354 NOTE TO CHAP. I. [APPENDIX. 



about the system not otherwise apparent. Thus I c, c h and h d 

 are in equilibrium with the load at 2. Again, a b and bo are 

 in equilibrium* with Y a minus Y c, as also are hd and de with 

 Ice minus Jch. Also kh, he, Yc and Y& are in equilibrium, 

 and Yc, cb and X b are in equilibrium with the reaction minus 

 the weight at 1, or with the shear to the right of 1. This last 

 principle is general. When a section can be made entirely 

 through a structure, the strains in the pieces cut are in equi- 

 librium with the shear at the section. If only three pieces are 

 cut, then, by taking as a centre of moments the point of inter- 

 section of any two, we can easily find, knowing the moment of 

 the shear, the strain in the third. 



Thus we have the general and easy method of calculation 

 given in Art. 14, Chap. I. The moment of the shear is, of 

 course, the sum of the moments of all the exterior forces be- 

 tween the section and one end. 



We have then two methods, one graphic and one by calcula- 

 tion, by which we can find the strains in every kind of simple 

 truss which can ever occur in practice. By " simple " we mean 

 merely resting at the supports, or not acted upon at the ends by 

 a couple or moment, as is the case, for instance, in the continuous 

 girder. 



When the structure is unsymmetrical, or complex, the deter- 

 mination of the different lever arms is often very tedious, involv- 

 ing a good deal of trigonometrical computation. On the other 

 hand, the frame can always from its known proportions be 

 easily and accurately drawn to scale, and then the exterior 

 forces, whatever their relative intensity or directions, can be 

 laid off, and the strains at once determined. Here we see, then, 

 one of the great advantages of our graphical method. An 

 unsymmetrical frame and different directions of the forces 

 requires no more time or labor than a more simple case. 



7. Application to Bridges Bow-string Girder. In Art. 

 12, Chap. I., we have alluded to this application, and shown 

 how by two strain diagrams only we can completely calculate a 

 bridge of any length. As this application is so important, and 

 as the method is stated by several authors to be inapplicable to 

 bridges,* or, at best, to be unsatisfactory, we will here call more 



Iron Bridget and Roofs Unwin p. 143. Economics of Construction 

 Bow- p. 61. 



