1000 ON FOR]\J AND MECHANICAL EFFICIENCY [ch. 



is effectively continuous from the head to the tip of the tail; and 

 at each point of support (A and 5) it is subjected to the negative 

 bending-moment due to the overhanging load on each of the 

 projecting cantilever arms AH and BT. The diagram of bending- 

 moments will (according to the ordinary conventions) lie below the 

 base line (because the moments are negative), and must take some 

 such forfn as that shewn in the diagram : for the girder must suffer 

 its greatest bending stress not at the centre, but at the two points 

 of support A and 5, where the moments are measured by the 

 vertical ordinates. It is plain that this figure only differs, from 

 a representation of two independent two-armed cantilevers in the 

 fact that there is no point midway in the span where the bending- 

 moment vanishes, but only a region between the two piers in which 

 it tends' to diminish. 



H A B T 



Fig. 477. Two-armed cantilever and its stress diagram. 



The diagram effects a graphic summation of the positive and 

 negative moments, but its form may assume various modific^ttions 

 according to the method of graphic summation which we choose 

 to adopt; and it is obvious also that the form of the diagram 

 rriay assume many modifications of detail according to the actual 

 distribution of the load. In all cases the essential points to be 

 observed are these: firstly that the girder which is to resist the 

 bending-moments induced by the load must possess its two principal 

 members — an upper tension-member or tie, represented by ligament 

 (whose tension doubtless varies along its length), and a lower 

 compression-member represented by bone: these members being 

 united by a web represented by the vertebral spines with their 

 interspinous ligaments, and being placed one above the other in 

 the order named because the moments are negative; secondly we 

 observe that the depth of the web, or distance apart of the principal 



