that is, within the elastic limit. If the load is increased, the deformation is also increased, that is, if a bar lengthens a given amount under a stress of 2,000 pounds, it will lengthen twice as much under a stress of 4,000 pounds and three

times as much under 6,000 pounds.

Deformation is also approximately proportional to length. If a block 6 inches long shortens .02 of an inch under 50,000 pounds, a similar block 12 inches long will shorten .04 of an inch under the same load.

If the stress is great and on removal, the body does not return to its original size and shape, the body has been deformed beyond its elastic limit and has been given a permanent set, or in other words the cohesive force of the molecules has been partially overcome. When the load is increased until the piece breaks,crushes, or shears, the breaking stress is reached and the force per unit of area applied at the moment of rupture is called the ultimate breaking strength.

Many experiments and tests have been made to determine the action and strength of different materials under various tensile and compressive stresses. The usual method is to place them in a testing machine and while the load is being gradually applied to carefully measure the deformation. By noting the load at the moment of rupture, the breaking strength is determined. By means of these experiments, together with experience, the following general laws applying to simple compression and tension have been established and may be taken as fundamental principles.

1. When a small stress is applied to a body, a small deformation is produced and on removal of the stress, the body returns to its original form. Materials may be regarded as perfectly elastic for small stresses.

2. Under small stresses, the deformations are nearly proportional to those stresses, and also approximately proportional to the length of the body.

3. When the stress is sufficiently great, a deformation is produced which is partly permanent, that is, the body does not spring back to its original shape when the stress or strain is removed. This permanent change of shape is called set or permanent set. In such cases, deformation is not proportional to stress. When the elastic limit is exceeded, deformation is not proportional to stress.

4. If the stress is still further increased, deformation increases until the piece breaks.

5. A sudden stress or shock is more injurious than a steady stress gradually applied.

The words small and great in the above laws have different values for different materials, that is, a large stress for wood would not be a large stress for steel.

The following table gives approximate constants for those materials in most common use:

According to the first law given above, materials are perfectly elastic for small stresses. When the load is large and the piece does not return to its original shape, it is said to have a permanent set. The unit stress at which permanent set is first visible is called the elastic limit.

The body being perfectly elastic within the elastic limit, laws describing its action can be formulated, but beyond the elastic limit, there being a permanent alteration of shape, these laws cannot be applied.

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In testing a specimen of any material, it is easy to reduce its stress to unit stress by the formula S = and its deformation to Α

unit deformation by the formula b =

B

Suppose the unit stress

L

and the unit deformation are known, the ratio of these is the Coefficient of Elasticity, that is, the ratio of the unit stress to the unit strain or deformation is the Coefficient of Elasticity or, expressed algebraically

For example, suppose the unit stress is 45,000 pounds and the unit deformation is .0015 inch. What is E?

A flat cast iron foundation ring, four inches high, whose area is 4 square feet, has a weight of 144 tons placed on the top. If the weight causes a shortening of .00016 of an inch, what is the Coefficient of Elasticity?

The Coefficient of Elasticity is also expressed, in the case of tension, as the unit stress which would elongate a bar to double its original length, provided this could be done without exceeding the elastic limit.

EXAMPLES FOR PRACTICE.

1. If a bar of steel is 8 inches long and 1 inch in diameter, and breaks under a load of 70,000 pounds, what is the unit breaking stress? Ans. 89,000 pounds (approx.) 2. If stone weighs 160 pounds per cubic foot and its ultimate compressive strength is 6000 pounds, how high must a tower be to crush under its own weight? Ans. 5409 feet.

3. Find the diameter of a round wrought iron bar, to stand a tensile stress of fifty tons. Breaking stress 50,000 pounds per square inch. Ans. 1.6-inches. 4. A tensile stress of 4500 pounds is applied to a wrought inch in diameter. Find the unit stress.

iron bar

Ans. 10,000 pounds (approx.) 5. Find the probable elongation of a wooden bar nine inches square and 12 feet long, under a tensile stress of 9000 pounds if the unit elongation is .008 inch. Ans. .096 inch.

6. A brick 2 x 4 x 8 inches is under a compressive stress of 24,000 pounds. If this stress is distributed uniformly over the surface, which is 2 X 4 inches, what is the unit stress?

Ans. 3000 pounds.