CHAPTEK XXin. 
EFFECT OF ?>1IAKES OX BOTTOM CHORDS. 
Afier roaming tliis treatise tlms f?ir some Japanese engineer may still liavo n,n 
iileii that some portions of the brulgos designed are too light, more especially i^ 10 
bottom chords. This is due to preconceived notions caused by the stiff lower clioi'^ 8 
ot the Japanese brklgGR. The chords here designed were proportioned for the 
combined eftects of tJit* maximum live load and the wind pressure : they can only 
too liglifc thevetoro, in resisting tho sliock of pas.siug loads. Let us investigate tliis 
point. The most destructive effect of a train would be when it is allowed to coiuo 
upon Uie bridge Avitli all the brakes set. To be on the side of safefcy let us assume n 
train ol engines, and take the coefficient of friction between wheels and rails to ^ 10 
0.8. Michael Keynokls C.E. in his treatise on u Continuons Bailways Brakes M p» 207 
makes the actual maximum value of this coefficient 0.25, although two pages 
tlier on he assumes it as wo have done to be 0.3. With tho train covering the 
Rpan the combined live and dead load tensions in the lower chords would bo so gi.ßM 
that the thrust of the braked wheels would most assuredly bo insufficient to overcome 
ifc, when tlie first pair of wheels conics u])on the bridge, the thrust which they 
pioduce will also be too small to counteract tlio dead load tension. Between thos 0 
two extremes there is one position of the loading which will be more effective tlift 11 
tiny otJier position in causing thrust upon the chords. Tlic train should be brought 
on at the expanding end af the span, iu which case the part upon which the thrust 
will act with greatest effect will be the end panels of the lower chord at the fixed cn^ # 
Lefc tlie dead load stress in the end panel of the bottom chord of one truss bo 
denoted by T, 
Let the variable reaction of the live load on one truss at the fixed end be repre- 
sented by /7, 
then the corresponding end panel bottom chord stress will be 7? tan 〇 
wliere Q is the inclination of tho batter brace to the vertical. 
Let w =5 the uniformly distributed live load per lineal foot on one truss 
1 = tlie coefficient of friction between wheels and rails 
I = lengtli of span. 
and x = length covered by the moving load, the origin of coordinates 
taken at the expanding end of the span. 
The reaction 
