x: 



206 JOHN C. KOCH 



in which V = Total vertical shearing force at section. 

 I = Moment of inertia of the cross section. 

 t = Thickness of the plane on which shearing takes 

 place. 

 (Da) = an infinitesimal elementary area. 



z = Distance of the shearing plane from the neutral 



sm-face in any section of beam. 

 c — Distance from neutral axis of beam to outermost 

 fiber of beam. 



= Sign of summation of all products for all values of 

 z between c and z, as limits. 

 Sh = Intensity of horizontal shearing force in pounds 

 per square inch. 



The expression 2Li- (■^^)- ^ i^ usually spK)ken of as the statical 

 moment of the given cross section. It is the summation of all 

 the products of the separate elementary areas by their respective 

 distances from the neutral axis, for the area lying between two 

 lines distant c and z, respectively, from the neutral axis. 



The formula above given may be simplified to the following: 



V 

 A 

 in which 



V = Total vertical shearing force at section. 

 A = Total area of cross section. 



Q = Factor by which the average vertical shear over the 

 section is to be multiplied, in order to obtain the 

 actual horizontal shearing force at the section. 



in which a^ = area lying above the plane on which the horizontal 

 shear is to be computed. 

 Ci = distance from neutral axis to the center of grav- 

 ity of the area, ai. 

 Moment of inertia of section / 

 Total area of section A 



t = width of plane on which the horizontal shear is 

 to be computed. 



