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where 7 is the distance between the supports, a a' the externa! and internal radii, w the breaking weight, f the strain upon a unity of section as a square inch at the top and bottom of the tube in consequence of the weight w, π = 3.14159. From this formula we obtain
As it will be convenient to know the strain ƒ per square inch which the metal at the top and bottom of the tube is bearing when rupture takes place, this value will be obtained from each of Mr. Fairbairn's experiments; the value w being made to include, besides the weight laid on at the time of fracture, the pressure from the weight of the tube between the supports, this last being equal to half that weight. Computing the results, we have, from
Fracture in all cases took place either by the tube failing at the top, or tearing across at the rivet holes: this happened on the average, as appears from above, when the metal was strained 13 tons per square inch, or little more than half its full tensile strength.
Elliptical Tubes.-The value of ƒ in an elliptical tube broken as before (the transverse axis being vertical), is expressed by the formula
where a a are the semi-transverse external and internal diameters, bb the semi-conjugate external and internal
diameters, and the rest as before, w including in all cases the pressure from the weight of the beam. Computing the results from Mr. Fairbairn's experiments, we have, from
Rectangular Tubes.—If in a rectangular tube employed as a beam, the thickness of the top and bottom be equal, and the sides are of any thickness at pleasure, then we have
in which d d' are the external and internal depths respectively, bb' the external and internal breadths, and the rest as before. Mr. Fairbairn's experiment No. 15 gives by reduction
This is, however, much below the value which some of my own experiments give, as will be seen further on.
The value of f, which represents the strain upon the top or bottom of the tube when it gives way, is the quantity per square inch which the material will bear either before it becomes crushed at the top side, or torn asunder at the bottom. But thin sheets of iron take a corrugated form with a much less pressure than would be required to tear them asunder; and therefore the value of ƒ, as obtained from the preceding experiments, is generally the resistance of the material to crushing, and would have been so in every instance if the plates on the bottom side (subject to tension) had not been rendered weaker by riveting. The experiments. made by myself were directed principally to two objects:
1. To ascertain how far this value of ƒ would be affected by changing the thickness of the metal, the other dimensions of the tube being the same.
2. To obtain the strength of tubes, precisely similar to other tubes fixed on,-but proportionately less than the former in all their dimensions, as length, breadth, depth, and
EXPERIMENTS UPON RECTANGULAR TUBES.
from one size to another, with more certainty than hitherto. thickness,-in order to enable us to reason as to strength
Length. Depth. Breadth. Supports. Weights. Plates.
Another object, not far pursued, was to seek for the proper proportion of metal in the top and bottom of the tube. Much more is required in this direction. In the three series of experiments made, the tubes were rectangular, and the dimensions and other values are given in the preceding page.
"The tube placed first in each series is intended to be proportional in every leading dimension, as distance between supports, breadth, depth, and thickness of metal,—and any variations are allowed for in the computation. Thus the three first tubes of each series are intended to be similar, and in the same manner of the other tubes, &c.
"Looking at the breaking weight of the tubes varying only in thickness, we find a great falling off in the strength of the thinner ones; and the values of ƒ show that in these the thickness of the plates being 525, 272, 124 inch-the resistance, per square inch, will be 19.17, 14.47, and 7·74 tons respectively. The breaking weights here employed do not include the pressure from the weight of the beam.
"The value of ƒ is usually constant in questions on the strength of bodies of the same nature, and represents the tensile strength of the material; but it appears from these experiments that it is variable in tubes, and represents their power to resist crippling. It depends upon the thickness of the matter in the tubes when the depth or diameter is the same; or upon the thickness divided by the depth when that varies. The determination of the value of f, which can only be obtained by experiments, forms the chief obstacle to obtaining a formula for the strength of tubes of every form.
"In the last Table of experiments the tubes were devised to lessen or avoid the anomalies which riveting introduces, in order to render the properties sought for more obvious. Hence the results are somewhat higher than those which would be obtained by riveting as generally applied.
"The tube 31 feet 6 inches long, 24 cwts. 1 qr. weight, and •272 inch in thickness of plates, was broken by crushing at the top with 22.75 tons. This tube was afterwards rendered
straight, and had its weak top replaced by one of a given thickness, which I had obtained from computation; and the result was, that by a small addition of metal, applied in its proper proportion to the weakest part, the tube was increased in strength from 22.75 tons to 32-53 tons; and the top and the bottom gave way together."
For the details of these and the subsequent experiments, which are too extended to be introduced in this place, we must refer to the elaborate work of Mr. Fairbairn upon the "Conway and Britannia Tubular Bridges," where they are given with a mass of highly interesting correspondence, in which the entire history of the proceedings is narrated, and reductions of the experiments furnished.
Description of the BRITANNIA BRIDGE—The Masonry-Britannia Tower -Anglesea and Carnarvon Towers and Abutments-Arrangements for constructing the Tubes-Main Tubes and Land Tubes-Description of their Construction-Scaffolding and Staging-Arrangements for floating the Tubes-the Pontoons-Raising the Main Tubes--The Hydraulic Press-Connecting the Tubes in the Towers-The CONWAY BRIDGE.
HAVING in the preceding section given an abstract of the preliminary experiments upon wrought-iron tubes, we have now to describe the structures erected over the Conway River and the Menai Straits, and to show the admirable manner in which the material has been disposed to obtain the necessary strength for rigidity for bridges of such vast extent, designed to sustain the heavy weight and momentum of railway trains.
Of these bridges, that over the Conway was the first constructed, and was in itself an instance of triumphant success in design and execution; but as the Britannia Bridge far surpasses it in dimensions, and embraces similar works upon an extended scale, besides others not required in the Conway