52 MOMENT OF ROTATION PARALLEL FORCES. [ciIAP. V 



the shear and moment increase as the load approaches, and 

 become greatest for any point when the load reaches that point. 

 At the moment of passing, these greatest values pass to their 

 smallest values, and increase afterwards as the load recedes. 



Since by the introduction of the load the shear for points 

 upon one side of 2 is diminished (between 2 and the load), and 

 on the other side increased, and the greatest moment is at the 

 point where the shear is zero, it follows that the point of greatest 

 moment moves in general towards the load. At a certain point, 

 then, both meet. As the load then advances this point accom- 

 panies it, passes with it the original position, and follows it up 

 to the point where it would have met the same load coming on 

 from the other side. From this point, as the load continues to- 

 recede, it returns, and finally reaches its original position as the 

 load arrives at the further end. 



It is evidently of interest to learn the position of these two 

 points, where the load meets and leaves the point of greatest 

 mcujcnt, or cross-section of rupture, and this in Fig. 32 we can 

 easily do. 



When P' t arrives at 1', we have evidently the reactions by 

 laying off L E equal to P'j, drawing A E, and through its 

 intersection with the vertical through the weight drawing the 

 horizontal A' B' . L B' is then the increase of reaction at B due 

 to P\. The entire reaction is B' B' 1} and the broken line A\ 

 1' 1", etc., holds good still, if we merely change the axis from 

 AO L to A' B' . The point of greatest moment, which is still 

 the intersection of the broken "line with the new axis, in the 

 present case is not changed by reason of the overpowering in- 

 fluence of P 2 . It does not move to meet the load, but awaits it 

 until it reaches P 2 , and until, therefore, the new axis takes the 

 position A" B" . 



If, however, the force P\ comes on from the right, we have 

 the reactions for any position as 2, by laying off A E' equal to 

 P' 1? drawing L E', and then the horizontal A'" B'" through the 

 intersection of L E', with the vertical through z. Then A A'" 

 is the reaction at A, due to this position of the load. The in- 

 tersection a;', corresponding to x, shows the point to which the 

 point of greatest moment 2 moves to meet the load. As the 

 load passes towards the left, this point moves towards the right, 

 and both come together evidently at the point V 1} correspond- 

 ing to the new axis Ao iv B iv . The point of greatest moments 



