The following is a table of factors of safety* which will be used in the problems: They must be regarded as average values and are not to be adopted in every case in practice.
Examples. 1. A wrought-iron rod 1 inch in diameter sus tains a load of 30,000 pounds. What is its working stress? If its ultimate strength is 50,000 pounds per square inch, what is its factor of safety ? The area of the cross-section of the rod equals 0.7854 X (diam eter)s=0.7854 X square inches. Since. the whole stress on the cross-section is 30,000 pounds, equation 1 gives for the unit working stress 30,000 = 38 pounds per square inch.
= 0.7854 Equation 3 gives for factor of safety 50,000 Q = 2. How large a steel bar or rod is needed to sustain a steady pull of 100,000 pounds if the ultimate strength of the material is 65,000 pounds ? The load being steady, we use a factor of safety of 5 (see table above); hence the working strength to be used (see equation 3) is S = 13,000 pounds per square inch.
The proper area of the cross-section of the rod can now be com puted from equation 1 thus: *Taken from Merriman's "Mechanics of Materials.' A bar 2 X 4 inches in cross-section would be a little stronger than necessary. To find the diameter (d) of a round rod of suffi
cient strength, we write 0.7854 7.692, and solve the equation for d; thus: 7.692 9.794, or d = 3.129 inches.
3. How large a steady load can a short timber post safely sus tain if it is 10 X 10 inches in cross-section and its ultimate com pressive strength is 10,000 pounds per square inch ? According to the table (page 12) the proper factor of safety is 8, and hence the working strength according to equation 3 is 10,000 8 =1,250 pounds per square inch.
The area of the cross-section is 100 square inches; hence the safe load (see equation 1) is P =-- 100 X 1,250 125,000 pounds.
4. When a hole is punched through a plate the shearing strength of the material has to be overcome. If the ultimate shear ing strength is 50,000 pounds per square inch, the thickness of the plate inch, and the diameter of the hole 4inch, what is the value of the force to be overcome ? The area shorn is that of the cylindrical surface of the hole or the metal punched out; that is 3.1410 x diameter X thickness --= 3.1410 XiXi=-- 1.178 sq. in. Hence, by equation 1, the total shearing strength or resistance to punching is P =1.178 X 50,000 — 58,900 pounds.