— 109 
Vb == I\l and V 
Pd 
Again taking the centre of moments 
A givos the value of the bending mo- 
inent Mon the strut at that point, thus 
Mz 
ド ひ -*) ~^Pd = ~ b ( b-2 
Let み =3 the distance between centres 
ofgiavity of tlio two ehaunels of which 
幻 10 upper lateral strut is composed, then 
the beuding stress will be 
O 
M 
T 
-JP »v —、 
The intensity of the working bending stress being six tons, tlio number of square 
⑽ ies to be added to the area of each channel in order to vesist the bendiug "will be 
A C Pd 0 s 
The stress in A B is found by takiug the eentro of moments at G, aud making 
10 moment of its stress R equal to tlie moment of the horizontal reaction at E, thus 
li 8 V\ =5 ^ Pd 
and 2? = ^5 Vi = 0.707 — 
Ä S 
• Tlie bending momeufc to be provided for in the post, considering it fixed at its 
• *4 
a nd tlie correspondiug stress on one channel will be given by the equation 
C = P(d-s\ 
4 m 
^ lere w lias th© same value as iu the last case. 
As before to make tlieso formulae applicable to a portal, make d equal to the 
en g 1 of the batter brace and P equal to one half of the sum of tlio pressures con ， 
c entiated at all the panel points of the upper lateral system. 
only one track of a double track bridge is covered by the moving load, 
Recording to the law of the lever, one truss receives more load than the other. Now 
tlie two trusses could act independently tins distribution would hold while the load 
coveied the track ; but if the two trusses were connected by perfectly inelastic ver- 
! Ca SWa y bracing they would have to deflect equally, which could only occur when 
f e l oa d s ou each truss were equal, so that a portion* of the load equal to the dif* 
, Glenco between the greater division by the law of the lever and one half of the whole 
would have to be transferred by the vertical sway bracing. In reality neither 
these conditions will exist, the true condition lying between tlie two ; for the trus- 
sos do not act independently as if there were no vertical sway braoiug, anti the latter 
18 ai f rom being perfectly inelastic. 
