16O CAMBRIA STEEL. 



GENERAL FORMULAE FOR FLEXURE OF BEAMS. 



NOTATION. 



A = Area of Section in square inches. 



d = Depth of Cross Section in inches. 



1 = Length of Span in inches. 



L = Length of Span in feet. 



p Stress in extreme fibre of section in pounds per square inch. 



Xi Distance of Center of Gravity of Section from extreme fibre in inches. 



Total Load, in pounds, Uniformly Distributed, including the Weight of 



Beam. 



Total Superimposed or Live Load, in pounds, Uniformly Distributed. 

 Total Weight of Beam, in pounds, Uniformly Distributed. 

 Total Safe Load, in pounds, Uniformly Distributed. 

 Load, in pounds, concentrated at any point. 

 Coefficient of Strength of the Tables of Properties = Safe Load, in pounds. 



W 



Wi 

 Wt 



w, 



p 



F 



for a fibre stress of 16 000 pounds per square inch for a span of one foot. 

 F' = Coefficient of Strength of the Tables of Properties = Safe Load, in pounds, 



for a fibre stress of 12 500 pounds per square inch for a span of one foot. 

 D = Total Deflection of Beam, in inches, due to weight W. 

 Dwi and D p = Deflections of Beams, in inches, due to the weights Wi and P 



respectively. 

 N = Coefficient of Deflection of the Tables of Properties = Deflection, in 



inches, due to a total load of 1 000 pounds uniformly distributed for a 



span of one foot. 

 N' = Coefficient of Deflection of the Tables of Properties = Deflection, in 



inches, due to a superimposed load of 1 000 pounds, concentrated at 



the middle of a Beam with a span of one foot. 

 H = Coefficient of Deflection, in inches, for fibre stress of 16 000 pounds per 



square inch, for any section used as a Beam subjected to its safe load 



Uniformly Distributed. (See table, page 98.) 

 H' = Coefficient of Deflection, in inches, for fibre stress of 12 500 pounds per 



square inch for any section used as a Beam subjected to its safe load 



Uniformly Distributed. (See table, page 98.) 

 M = Total Bending Moment, in inch pounds, due to the Weight of Beam and 



Superimposed Load. 



[ = Moment of Inertia, in inches 4 , Axis through Center of Gravity. 

 Ii = Moment of Inertia, in inches 4 , Axis parallel to above but not through 



Center of Gravity. 



v = Distance, in inches, between these Axes. 

 S = Section Modulus in inches 3 , 

 r = Radius of Gyration in inches. 

 E = Modulus of Elasticity, in pounds, per square inch (Steel = 29 000 000). 



GENERAL FORMULA 



- Or for Symmetrical Section M = 



3 d 



For Beam supported at both ends and Uniformly Loaded: 



SAFE LOADS. 



F = ?5? where p = 16 000 pounds and 1 = 12" therefore F = -|- 16 000 S 

 I 



F' = ?? w here p = 12 500 pounds and 1 = 12" therefore F'= ^- 12 500 S 



1 o 



To obtain the Safe Load for any span in feet, for fibre stress of 16 000 pounds 

 per square inch: 



o r T w ' 2 16000 S F 



Safe Load = W s = -- ^ = 



To obtain the Safe Load for any span in feet, for fibre stress of 12 500 pounds 

 per square inch: 



