144 



LECTURE 



point b. To do this Ave may either introduce a strut, c b, or a tie, a d, as 

 in Figs. 18 and 19. If we use a strut or wooden "brace, we shall have 

 the arrangement shown in Fig. 33. 



Fig. 33. 



In this arrangement the heam cannot assume the shape shown in 

 Fig. 32, without its diagonals becoming shorter ; and since the braces 

 are in the most favorable position for resisting — that is, with the 

 strain acting in the direction of their length— a small amount of mate- 

 rial will do a great deal of work. If it is desirable to use an iron tie 

 instead of a wooden brace, we shall have the form shown in Fig. 34. 



Fig. 34. 



For any beam or truss, which is only intended to bear a constant 

 and quiet weight, this bracing is sufficient, but if the load is variable 

 and passing, as in the case of a railroad bridge, something more is 

 needed. 



In a structure of considerable length, the effect of the load at any 

 point between the centre and the end will be to cause a rise of the cor- 

 responding point on the other side of the centre ; and since the braces 

 are not calculated to prevent such a rise, oscillations will take place 

 which may soon destroy the structure. Such a rise at any point can 

 only take place by a change in the shape of the rectangle ; and if, 

 therefore, we introduce another brace in the direction of the other 

 diagonal, we shall prevent change of figure in either direction. 



In Fig. 35 we have such an arrangement. Such braces are called 

 counter braces, and since the strain upon them is a secondary one, and 

 always small, they maybe made much lighter than the main braces. 



A little consideration will show that ties may be substituted for 

 struts in a variety of ways, and vice versa. For instance, in Fig. 33, 

 the addition of ties running in the same diagonal as the struts will 

 counter brace the truss, and in Fig. 34, the counter braces may be 

 light struts in the same diagonal as the ties. Again, we may do all 

 the bracing by ties, as in Fig. 35, or we may use struts for both braces, 



