— 106 — • 
end main diagonal to any conveniem; scale, and nnd the value of their resultant bv 
tlio parallelogram of forces. This resultant will determine tlie thickness of the bear- 
ing, a trial diameter beiug first assumed. Ifc is possiblo that tliis bearing will have 
to be increased, so that there will be enough iron to transfer tlie stresses from the 
batter brace, liip verticals, and diagonals, to the chord, as will be explained in the 
next chapter. An approximate test of the sufficiency of the bearing in this respect 
maybe obtained as follows : — 
Let 
d = tlie area of the section of the end panel of the top chord, 
d = depth of chord channels, 
t = thickness of web of an end chord channel ; 
then the bearing should not be less than that given by tlie formula 
B =4d +t 
Next find tlie distance l between the centre of the bearing of tlio chord and that of 
tbo diagonal, also tlio distance V between the former and that of tlie liip vertical, the 
latter being on the inside. Calling the stress iu tlie liip vertical F, and that in tlie 
diagonal S, tlie vertical moment will be FI ’， and tlie inclined one SL Next lay out 
these components to any convenient scale in tlieir proper directions, and find their 
resultant by the parallelogram of moments. This resultant will determine the 
diameter of tlio pin. 
If the diameter found agrees with the one assumed, or if it does not agree, pro- 
vided that the bearing was not determiued by the trial diameter, all right ; but if the 
bearing were so determined, and the two diameters do not agree, another trial must 
be made. 
Where there are more than two main diagonals coupled at tlie hip, as is tlie 
case in double-intersection and in heavy single-intersection bridges, ouo pair is 
coupled on the outside of the bearing, and the other on the inside ; so that theor- 
etically the greatest bending-moment is equal to the stress in tlie outer bar multi ， 
plied by the distance between tlie centre of the bar and tlie centre of the bearing. 
But practically tlie moment may be greater, for the distribution of stresses among 
tlie diagonals may not bo as assumed : so it is well to determine tlie moment by 
imagining the outer bar not to exist, and proceeding as explained above for the case 
of only two main diagonals at the liip, excepting, of course, that tlie thickness of tlie 
bearing must be ascertained by finding the resultant of tlie stresses in the two diag- 
onals and tlie liip vertical. 
To calculate tlie size of an intermediate upper chord piD, tlie widths of chord 
and post boarings are to be determined as shown in the next chapter. The former 
is given approximately by the last formula, where A is the section of the panel of 
the chord on the side of the pin towards tlie middle of the bridge, and t the thickness 
of tlie corresponding cliannel. The other is given by tlie formula 
B= T 3 
