ON BRIDGES BEAMS. 



141 



Fig. 21 



D 



Fig. 23. 



the bridge, we can put it above by a simple change, as in Fig. 21, 

 where the point C is firmly fixed by 

 the braces A C and C B, and there- 

 fore the centre point of the beam, A 

 D, may be suspended from C by the 

 tie rod C D, thus changing the long 

 span, A B, into two short ones, A I) 

 and D B. 



Again, if we find that A C and C B are so long as to be too flexi- 

 ble, we may support their center points by 

 additional braces, D E and D F, Fig. 22; 

 thus firmly fixing the points E and F, and 

 should A D and D B be too weak they can 

 be supported from the fixed points E and 

 F by tie rods E G and F H. So we arrive 

 by this simple process at a form which is comparatively complex. 



If it is desirable to make use of a material like wrought iron for 

 stiffening, since it is peculiarly adapted to bear tensile strain, we may 

 make use of it in a most economical 

 manner. In Fig. 23 we have a beam, 

 A B, trussed, as it is termed, by the 

 iron rod, ADB, which passes under 

 a post or strut, C D ; now it will be im- 

 possible, when all the parts are tight, for the point C to sink without 

 the lines A D and B D becoming longer. Since the strain upon the 

 tie in this case is a direct tensile strain each fibre will be made to bear 

 its share of the load, and it will be a very economical mode of using 

 our material. We may modify this in such a way as to show that 

 the strain upon such a tie is precisely the same as on the lower edge 

 of a beam. 



Let us suppose, in Fig. 24, that the strut £ f* 



is made so short as to disappear, and permit ^ D 



the rod to touch the beam throughout its Fi g . 24. 



whole length, it will still act as the tie in 



Fig. 23, but with diminished effect, owing to its being nearer to the 

 neutral axis, and the moment of the resistance of its fibres being 

 therefore less. 



This mode of strengthening a beam is some- 

 times resorted to in carpentry; but that shown 

 in Fig. 23 or Fig. 25 is preferable. 



If the distance between A C to C B, in Fig. 23, is so great as to 

 cause flexure of those parts of the 

 beam, we may truss them again 

 by an intermediate strut and tie, 

 as in Fig. 26, in which the points 

 E and F are supported in this 

 way. 



Many roofs are constructed on this plan, and up to very large spans 

 it is the most simple and economical arrangement of wood and iron 

 that can be made for the purpose. 



Since, in a roof, the principal rafters are inclined, we shall have the 



Fig. 25. 



