<936 PROCEEDINGS OP SECTION H. 



the posts, so far as an isolated load is concerned, are those at 0'247 I 

 from each end. 



In Fig. 14, Ri, plus the vertical component of the tension in the 

 rod, is equal to the actual supporting force afforded by the adjacent 

 abutment. R3 is that portion of the vertical component of the 

 tension in the rod which holds the beam down : the remainder of that 

 vertical component is the actual supporting force afforded by the 

 abutment adjacent to R3. 



The formula for R.j for the case where there is a single post may 



be deduced from that last found by putting for /,. 



Then E, 



And, as this represents the stress in each half of the single post, 

 formed by bringing two posts together, we have, for the whole stress 

 in the post — 



which is the expression previously found for the single post truss. 



B. — Uniformly Distributed Load. 



This case difl'ers from that in which a beam is supported sym- 

 anetrically at two points, Avhile its ends overhang, in that the ends, in 

 the trussed beam, are kept at a fixed level, viz., the level of the top 

 of the posts. They must be held down to that level by the tension 

 rods if the posts are nearer to the ends than 0'2143 I, as will be 

 shown later on. On the other hand, if the posts are fuii:.her from the 

 ends than the said distance, the abutments keep the ends up to the 

 said level. The latter case is that of a continuous beam, supported 

 at the ends and at two points equidistant from the ends ; but this 

 does not appear to be one of the examples chosen by writers of text- 

 books to illustrate the subject of continuous beams. 



As in the cases previously considered, we shall make use of the 

 work done by Avriters of text- books as far as that work is of service 

 to us. In Lanza's " Applied Mechanics,^' 3rd edition, p. 293, equation 

 '(2) gives the deflection at a point, distant x from the end of a beana 

 "which is uniformly loaded and supported at the ends, viz. — 



w 



wheie W is the load, per unit of length, and the other symbols have 

 the same meanings as before. 



But, by reason of the convention as to signs, which Lanza 

 adopted, this expression for v is negative, and, as before, for con- 

 venience, we shall employ its positive value, and, hereafter, we shall 

 make use of the formula — 



