Art. 144. POSITION OF LOAD FOR MAXIMUM MOMENT. 280 



above principles, the different positions to try will be limited 

 to but a few when the following facts are taken into consideration. 



If a moment diagram be made for a series of wheel loads on 

 a beam, as in Fig. 118, it is evident that the maximum moment 

 comes under a wheel. Of all the possible positions, therefore, 

 which a series of loads may have, it is only necessary to try those 

 in which some wheel comes at the center of moments, if this is 

 possible, because the maximum moment at this point is wanted. 



Likewise for shear, by principle (1) above, the shear increases 

 as the loads move up to the section in question, and suddenly de- 

 creases as a load passes the section, therefore, the shear is a maxi- 

 mum with a load at the section. This is illustrated in Fig. 118. 



By principle (2) above, the shear increases as the londs move 

 toward the nearest panel point and decreases as a load passes 

 this point, therefore (as in the case of a solid beam) there must 

 be a load at a panel point for a maximum shear in the panel 

 ahead. 



The above principles are not perfectly general because they 

 assume that chord stresses are gotten from moments and web 

 stresses from shears. 



144. Position of Load for Maximum Moment at Any 

 Point of a Truss or Girder. In order to develop a criterion 

 for the position of the typical loading that will give a maximum 

 moment about any point, let us take some point of the truss 

 shown in Fig. 200, as point G for instance. We have, 



r =R aG (a a x}G p (a*-{-xnp) c 

 6 i- i( -' i ) 2 p 



'4 





I ' i 7 



P^^q~ 



G, =ftesu/font of 

 Loads in l~-5 

 G 2 = Resu/tanf of 

 Loads in S~7 



G 3 -- Resultant of Loads in 7~/5 

 G = Resultant of all Loads on the span 

 Fig. 200. 



-/v/ 



