— 135 — 
the middle, according to the number and arrangement of tlio cliord bars. The ver- 
tical component of the bending- moment on any one of these pius is so small in com- 
parison with the horizontal component, that it may be neglected. For bridges with 
mi even number of panels, — 
Let 
T = tension in middle panels of lower chord , • 
anil 
w = the average thickness of chord bars in these panels ; 
then, approximately, 
^ = bending- moment on middle pin. * 
his formula may be applied, but perhaps with less accuracy, to a bridge having an 
0 ⑽ number of panels ； and, it* the chord be properly packed, the error will be 
upon the side of safety. 
With the exception of the chord pins at the shoes and at the first panel points 
^ 10m the ends of the span, all the lower chord pins may have a diameter corres- 
ponding to this maximum bending-moment, unless the bridge be a long or very 
heavy one, when some of the intermediate pins may have their sizes determined 
Gitiiei* by calculation or by interpolating ; taking care in the latter case that they be 
liberally proportioned ; for tlie strength of a pin reduces rapidly with the diameter. 
To find the sisse of the lower chord pin at the first panel point, use the formula, 
for the horizontal component of the moment, and the formula 
T - t J ( d + d’ ) 
. V ~ 4 
ぐ ? 1 山 6 vertical component ； t being the intensity of working- stress for the liip ver- 
1Ca k, a their area (S. E.), to be taken from Table YII, d the diameter or thickness 
of a hip vertical, and cV that of a beam hanger. 
Tlie moment giyen by the formula 
M = \/>I 2 + F 2 
^Pplied to Table XIV will determine tlie diameter required. This diameter 111 ay 
e used also for the pin at the shoe. 
Where a bottom chord is composed of a continuous strut and eye-bars, the 
8 less on the former cannot affect the pin, for it lias no lever arm, consequently in 
Pjopoifcio^j n g an y bottom chord pin except that at the shoe for such a case tlie value 
° T is to be found by multiplying tlie sum of the areas of all tlie chord bars in tbe 
COn sitlered by tlie intensity of working stress for those bars. 
To fiud the size of a liip pin, lay off the stresses in one liip vertical and one 
whioVi Ver y l on 叾 span double track bridges this formula will give an excessive diai^ete 卜 in 
foments 868 arran S emen t of the chord packing must be relied on to reduce the bending 
