294 REPORT—1858. 
sec ¢=length of chain at top or highest part.) corresponding to 1 foot 
sec ¢'=ditto at bottom or lower part. in length, measured 
k=load on the chain. (See explanations, ec.) horizontally along the 
l=weight of the chain and its appendages. chord of the para- 
k+lJ=p=total maximum load on chain for cal- bolic curve of the 
culating tension. chain. 
T=tension at any part of the chain. 
r=height or depth of abutment. 
P=half length of abutment. (See explanations, d.) 
W=theoretical weight of abutment to resist 
tension. 
FORMULE. 
kx Vi? +2" 
o= ——— for sectional area of chain. 
e—u.n.sece pV hi +2" 
T=pVi?+x> . . . for tension of chain. 
Tr 
W=p . . . + . for resistance to tension. 
a. Appendages of the Chains.—The minimum sectional area of the chains 
is the product of the breadth and thickness of the iron thereof in its smallest 
dimensions. But the links of plate-chains overlap each other at their extre- 
mities, which are enlarged and connected together by screw-ended short bolts 
of large diameter, secured by nuts and keys; these additions to the simple 
chains constitute their appendages, and increase the weight (and consequently 
the average sectional area) by about from 20 to 25 per cent. of the minimum 
area. Where wire is employed for the suspension in the form of cables, the 
appendages thereof will bear a very much smaller proportion than the above 
to the minimum area, as they consist merely of the wrappings around the 
steel strands of the cables. 
b. Maximum Weight admitted on the Chains.—The maximum weight or 
strain on the chains or wire cables of suspension bridges, should not exceed 
a fourth or a fifth of the breaking weight or strain, nor should it exceed 
materially the half of that strain which would produce a permanent effect 
upon the natural elasticity of the iron. The breaking weight or strain of 
good wrought iron varies from 20 lbs. to as much as 28 lbs. (avoirdupois) 
upon the square inch of the section of the bar. The strain which causes 
wrought iron to take a permanent set (that is, which so stretches the fibres 
of the iron that their elasticity is injured, whereby the iron no longer returns 
to its normal length when the strain is taken off), varies from 10 lbs. to 
14 Ibs. per square inch. Consequently the expression (e) in the formula 
ought not to be taken higher than from 5 Ibs. to 7 lbs., or from 00022 ton 
to 0:0032 ton. 
f& c. Load on the Chain—This quantity comprises the weight of the sus- 
pension rods (dependent from the chains or cables, and from which the 
platform of the bridge is suspended), also the weight of the roadway or plat- 
form, and the greatest weight with which the platform can be loaded. These, 
together, constitute the load on the chains, exclusive only of the weight of 
these chains themselves and of their appendages. 
d. Dimensions of the Abutment.—The height or depth of the abutment is 
to be measured from the point on the outer face thereof, at which the chains 
enter therein; and the length of the abutment is to be measured from that 
same point to the point at the opposite or inner side of the abutment to 
