INFLUENCE DIAGRAMS Si 



Pi + P 2 +^3 



p -~r^ <<> 



From (f) it follows that the maximum shear in the panel ivill occur 

 when the load on the panel is equal to the load on the bridge divided 

 by the number of panels in the bridge. 



Uniform Loads. From Fig. 5ob, it will be seen that for a uni- 

 form load the maximum shear in the panel will occur when the uniform 

 load extends from the right abutment to that point in the panel where 

 the line 2-3 passes through the line 1-4 (where the shear changes sign). 

 For a minimum shear in the panel (maximum shear of the opposite 

 sign) the load should extend from the left abutment to the point in 

 the panel where the shear changes sign. For equal joint loads, load 

 the longer segment for a maximum shear in the panel, and load the 

 shorter segment for a minimum shear in the panel. 



Maximum Floor Beam Reaction. It is required to find the 

 maximum load on the floor beam at 2' in (a) Fig. 5oc for the loads 

 carried by the floor stringers in the panels i'-2' and 2'~3'. 



In (a) the diagram 1-2-3 1S tne influence diagram for the shears 

 at 2' due to a load unity at any point in either panel. In (b) the dia- 

 gram 1-2-3 is tne influence diagram for bending moment at 2' for a 

 unit load at any point in the beam. Now diagram in (a) differs from 

 diagram in (b) only in the value of the ordinate 2-4. It will be seen 

 that the reaction at 2' in (a) may be obtained from the diagram 

 in (b) for any system of loads if the ordinates are multiplied by 



. We can therefore use diagram (b) for obtaining the 



d^ + d 2 

 maximum floor beam reaction if we multiply all ordinates by . 



To obtain the maximum floor beam reaction, therefore, take a 

 simple beam equal to the sum of the two panel lengths, and find the 

 maximum bending moment at a point in the beam corresponding to 



d-i ~\~ d<y 

 the panel point. This maximum moment multiplied by will be 



the maximum floor beam reaction. If the two panels are equal in 



