996 ON FORM AND MECHANICAL EFFICIENCY [ch. 



and taking the simplest case of a uniform load, whether supported 

 at one or both ends, they will be represented by points on a parabola. 

 If the girder be of uniform depth and section, that is to say if its 

 two flanges, respectively under tension and compression, be equal 

 and parallel to one another, then the stress upon these flanges will 

 vary as the bending-moments, and will accordingly be very severe 

 in the middle and will dwindle towards the ends. But if we make 

 the dejpih of the girder everjrwhere proportional to the bending- 

 moments, that is to say if we copy in the girder the outlines of the 

 bending-moment diagram, then our design will automatically meet 

 the circumstances of the case, for the horizontal stress in each flange 

 will now be uniform throughout the length of the girder. In short. 



Fig. 474. 



in Professor Fidler's words, "Every diagram of moments represents 

 the outline of a framed structure which will carry the given load 

 with a uniform horizontal stress in the principal members." 



In the above diagrams (Fig. 474, a, b) (which are taken from 

 the original ones of Culmann), we see at once that the loaded beam 

 or bracket {a) has a "danger-point" close to its fixed base, that is 

 to say at the .point remotest from its load. But in the parabolic 

 bracket (6) there is no danger-point at all, for the dimensions of 

 the structure are made to increase jpari passu with the bending- 

 moments: stress and resistance vary together. Again in Fig. 475, 

 we have a simple span (A), with its stress diagram (B); and in 

 (C) we have the corresponding parabolic girder, whose stresses 

 are now uniform throughout. In fact we see that, by a process of 

 conversion, the stress diagram in each case becomes the structural 



