158 METHODS OF LOADING [CHA1 ; . XL 



are the moments at the supports. We have already seen that 

 the inflection points O and P (for which the moment is zero) 

 lie outside of the fixed points. We can therefore assert that 

 WITHIN the fixed points the moments are negative wherever tht 

 weight may be placed. From the Fig. we see at once that the 

 inflection points O and P move to the right or left as the weight 

 moves to the right or left. Accordingly when for the weight 

 at D the moment at O is zero, the moment at this point will be 

 positive when the load moves to the right of D, negative when 

 it moves to the left of D. 



Hence for the maximum moment we have at once the follow- 

 ing principle : 



For any point O outside the fixed points the moment will be 

 a positive or negative maximum when the load reaches from 

 the point D, where a load must be placed to cause the moment 

 at O to be zero, to the right or left support respectively. For 

 the negative maximum, therefore, the load reaches from A to D; 

 for the positive, from D to B. 



If the point O is given, it is indeed possible to determine by 

 construction the point D to which the load must reach. It is, 

 however, simpler to assume D and then construct O. 



If we choose for the different positions of D an arbitrary 

 length for C' D' (Fig. 67), so that the point C' falls in a parallel 

 Q R to A' B' (Fig. TO), and, moreover, take D at equal intervals, 

 then the points L and M will be at equal distances (Fig. 67), 

 and hence the points I and K (Fig. 70), in which the verticals 

 through the fixed points are intersected by the lines A' M and 

 B' L (Fig. 67), will be at equal distances. We have, then, the 

 following simple construction [Fig. 70, PL 18] : 



Between the verticals through the supports draw two parallel 

 lines A B and Q R at any convenient distance apart, and divide 

 Q R into a number of equal parts ; four or five are sufficient. 

 Draw lines from A to R and the middle S intersecting the ver- 

 tical through the fixed point I in I x and T 2 . In the same way find 

 K! and Kg. Divide I x I 2 and K t Kj into the same number of 

 equal parts as Q R has been divided into, and join these points 

 in reverse order by lines. The intersection of these lines with 

 the lines drawn from A and B to the points upon Q R give the 

 points O, for which the moment is a maximum when the load 

 is limited by the corresponding point upon Q R. 



This construction was first given by Mohr. 



