Note on Continuous Beams. 311 



the two reactions due solely to the load on that span. Adding 

 together the reactions duo to the loads on adjacent spans we 

 find : — 



R A =52 tons ; R D =282 tons ; R G = 254 tons; Rj = 12 tons. 



Mr. Wilson gives : — 



R A =52tons; li D = 281-9 tons; B G = 253-5 tons ; Rj=12'6tons. 



It would be difficult, perhaps, to say which are the more 

 correct set of values, as Mr. Wilson has not used a purely 

 arithmetical process, but what is quite clear is that for all 

 practical purposes either set of results will suffice. Their 

 differences are not of any practical importance. The eighth 

 and last stage of the work is to break the true bending- 

 moment curve (i. e. the part intercepted between the parabolas 

 and the numbered base-line) up into elements, to plot these 

 elements down a vector line and to draw a link (funicular) 

 polygon for them as if they were a system of forces, acting 

 in the mid-lines of the elements. The poles of these vector 

 polygons are determined by parallels to the support-tangents, 

 and they are figured to the right of the drawing as " vector 

 polygons for the elastic line." They are obtained by plotting 

 1 in. = 20,000 sq.ft. tons for elements of area of bending-moment 

 curve, or, what is the same thing, by plotting 1/8 of the mid- 

 ordinates of the elements by aid of a pair of proportional 

 compasses. The link polygons together give the true form of 

 the elastic line, and the scale of the deflexions has been so 

 selected that the actual deflexions in the girder would be 

 J of those in the original drawing, or about § of those in the 

 photographic reproduction. The scale of the exaggeration 

 of the elastic line depends upon the value selected to represent 

 the standard flexural rigidity, and it can often be chosen so 

 that the deflexions on the drawing-board are precisely equal 

 to those of the actual girder at the corresponding points. 



(4) Our work is now fully described ; it determines the 

 unknown reactions at the points of support, the shear curve 

 for the girder, the true bending-moment curve for the girder 

 (from which the curves of tensile and compressive stress can 

 be found so soon as we know the dimensions of the cross- 

 section) with the support-moments and the curve of deflexions. 

 We have given no proofs of the constructions used, but have 

 endeavoured to show how graphical processes already in wide 

 use on the Continent, and also to some extent in this country, 

 provide a short and comprehensive solution of such important 

 practical problems as that dealt with only partially by Mr. 

 Wilson, and at the expense of what we consider a very large 

 amount of arithmetical labour. 



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