148 UNIVERSITY OF COLORADO STUDIES 



rib's neutral curve joining the points 1 — 18, 2 — 17, etc. Proceed 

 then to draw the arch deflection polygon Yls by the regular methods 

 of graphics statics and likewise construct P^^; for the trial frame. 

 The closing lines rk=p and TS=q^ are proportional to 2M,?/ and 

 SM„y respectively. If the trial polygon were the true polygon 'p 



would equal q. In order that 2^,Mj2/=2-^,M„2/=0 they must be 



equal. 



By scale: ^=18.83 and 5- = 19.83. Since j9 is less than </, the 

 (quantities M, of the trial polygon are too small and the pole distance 

 is too large. This statement is correct when we remember that a 

 pole distance is always inversely proportional to the vertical inter- 

 scepts of the funicular polygon corresponding to it. Hence the 

 interscepts, column 15, of the true frame are found by multiplying 



Q 



the figures of column 11 by - and the true pole distance ZD is 

 found by multiplying the assumed pole distance by - . 



The true pole D can now be located by scale on the line ZD; 

 ZD = 20i,8001bs. 



Column 16 gives lines proportional to the true bending moments 

 in the rib, found by subtracting column 12 from column 15. 



Column 17 gives these bending moments found by multiplying 

 the lengths in feet in column 16 by the true pole distance in pounds. 



The true equilibrium frame can now be located by two different 

 methods: — Its vertices E, F, G, etc., can be located by laying off the 

 interscepts of column 16, observing their signs, from the points on 

 the rib's neutral curve; or the frame can be constructed by drawing 

 its sides in order parallel to the rays of the true force diagram ADB, 

 It is well to locate the frame in both ways as it gives a check upon 

 the preceding computations. 



The extreme rays DA and DB of the true force diagram repre- 

 sent the resultant thrusts on the abutments. Resolving these thrusts 

 into components respectively parallel and perpendicular to the tan- 

 gents to the neutral curve of the rib at the respective springing 

 points y and V we get the normal thrusts and the shears on the 



