86 APPLICATION TO BRIDGES. [PART IT. 



Yertlcal Direction. The strain in any cross-section depends 

 upon, first, the resultant of all the outer forces acting either 

 side of the cross-section ; and second, the statical moment of 

 these forces with reference to the cross-section. The first, or 

 the algebraic sum of all the forces acting between the cross- 

 section and either end, we call the shearing force for this cross- 

 section, and indicate it by S. It is also designated as vertical 

 force, or transverse force. The moment of the resultant, or 

 the algebraic sum of the moments of all the exterior forces, 

 with reference to any cross-section, we call the moment for this 

 cross-section, and indicate it by M. It is also called bending 

 moment, or moment of rupture. For example, in a lattice 

 girder with horizontal flanges the strains in the web are pro- 

 portional to the shearing forces, those in the flanges to the 

 bending moments. 



The shearing force is considered positive when it acts on the 

 left side upwards, or on the right side downwards. The mo- 

 ment M is positive, when on the left side the tendency of rota- 

 tion is to the left, on the right side to the right, or when it tends 

 to make the girder convex upwards, that is, causes compression 

 in the lower fibre or flange. 



