628 PROCEBDmGS OF SECTION H. 



three posts, this relation being the same as that existing at the joints 

 in a chain, which, being suspended as a festoon, is deformed slightly, 

 the chain having four long links, corresponding in length and incli- 

 nation to the four sections of the tension member. These results 

 follow from our assumption as to inextensibility and incompressi- 

 bility of materials. With regard to our assumption as to deforma- 

 tions being negligible, we have, as consequences, first, that, in Figs. 2, 

 2a, 3, and 3a, under all conditions of loading, the tensions in sections 

 of the tension member symmetrically placed with respect to the 

 centre must be equal. [In Fig. 3, where the posts bisect the angles 

 between adjacent sections of tension member, the tension in the latter 

 is the same throughout.] Secondly, in Figs. 2, 2a, and 3, the com- 

 pressive stresses in the posts will be equal, and, in Fig. 3a, the stresses 

 in the two side posts will be equal. 



Such being our assumptions and their corollaries, it is proposed 

 now to show how the stresses in the various members, under various 

 loads, may be ascertained, also to ascertain the most advantageous 

 spacing of the posts in the case of the tinissed beam with two posts, 

 under both isolated and unifonnly distributed loads, and, lastly, to 

 compare the advantages of trie single and double post structures. 

 Time has not been available for canying the investigation fully into 

 the case where three posts are employed. 



DETERMINATION OF STRESS. 



Case I. — Single Post Trussed Beam. 



A. — Isolated Load. 



(a) When the load is at mid-span, i.e., over the post, there is 

 no bending, and the calculations are of the simplest character. The 

 whole of the load is transmitted through the post to the tension rods, 

 and these impose a direct compressive stress upon the. beam. The 

 compressive stresses in beam and posts and the tension in the rods 

 all have their maxima values as compared with the values of these 

 stresses when the load is at other points. Referring to Fig. 4, it is 



W 



seen that the stresses are f, — cot 6 in the beam, W in the post, and 



W . . 



-^cosec in the teiisioirods. 



fb) When the load is between the post and one of the abutments, 

 the beam endures bending stresses, which have to be compounded 

 with the direct compressive stress in it. Referring to Figs. 5 and 6, 

 it is seen that the beam is acted upon by four transverse forces, only 

 one of which, W, is known. We, therefore, need three equations to 

 determine the three unknown forces, R^, R^, and Rg. Our first two 

 equations are the ordinary statical ones, such as— 



W-hIt. = R + R, (I.) 



KJ + ll^^ = Wa (II.) 



For our third equation, the simplest appears to be that which 

 expresses the condition that the two ends and the middle of the 

 beam remain at the same level; in other words, that, whatever 



