<; i:\rn 1C STATICS 



GRAPHOTYPE 



i\ an-!.- of the structure. At the angles 

 1-22 ami 12-13 the upward pressure of the piers in 

 p.-irtly neutralised by the local weight of o tons; 

 tin- vertical l>urs 1 and 12 have each an upward 

 tlinistof 45 tons, which carries the girder ; but at 



angles there are no horizontal components 



\ 



\ 



5, 



Fig. 3. 



along 22 and 13, which, therefore, have no thrust 

 along them, and are neither compressed nor in ten- 

 sion. If a vertical line a t (fig. 3) be drawn, each 

 division in which represents 10 tons, the distribution 

 of load may be set out by taking a starting-point, 

 A : then there is in the girder, from 1 round to 12, 

 no load introduced ; between 12 and 13 there is in- 

 troduced what is equivalent to an upward force of 

 45 tons in bar 12, and the representation of this is 



22 



3 = A&; 8 = Ad; 4 = A/; 5 = AA; 



Ag; 11 = As. 



LOWER BABS, TENSIONS : 



22 = 22- = ; 21 = 21-c; 20 = 20-e 



19 = 19-0; 18 = 18-i; 17 = 17-i 



18 = 16-n; 15 = 16-p; 14 = 14-r 



18 = 13- = 0. 



upwards, to 14 ; HO for each of the junctions a* far 

 aft 21-22, and then at 22-1 there U an upward 45 

 tons in liar 1, the netting -off for which brings UH back 

 to A. At the junction 1-2 we have three bars in 

 ripiililirium ; tliexe are 1, 2, and ab ; the strew* in 1 

 is 45 tons ; drawing a triangle, Aub ( tig. 3), in which 

 the sides are parallel to 1, 2, and ab, we find the 

 relative compressions in 1 and 2, and tension in ab. 

 At the next junction, ab-bc (fig. 2), we have four 

 balanced forces, the tensions in 21 and ab, compres- 

 -i< >M in '"-. and a load of 10 tons. From the extremi- 

 ties of uli ( fig. 3) draw 22-21 representing the 10- ton 

 load acting downwards, and be a line parallel to // 

 in fig. 2; join 21 and the line be by a line parallel 

 to the rod 21, the tension in which i- now repre- 

 sented by the line 21-c, while be (fig. 3) represent* 

 the compression in be (fig. 2). Next consider the 

 junction 2-3 ; four bars, 2, be, cd, and 3 ; 2 we know 

 ( = Ab, fig. 3), and also be; we draw a line cd, and 

 a line parallel to 3 which, in order to complete the 

 polygon, can only start from A ; Arfand erf represent 

 compression ana tension in 3 and cd respectively. 

 At the next junction, 21-20, we have 21 (= 21-c), 

 cd ( = cd), de (unknown), 20 (unknown), and a 

 10-ton load ; the polygon is completed by 20<? and 

 de drawn from the ends of the broken line rfc 21-20. 

 Step by step, by mere drawing of intersecting lines, 

 ana by a process which, once the foundation has 

 been laid by setting out the distribution of 

 loads, is far more expeditious arid simple than 

 the explanation of it can at first enable it to appear, 

 fig. 3, the measurable diagram of the girder-bar 

 stresses, is evolved, and it is seen that as we near the 

 centre the tensions on the diagonals diminish, that 

 the vertical bar jk is neither under compression nor 

 tension, and that the bars 6 and 7 are under the 

 maximum compression ( = A-jk ), and the bars 1 8 and 

 17 under the maximum tension ( 18-t, ll-l). It will 

 l)e seen that the diagram is symmetrical ; but, if we 

 take the case of a non-uniformly distributed load, 

 the diagram becomes unsymmet- 

 rical. Suppose another 100 tons 



UPPER BAR, COMPRESSIONS: 



= AO; a = Aa; * = A/, o = .a, , , . \* ., , , 



6,7 = Ajfc; 8 = Am; 9 = Ao; 10= to be laid uniformly upon the 



Fig. 4. 



prepared for by setting off 4} divisions downwards; 

 then between 13 and 14 there is a downward load 

 of 10 tons, and the diagram sets off one division 



lower booms of the left-hand 

 half of the girder : now the piers 

 respectively support 125 and 75 

 tons ; the stresses in bars 1 and 

 12 are 110 and 70 tons ; the dia- 

 gram, built up on the same 

 principles as in the preceding 

 case, and drawn to a scale 

 reduced to three-fourths, takes 

 the form shown in fig. 4. 



See R. H. Smith, Graphics; 

 or the Art of Calculation by 

 Drawing Lines ( 1889). 



Graphis (Gr. graphd, 'I 

 write ' ), a genus of lichens, 

 which gives its name to a tril>e, 

 Graphidea*, remarkable for the 

 resemblance which the fructifi- 

 cation (apothecia, or shields) 

 assumes to the forms of the 

 letters of oriental alphabets. ' '. 

 scripta is common in northern 

 1 Europe, but of the twenty species 



the great majority are tropical. 

 Some are said to assist in the 

 identification of cinchona barks 

 of particular species, growing on 

 certain kinds and not on others. 

 Graphite. See BLACK LEAP. 



Graphophone. See 



PHONOGRAPH. 



Graphotype was one of the many processes 

 intended to supersede wood -engraving. The design 

 was sketched with silicate on a prepared chalk 



