TRUSSED BEAMS, ETC. 639 



is et|ual to the maximum bending moment in the end bay, and the 

 bending moment at mid-span is a very small negative quantity, i.e., 

 the beam, at mid-span, is slightly bent upwards. It is clear, from the 

 diagram, that, moving the posts nearer the ends than 0-357 I 

 increases the bending moment over the post, and, also, the bending 

 moment at mid-span, while moving the posts fuii;her away from the 

 ends increases botli the Ijending moment over the post and that in 

 the end bay. 



We conclude, then, that the most favourable positions for the 

 posts to occupy, when the load is imiformly distributed, is 0'357 I 

 from each end. The bending moment is then O'Ol tt'/-. 



B}" "most favourable positions for the posts," we mean favour- 

 able so far as hending stresses in the beam are concerned. The 

 direct stresses will be less in a single-post truss than in any double- 

 post truss, provided the inclination of the tension rods to the hori- 

 zontal is the same. 



We saw, previously, that, for an isolated load, the most favour- 

 able positions for the posts, so far as bending of the beam is con- 

 cerned, is at one-fourth and three-fourths of the span. If, then, a 

 structure is to be designed to carry, sometimes, a distributed load 

 and sometimes an isolated load, Ave must ascertain the magnitude of 

 the bending moments, under both circumstances, and so space the 

 posts as to reduce to a minimum the bending moments in the beam. 



Referring, again, to Fig. 19, we obsei-ve that the bending 

 moment over a post is again equal to the maximum bending moment 

 in the end bay when /^ = 0'425Z; but the common value of the 

 bending moment, in this case, is greater than when Z^ = 0*357 I. 

 Posts, at 0'425 I from the ends, would be still less suited for isolated 

 loads than those at 0'357 / from the ends. 



We observe, fur-ther, that, if the posts be placed 0'307 / from the 

 ends, the bending moment, at mid-span, and the maximum bending 

 moment in an end bay are equal, the cori'esponding value of the 

 bending moment over a post being somewhat greater than when the 

 posts are 0'357 I from the ends. The difference is about O'OOl wZ^. 

 0"307 1, from each end, would, therefore, not be an unsuitable 

 position for each post, especially if the structure be sometimes sub- 

 jected to the imposition of an isolated load. 



In the case of a double^post trussed beam, as in that of a single- 

 post one, if the moments of the external forces, acting on the 

 structure, on one side of a vertical section through a point of con- 

 trary flexure, be taken about that section, then that moment, i.e., the 

 bending moment on the stimcture, as a whole, will be equal to the 

 moment of the couple whose force is the compressive stress in the top 

 beam (or the equal horizontal component of the stress in the tension 

 member), multiplied by the vertical distance between the neutral axis 

 in the beam and the centre of the tension member. 



Coiwparison of Single and Double Post Trussed Beams. 



Tliis is best effected by summarising the principal results so far 

 obtained. Such a summary is shown on the diagram containing Figs. 

 21-23, 25-26. 



