TRUSSED BEAMS, ETC. 633 



To find v' -p we write, in (a), E,, for W, (I — I,) for a, and /, for x, 

 thus obtaining — 



Hence — 



and, since — 



:. E, I, ('SI - 4/J = J W i'Sa I - l;- - 8rt-) 



-p -^ 3«Z — Z,- — S(r 



" ' ~^ 2/, "(37— 4/,) 



Then, by means of the ordinary statical equations, we can find 

 Ri and Ey, and, hence, the bending moments at various parts of the 

 beam. 



The forces, Rj and Eg, are those portions of the vertical com- 

 ponents of the tensions in the inclined rods which hold the ends of 

 the beam down : the remaining portions of the said vertical com- 

 ponents are equal to the supporting forces at the abutments. It is 

 clear that, when the load is between the posts, the tension in the 

 rods is gi-eater than it would be if the structure were completely 

 braced and the load had a panel point beneath it. 



The force Rq is the vertical component of the compressive stress 

 in e^ch of the posts. In a given case, therefore, the stress in the 

 posts is readily found, and, from that, the stress in the tension rods. 



On the diagram, Fig. 13, is plotted a curve, representing the 

 values of the bending moments at mid-span, when the load is there ; 

 nlso. another curve, giving bending moments at top of post when the 

 Ic-ad occupies that position. These values of the bending moments 

 correspond to different positions of the posts. The abscissa-, in the 

 diagram represent values of 1^ — i.e., of the distance between post and 

 end of beam : the ordinates represent binding moments. This 

 diagi'am will be compared, presently, with that on Fig. 16, Avhich 

 represents bending moments between post and abutment as the load 

 moves from one towards the other. Confining our attention, for the 

 present, to Fig. 13, we observe that, if the posts be placed at 0"385? 

 from the ends, the bending moment at mid-span, when the load is 

 there, is equal to that at a post when the load is there, the common 

 value of the bending moment being 0'044W7. But we shall find, 

 when examining Fig. 16, that, if the posts be placed so far from the 

 ends as 0'385?, then, when the load comes between an abutment and 

 a post, a much greater bending moment; than 0'044 WI will be 

 endured by the beam, and thus it is seen that the condition of equal 

 maxima bending moments, over a post and at mid-span, is far from 

 giving the most favourable spacing^ of the posts. 



