Art. 149. MAXIMUM SHEAR IN A PRATT TRUSS. 



295 



C 1 

 right hand end of the panel in question, and when 6r 2 <-vr and 



s~1 



G 2 +P>-jj . In words, the total average load per panel must 



equal the load in the panel in ivhich the shear is wanted. 



It should be remembered that for maximum shear in panel 

 3-4, for instance, Fig. 204, a load near the head of the train (a 

 driver) should generally be at 4, so that as much load as possible 

 is concentrated at 4 and to the right of 4. A trial of 2 or 3 wheels 

 at 4 by equation (89) will generally be sufficient. 



For all web members the center of moments is at an infinite 

 distance, but the section changes. . For 3'-4 the section is pq and 

 the panel in question is 3-4; for 3'-3, the section is Im, and the 

 panel also 3-4 ; for 4'-4, the section is rs, and the panel is 4-5. The 

 position of the loads for a maximum stress in 3'-4 and 3'-3 is just 

 the same. 



150. Fields of Shear in a Truss. From equation (89) we 

 have GNG 2 . If P be the load at any panel point, G varies be- 

 tween NG 2 and N(G 2 -{-P) for maximum shear in the panel to the 

 left of the point where P is located. Then P governs for all panel 

 points for which the position of the load is such that the total 

 load on the bridge lies between NG 2 and N(G 2 -\-P). The points 

 en the diagram of loads at which G is equal to these two limits, 

 may easily be found. Since the right end of the bridge must lie 

 between these limits, when the load moves so that the end of the 

 bridge passes from one of these limits to the other, the load P 

 passes the panel points at which it governs for maximum shear. 

 This range of P is called its field of shear. In this way we are 

 saved the labor of testing a number of wheels at eaeh panel point. 



151. Position of Load for Maximum Shear io a Girder or 

 Beam. Let it be required to find the maximum shear at any point 

 C in the beam of Fig. 



205. It is evident that 



the maximum shear 



at C occurs when R L 



is a maximum, so long 



as there are no loads Fig. 205. 



to the left of C. Loads coming on from the right and moving to 



the left increase R t until P reaches (7, when the shear at C is a 



maximum. As soon as Pj passes C, the shear is suddenly de- 



