SECTION III 



BENDING-MOMENT AND SHEAR DIAGRAMS 



25. Conditions of equilibrium. In order that any structure may 

 be in equilibrium, the external forces acting on it must satisfy 

 two conditions : 



1. The sum of the forces acting in any given direction must be zero. 



2. The sum of the moments of the forces about any point must be zero. 

 If force and moment are denoted by F and Jf, respectively, these 



conditions are expressed more briefly in the form 



2-F =0; 



(28) 



For equilibrium 



^M=0. 



If the forces all lie in one plane, the condition V ^ = is expressed 

 more conveniently in the form 



(29) 



vertical forces = O ; 



horizontal forces = O. 



\ 



To illustrate the application of these conditions, consider a simple 

 beam AB of length ?, supported at the ends and bearing a single 

 concentrated load P at a 

 distance d from one end A 

 (Fig. 37). Let the reac- 

 tions of the supports at A 

 and B be denoted by R v 

 R^ and, to find the value 

 of these reactions, apply' 

 the condition ^ M = ; that is, equate to zero the sum of the 

 moments of all the external forces with respect to any convenient 

 moment center, say A. Then 



4 > 



B L 1 ^ 



FIG. 37 



whence 



35 



