_ CONSOLIDATED STEEL CORPORATION _ 159 



NOTES ON THE STRENGTH AND DEFLECTION 



OF BEAMS 



The general notation employed throughout is as follows : 

 a = area of section, in square inches. 

 L = length of span, in feet. 

 1= length of span, in inches. 

 W=load uniformly distributed, in pounds. 

 P = load concentrated at any point, in pounds. 

 d = depth of cross-section, in inches. 

 M = bending moment, in foot-pounds. 

 m = bending moment, in inch-pounds. 

 n greatest distance of center of gravity of section from top or from bot- 



tom, in inches. 

 /= stress, in pounds per square inch in extreme fibers of beam, either top 



or bottom, according as n refers to distance from top or from bottom 



of section. 



D = maximum deflection, in inches. 



I = moment of inertia of section, neutral axis through center of gravity. 

 I" = moment of inertia of section, neutral axis parallel to above, but not 



through center of gravity. 

 z = distance between these neutral axes. 

 S = section modulus. 



R= least moment of resistance of section, in inch-pounds. 

 r = radius of gyration, in inches. 

 C = coefficient of transverse strength, in pounds. 

 E = modulus of elasticity (29,000,000 for steel). 



For a beam of any cross-section the relations existing between the proper- 

 ties of the section are as follows: 



/" = I + az2 r= V/ 1 S=- 



v a n 



The moment of resistance of the internal stresses of the beam resisting 

 flexure must be equal to the moment of the external forces which act on the 

 beam producing bending. The moment of resistance of a section is usually 

 expressed in inch-pounds, in which case the bending moment must be expressed 

 also in inch-pounds. 



