E is a number depending on the stiffness of the material, the average values of which are, for timber, 1,500,000; and for structural steel 30,000,000.*

S1= Mc1/ I + Pl2/ 10E, and S2 = Mc2/I + Pl2/10E (8)

The plus sign is to be used when the end forces P are pulls, and the minus sign when they are pushes.

It must be remembered that S1 and S2 are flexural unit-stresses. The combination of these and the direct unit-stress is made exactly as in articles 74 and 75.

Examples. 1. It is required to apply the formulas of this article to the example of article 74.

As explained in the example referred to, M = 108,000 inch-pounds; c1 = c2= 3 inches; and I = 36 inches4. Now, since l = 12 feet = 144 inches,

S1=S2=(108,000x3)/45,000x1442=324,000/36+3.11=8,284pounds, 36+(45,000x144)/10x30,000,000 per square inch, as compared with 9,000 pounds per square inch, the result reached by the use of the approximate formula. As before, S0 = 3,750 pounds per square inch; hence

Sc = 8,284- 3,750 = 4,534 pounds per square inch; and St = 8,284 + 3,750 = 12,034 " " " "

2. It is required to apply the formulas of this article to the example of article 75.

As explained in that example,

M = 12,000 inch-pounds; c1 = c2 = 3 inches, and I = 108 inches4. Now, since I = 120 inches, per square inch, as compared with 333⅓ pounds per square inch, the result reached by use of the approximate method. As before, S0 = 250 pounds per square inch; hence

S1=S2=(12,000x3)/9,000x1202=36,000/108-8.64=362 pounds, 108- (9,000x120)/10x1,5000,000

* Note. This quantity " E " is more fully explained in Article 95.

Sc = 362 + 250 = 012 pounds per square inch; and St = 362 - 250 = 112 " " " "

Examples For Practice

1. Solve the example for practice of Art. 74 by the formulas of this article.

Ans.

Sc

=

12,820 pounds per square inch.

St

=

20,320

2. Solve the example for practice of Art. 75 by the formulas of this article.

Ans. -

Sc

=

430 pounds per square inch.

8t

=

70 " " " " (compression).