GIRDERS AND SUSPENSION CHAINS COMBINED. 247 
_ The deflection of the Britannia Tube, if reduced to 150 tons, would be 12°5 
inches. 
‘The depth, practically, of the proposed peauondarty Bridge is 16} feet, a8 
of the Britannia Tube 28 feet,—16° : 28° :: 125, or 449°21 : 219520 : 
12°5 : 6:07 inches, which has. to be reduced in the ratio of the cube of the span, 
460° : 440% :: 60°7 : 53:08 inches, the deflection of the Londeonderry girder 
with 200 tons all over. 
_ The mean of the three results indicates 41°25 inches as the deflection of a 
_ girder of 150 tons, loaded all over with 200 tons, and 33 inches when loaded 
in the middle with 100 tons: == 192 will therefore be the deflection when 
attached to the chain *. 
B. 
Dimensions of Londonderry Bridge, and calculation of Strains and Deflection. 
_ Span between points of support, 451 feet; length of the girder, 440 feet ; 
depth at high tower, 88 feet ; depth at side tower, 59 feet ; centre catenary 
half horizontal length, 246 feet ; side catenary, half horizontal length, 205 
feet ; length, half chain (centre), 266°2 feet; length, half chain (side), 
915°5 feet. 
Strain on cables at high tower with 3 tons per foot load, assuming jth to 
_ be supported by the girder and 2} tons by the chain, according to the for- 
~ mula 
=> Vie typa x “4 x 88? + 2467=1031 tons, 
x being the depth of catenary, y the half span, w the weight equally distri- 
_ buted, and T the tension. 
_ Section of the cable at high tower, so that no strain exceeds 5 tons per 
inch, 206 inches. 
Strain of the cable at the side tower, 
x88 X / 4x 597+ 205°= 1000 tons. 
4 Baction of cable at side tower, 200 inches; horizontal strain, 840 tons; 
section of iron at bottom of chain, 168 inches. 
a Deflection from Expansion and Contraction. 
"This calculation assumes that the expansion between summer and winter 
youth part of the length, and that it produces a strain of 5 tons per inch, - 
exact length of the chain from the formula 
a VP t te + 3x" or / 246? + £88"= 26616, 
z being half length of catenary, 
y being half chord, 
x being versed sine. 
Add elongation of half the cable 133 
266°293 
re V32—y= /3266:293° —2462= 88:3. 
deflection, dierefate, from the temperature will be 4rd of a foot, or 4 
aches, a deflection much under that of ordinary suspension bridges, arising 
e deflections are here estimated to vary as the cube of the depth, in order to obtain 
eme amount. The more correct result in a beam of this form will be from the 
e, 80 that the means here given of 41-25 and 33 inches will considerably exceed the 
al deflection. 
