FORMULA. 45 



The symbols used have the following meanings : 



D = the outer diameter of a hollow cylindrical shaft in 

 inches. 



E = the modulus of elasticity in tension per square inch. 



G = the modulus of rigidity in shearing and torsion in 

 pounds per square inch. 



I = the moment of inertia of a beam section. 



K = the modulus of elasticity of volume in pounds per 

 square inch. 



M = the bending moment on a beam, in inch-pounds. 



T = the twisting moment on a shaft in torsion, in inch- 

 pounds. 



W = the central load on a horizontal beam, in pounds. 



Z = the modulus of the section of a beam. 



6 = the breadth of a beam in inches. 



d = the internal diameter of a hollow, or the external 

 diameter of a solid, shaft in inches ; also used to 

 denote the depth of a beam in inches. 



f = the maximum stress on a beam section, or on the 

 section of a cylindrical shaft, in pounds per 

 square inch. 



I = the length of a beam or shaft in inches. 



m = Poisson's ratio. 

 r = the radius of a solid shaft in inches. 



8 = the central deflection of a beam in inches. 



< = the angle of twist of a cylindrical shaft in radians. 



= angle of twist in degrees. 



TT = the ratio of the circumference of a circle to its 



diameter = 3'1416. 

 ELASTICITY. 



G = 1 



E ^(^ I 



M I x n 



\ m 



In the metals m = 4, so that in this case 

 G _ 2 

 E ~ 5 



6 K -f- 2G 



Als ' m= 3K-2G 



CROSS-BREAKING, BEAMS. 



v _ W I 3 for a central 



and ' 48 6 I concentrated load. 



