INFLUENCE DIAGRAMS 



77 



INFLUENCE DIAGRAMS. An influence diagram (commonly 

 called an influence line) shows the variation of the effect of a moving 

 load or a system of loads on a beam or truss. The difference between 

 bending moment or shear diagrams and influence diagrams is that the 

 bending moment and the shear diagram gives the moment and shear, 

 respectively, at any point for a fixed system of loads, while an in- 

 fluence diagram gives the moment or shear, etc., at a fixed point for 

 a moving system of loads. Influence diagrams are used principally 

 for finding the position of moving loads that will produce maximum 

 shears, moments, reactions, or stresses, although they may be used 

 for calculating the quantities themselves. For convenience where a 

 number of loads are considered the influence diagrams are drawn for 

 a single unit load. The unit influence diagram may then be used for 

 any load by multiplying by the given load. The unit influence diagram 

 will be referred to in the following discussion. 



Maximum Moment in a Truss or Beam. Let P in Fig. 5oa, 

 represent the summation of the moving loads to the left of the panel 

 point 2' and P 2 be the summation of the moving Idads to the right. 



u- a -If : 



a, - j '-dx 4 L -dx '-a 2 3 



FIG. 5oa. INFLUENCE DIAGRAM FOR MOMENTS. 



The influence diagram for the point 2' is constructed by calculating 



a(L a) 



the bending moment at 2' due to a unit load, = = ordinate 



L 



