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 1,000 pounds. What is the value of the unit-stress ? Here P = 1,000 pounds, A= 2 square inches; hence.
1,000 S = = 500 pounds per square inch.
2. Suppose that the rod is one-half square inch in cross-sec tion. What is the value of the unit-stress ? • 1 A 2 --square inch, and, as before, P= 1,000 pounds; hence S = 1 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.
7. 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.
To find the value of a unit-deformation: Divide the whole deformation by the length over which it is distributed. Thus, if D denotes the value of a deformation, 1 the length, 8 the unit-deformation, then ' also D=78. (2) Both D and l should always be expressed in the same unit. Example. Suppose that a 4-foot rod is elongated I inch. What is the value of the unit-deformation? Here D=i inch, and /=4 feet=48 inches; hence inch per inch.
That is, each inch is elongated inch.
Unit-elongations are sometimes expressed in per cent. To express an elongation in per cent: Divide the elongation in inches by the original length in inehes,and multiply by 100.
We may classify bodies into kinds depending on the degree of elasticity which they have, thus: 1. Perfectly elastic bodies; these will regain their orig inal form and size no matter how large the applied forces are if less than breaking values. Strictly there are no such materials, but rubber, practically, is perfectly elastic.
2. Imperfectly elastic bodies; these will fully regain their original form and size if the applied forces are not too large, and piactically even if the loads are large but less than the breaking value. Most of the constructive materials belong to this class.
S. Inelastic or plastic bodies; these will not regain in the least their original form when the applied forces cease to act. Clay and putty are good examples of this class.
9. Hooke's Law, and Elastic Limit. If a gradually increas. ing force is applied to a perfectly elastic material, the deformation increases proportionally to the force; that is, if P and P denote two values of the force (or stress), and D and D' the values of the deformation produced by the force, This relation is also true for imperfectly elastic materials, provided that the loads P and P' do not exceed a certain limit depend ing on the material. Beyond this limit, the deformation increases much faster than the load; that is, if within the limit an addition of 1,000 pounds to the load produces a stretch of 0.01 inch, beyond the limit an equal addition produces a stretch larger and usually much larger than 0.01 inch.
Beyond this limit of proportionality a part of the deformation is permanent; that is, if the load is removed the body only partially recovers its form and size. The permanent part of a deformation is called set.
The fact that for most materials the deformation is propor tional to the load within certain limits, is known as Hooke's Law. The unit-stress within which Hooke's law holds, or above which the deformation is not proportional to the load or stress, is called limit.
so. Ultimate Strength. By ultimate tensile, compressive, or shearing strength of a material is meant the greatest tensile, compressive, or shearing unit-stress which it can withstand.