86 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



fMAncii, 



APPENDIX (A) TO REPORT ON IRON. 



By Eaton Hodgkinson, Esq. F.R.S. 



The following; series of experiments was conducted by the author, 

 partly in London, and partly in Manchester. The description and 

 tabular results of the whole are given in this Appenilix, with such 

 general conclusions from them, as tlie limited period of the time 

 of preparing the results for the press permitted. 



In accordance with the instructions under which the Commis- 

 sioners acted, the experiments were directed principally (though 

 not wholly) to determine the effects of impacts and vibrations 

 upon iron. Several distinct classes of experiments have therefore 

 been undertaken, for the purpose of exhibiting the properties of 

 cast-iron, in particular, when subjected to different mechanical 

 tests, and the numerous tables appended wiU show the e.xtent and 

 variety of these inquiries. 



An extensive experimental inquiry, not yet published,* had been 

 recently concluded by the author, of which the object was to 

 determine the mechanical conditions to be observed, in the con- 

 struction of the tubular bridges across the Menai Straits and the 

 Conway. 



Among other results, it was ascertained that a great saving of 

 metal for an assigned degree of strength might be effected by 

 employing cast-iron longitudinal ribs in the top of wrought-iron 

 tubes. It seemed, therefore, very desirable to ascertain for the 

 purpose of this Commission, whether, and in what manner, the 

 combination of wrought and cast-iron might be advantageous in 

 trussed girder bridges. For such experiments, peculiar facilities 

 existed, as they might have been made with apparatus of a very 

 complete and costly description, which had been constructed for 

 former experiments on the strength of materials, and much 

 extended for those on tubular bridges. 



Of the latter, some of the models experimented upon were large, 

 and varied in weight from three to seven tons. Had experiments 

 on trussed girders of h.alf that weight at least, been made, it is 

 probable that valuable conclusions, directly applicable to the prac- 

 tice of engineering, might have been obtained. The expense 

 attendant on such experiments would, however, have been great, 

 and the limited extent of the grant to the Commission, rendered 

 it necessary to confine the inquiries to those subjects on which 

 a knowledge of fundamental principles was most required. It 

 became then a matter of careful consideration to devise the 

 experiments in such a manner that their practical utility might be 

 as little as possiI)le affected by the restriction referred to, as the 

 scale of the experiments did not always permit direct and imme- 

 diate comparison, with the actual practice of railway construction. 



The experiments were therefore conducted, so as to obtain 

 principally those scientific data, which appear to be most required 

 for completing the mechanical theory of elastic beams. 



Defect of Elasticity. 



In any general investigation of the properties of elastic beams, 

 the powers of tlic material to resist direct tension and compression 

 are necessary data. If a beam be in any manner bent, its concave 

 side will be compressed, and its convex side extended. The mate- 

 rial is, consequently, sulijected to both tensile and compressive 

 forces; of which, therefore, an exact knowledge must precede any 

 accurate general theory of the laws of deflection, vibration, and 

 ru))ture. 



The longitudinal compression and extension of iron within 

 certain limits are usually assumed to be directly proportional to 

 the external forces by which they are respectively produced. The 

 law is known by the name of Doctor Hooke, the first proposer of 

 it, and has generally been made the basis of mathematical investi- 

 gations respecting the deflection and strength of loaded beams. 



Doctor llooke's law, expressed by liim in the phrase "«; tensio 

 sic vis," is not, perhaps, accurately true in any material. Its 

 deviation from trutli in cast-iron, uiuler every degree of strain, 

 even the smallest, was first shown by experiments made by the 

 author, and reported in the sixtli volume of tlie Transactions of 

 the British Association for the Advancement of Science. In his 

 SHl)se(iuent researches on the elasticity of various materials, it 

 was shown that this defect was considerable in stone, and other 

 crvstalline bodies tried; and existed in a less degree iii wrought- 

 iron, steel, timber, and laminated sul)stances. 



It is a necessary consequence of tlie ordinary law of elasticity 

 that the deflection of a horizontal beam by a vertical pressure 

 should be directly proportional to that pressure. This conclusion, 



♦The work here mentioned appears In Ihe Report, under the designation of Appen- 

 dix AA. 



as might be expected, does not, however, coincide with experiments 

 on beams of those materials, of which the elasticity has been above 

 stated to differ considerably from that assigned by Doctor Hooke's 

 law. 



As the law of elasticity constitutes the very basis of all sound 

 knowledge of the statical and dynamical properties of girders, the 

 revision of that law, with respect to cast-iron at least, became, in 

 the author's opinion, an indispensable requisite in the present 

 inquiry, He, tlierefore, obtained liberty to make some experiments 

 on the extension and compression of rods of iron, in order to 

 deduce from them, if possible, the general relations between the 

 weights and the clianges of length produced. 



To numerous experiments respecting impacts, occupying 97 

 tables, and to others made to determine the direct tensile and 

 crushing strength of irons, not previously tried — besides some of 

 smaller magnitude — the following experiments are added: — 



1st. To determine with precision the direct longitudinal exten- 

 sions and compressions of long bars of cast and wrought-iron, by 

 weights varied by equal increments, up to that producing, or nearly 

 producing fracture. 



2nd. To seek for general formulae, connecting the weights with 

 the corresponding longitudinal tensions and compressions of cast- 

 iron, and likewise, if practicable, with the "sets," or permanent 

 alterations of the length of the rods remaining after the removal 

 of the external forces: in order that the former may be directly 

 applied to the determination of the situation of the neutral line, 

 and the strength of cast-iron beams of every form of section. 



3rd. To determine with equal precision, the deflection of hori- 

 zontal bars produced by various transverse pressures, and to 

 compare the effects with those produced by impacts. 



1th. To seek for general formula; connecting the transverse 

 pressure, the deflection, and the set remaining after the pressure 

 was removed. 



The great defect of elasticity of cast-iron, and particularly as 

 compared with that of wrought, may be rendered \ery obvious by 

 the results of the experiments on each of the irons, with respect 

 to extension, compression, and transverse flexure. 



The theories in common use, at the present time, proceed on the 

 supposition, that bodies strained are perfectly elastic; and there- 

 fore the extensions, compressions, and transverse flexures are 

 assumed to be, within certain limits, as the forces producing them. 

 Thus, w := the weight applied to stretch a body, and e ^= the 



V} 



extension produced by that weight, the ratio - ought to be con- 

 stant with different weights laid on the same bar, and it will be 

 found much more ne.arly so in wrought-iron, than in cast, but in 

 neither strictly so. If, in like manner, uj' be the weight applied to 

 compress a bar, and d the decrement of length it has sustained, 



-r ought to be constant, but there will be a falling off, analogous to 



the last, in cast-iron particularly. In the transverse flexures ot 

 bars, if i«^ represent the weight laid on, and d the deflection pro- 

 duced, - ought to be constant, but the falling off will be as in the 



"i 

 preceding cases. 



Formulce for the Resistance of Bars to Horizontal Impact. 



In an experimental inquiry by the author, into the power of 

 beams to sustain impact from a body striking them horizontally, or 

 falling directly upon them, it was shown that if blows of the same 

 magnitude were given upon the middle of a beam, either by elastic 

 or inelastic bodies of the same weight, the same effect would be 

 produced. The striking body appears to proceed with the beam 

 after impact, as if they were one mass. — (5th Report of the British 

 Association, 1835.) 



In tlie inipiiry above, formulse were deduced according to these 

 conclusions, both for horizontal and vertical impacts, taking into 

 consideration the effect of the weight or inertia of the body struck. 



Formuls for horizontal impacts are comparatively simple, and 

 that given below is the same as that of Tredgold. — (Essay on the 

 Strength of Iron, Art. 302.) 



/( w- pe 



w -\- w 2 



where w = the weight of the striking body, h == the height due to 

 the velocity of the impact, ;* ^ a pressure which applied gradually 

 to the middle of the beam, would bend it to an extent equal to tliat 

 jiroduced by the impact e =; the deflection caused by that pres- 



