194

RAILWAY.

to this value will be found in the lower line of the Table; and since for smalldeflections the strain may he considered to increase with the deflection, the greatestload to which the bridge could be practically exposed should be diminished in theproportion of the total increment of statical deflection in the Table.

Strength of Iron . —The cheapest and most prevalent description of iron bridges inuse upon railways is the simple cast-iron girder bridge, and the form usually adoptedis that recommended by Mr. Hodgkinson, the top and bottom flanges being madeparallel for convenience, and the sectional area of the bottom flange being made fromfour to six times greater than that of the top, on theassumption that the strength of cast iron to resist atensile force is less than its strength to resist acrushing force in that proportion; and the breakingweight may be calculated from the following formula,where W = breaking weight in the middle of thebeam, l = distance between the supports, in feet,a = area of section of bottom flange in the middle,d = depth of beam in the middle,—

,, 2-166 ad

W = — I-'' 1

or, if the effect of the vertical part between the flangeswhole depth, d' = A B = depth to bottom flange, h = D E = breadth of the bottomflange, i' = F G = thickness of the vertical part,

W -3^{^ 3 -( S —

The following formula;, expressing the relation between the extension and com-pression of cast iron, and the weight producing them respectively, are given inthe Report of the Commission on the Application of Iron to Railway Structures, viz.

For extension, w = 13934040 - — 2097432000 e — .

I l 2

Fig.

A

is included, and d = A C =

d d 2

For compression,® = 12931560 — — 522979200 — >

where w = weight per square inch of section, l = length of bar in inches, e — exten-sion in inches, d = compression in inches.

Formulae have, however, been derived by Mr. Tredgold from the same experiments,which appear to be more convenient in calculating the strength of beams, from theconsideration of the forces of extension and compression acting round the neutralaxis: the formula; are—

For extension,

14173080 el + 288-84 e

For compression, w =

13002840 dl + 51-6 d ‘

The mean tensile strength of cast iron is 1571 libs, per square inch, and theultimate extension of the length ; this weight would compress a bar of cast ironof the same section of its length. The general ratio of the power of cast iron toresist tension to that to resist compression is 1 : 5'6603. In wrought iron theextensions and compressions with equal weights are nearly equal, and a rod will extend•01124 inch for each foot in length with a weight of 11 tons per square inch. Upto this weight the extension may be assumed to vary nearly with the weights; but