CHAPTER XII. 
PROPORTIONING OF TRACK STRINGERS, PLATE GIRDERS. 
ELOOll BEAMS AND BEAM HANGERS. 
The economic depth for a track stringer or plate girder will not generally vary 
much from one eighth of tlie span, al though English engineers usually adopt one 
twelfth. Tlie best American specifications give preference to girders in wliicli the 
depth is not less than one tenth of the span. Other things being equal tlie deeper 
tlie girder tlie less will it deflect, so a depth of one eighth is preferable to 011 o of one 
twelfth of the span, unless it necessitate the use of more iron, which it should not. 
There can be considerable variation in tlie designing of ginlers, wliicli will involve an 
appreciable difference in tlieir weights and economic depths. 
As the function of tlie web is to resist shear alone, the formula for the area of 
tlie upper flange of a girder will be 
and tliat for the lower flange 
M 
Td 
+ A rf 
where M is tlie greatest bending moment on the girder afc the point considered, T = 
the intensity of working stress = 4 tons for built girders or 5 tons for rolled one?, 
d the depth between centres of gravity of flanges, and the area lost from the 
lower flange at the point considered by the rivet holes. As a table of equivalent 
imiformly distributed live loads for all cases is given in Cliapter YI and another 
corrected for shock in Chapter VII， the valao of the greatest bending moment at any 
point of a girder will be given by the equation 
M = — ^ - . {I — x) 
