STRENGTH OF MATERIALS.

GENERAL PRINCIPLES.

1. When a force is applied to a body, it changes either its form or its volume. A force, when considered with reference to the internal changes it tends to produce in any solid, is called a stress.

Thus, if we suspend a weight of 2 tons by a rod, the stress in the rod is 2 tons. This stress is accompanied by a lengthening of the rod, which increases until the internal stress or resistance is in equilibrium with the external weight.

2. Classification of Stresses.-Stresses may be classified as follows: Tensile, or pulling stress; transverse, or bending stress; compressive, or pushing stress; shearing, or cutting stress; torsional, or twisting stress.

3. A unit stress is the amount of stress on a unit of area, and may be expressed either in pounds or tons per square inch or per square foot; or, it is the load per square inch or per square foot on any body.

Thus, if 10 tons are suspended by a wrought-iron bar that has an area of 5 square inches, the unit stress is 2 tons per square inch, because 10 = 2 tons.

4. Strain is the deformation or change of shape of a body resulting from stress.

For example, if a rod 100 feet long is pulled in the direction of its length, and if it is lengthened 1 foot, it is strained. its length, or 1 per cent.

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5. Elasticity is the property by virtue of which a body regains its original form after the external force on it is withdrawn, provided the stress has not exceeded the elastic limit. It is a property possessed by all bodies.

Consequently, we see from this that all material is lengthened or shortened when subjected to either tensile or compressive stress, and the change of the length within the elastic limit is directly proportional to the stress.

For stresses within the elastic limits, materials are perfectly elastic, and return to their original length on removal of the stresses; but when their elastic limits are exceeded, the changes of their lengths are no longer regular, and a permanent set takes place. The destruction of the material has then begun.

6. The measure of elasticity of any material is the change of length under stress within the elastic limit.

7. The elastic limit is that unit stress under which the permanent set becomes visible.

8. The elasticity of wrought iron and of all grades of steel is practically the same; that is, within the elastic limit each material will change an equal amount of length under the same stress. The elastic limit, however, is not the same for steel as for iron; it is higher for soft steel than for wrought iron, and, in general, the harder and stronger the steel the higher will be its elastic limit. As a consequence, steel will lengthen or shorten more than wrought iron, and hard steel more than soft, before its elasticity or ability to return to its original dimensions is injured.

TENSILE STRENGTH OF MATERIALS. 9. The tensile strength of any material is the resistance offered by its fibers to being pulled apart.

10. The tensile strength of any material is proportional to the area of its cross-section.

Consequently, when it is required to find the safe tensile strength of any material, we have only to find the area at the minimum cross-section of the body, and multiply it by the load per square inch that it can safely carry, as given in the following table under the heading "Safe Loads."

NOTE. The minimum cross-section referred to in the above paragraph is that section of the material which is pierced with holes, such as bolt or rivet holes in iron, or knots in wood, if there are any.

11. In metals, a high tensile strength in itself is no indication of the ability of the metal to stand repeated applications of sudden stresses, as a high tensile strength usually involves a lesser degree of ductility than is obtained in metals of lower tensile strength. Steel of a tensile strength higher than 75,000 pounds is seldom used merely on account of its superior strength, but rather on account of its hardness, which enables it to better withstand abrasion.

12. The loads given in Table I are conservative safe loads deducted from experience and observation. They are given for material free from welds for such material as can be welded. While it is possible to make a weld as strong as the solid bar, the chances of the weld being imperfect are so great that it is unsafe to rely on such a degree of strength in welded bars. Furthermore, the value of the weld is an uncertain quantity that cannot be determined by an ocular inspection or any other inspection short of actually pulling the weld apart in a testing machine. Hence, it is advisable to reduce the safe loads given in the above table by 25 per cent. when a welded bar is subjected to a tensile stress. When judging the safe load of timber, due allowance must be made for knot holes and sappy spots.

13. It is often rather hard to determine whether a stress is steady, gradually varying, or gradually applied, or sudden. For example, considering the shell of a boiler, it would appear on first thought as though the tensile stress in the shell plates was a steady stress. But looking further into the problem, it will become apparent that the stress varies with the steam pressure, which gradually fluctuates within narrow or wider limits. Hence, most designers would consider the stress in a boiler shell as a gradually applied stress. In a piston rod or connecting-rod the load is applied almost instantly as soon as the crank passes over the center, and, hence, the stress would be considered to be a suddenly applied stress. When in doubt, it is good policy to err on the side of safety, that is, to choose a smaller safe load per square inch of section.

For special work, experience has indicated safe loads for different materials that fall below, or are above, those given in the table. Examples of this will be given later on.

14. The safe load per square inch of section is often called the working stress per square inch, or the working load per square inch. Care should be taken not to confound these terms with working load, working stress, safe load, or safe tensile strength, which, when applied without the limitation as to the unit of area, refer to the safe load the whole bar can carry.

RULES AND FORMULAS FOR TENSILE STRENGTH. 15. Let W= safe load in pounds;

A

S

=

area of minimum cross-section;

working stress in pounds per square inch, as given in Table I.

Rule 1.-The working load in pounds for any bar subjected to a tensile stress is equal to the minimum sectional area of the bar, multiplied by the working stress in pounds per square inch, as given in the table.

EXAMPLE.-A bar of good wrought iron that is 3 inches square is to be subjected to a steady tensile stress; what is the maximum load that it should carry?

SOLUTION-According to the table, a working stress of 13,000 pounds may be allowed. Applying the rule, we have

W = 3 × 3 × 13,000 = 117,000 lb. Ans.

Rule 2.-The minimum sectional area of any bar subjected to a tensile stress should be equal to the load in pounds, divided by the working stress in pounds per square inch, as given in the table.