THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



ISiO.J 



dW AA. Inquiries to supply data for the erection of the Tubular 

 Bridses; Appendix B. An Essay by Professor VV illis on the 

 deflection of Beams by travelling loads, with researches by Pro- 

 fessor Stokes; Experiments on the same suliject, by taptiiin 

 James and Lieut. Galton; also on statical pressure and sUnvly- 

 moving weights; Evidence by eminent engineers; Replies to circu- 

 lars sent to Iron-masters and Iron-founders; &c. 



The plates in the second volume are illustrative of the several 

 kinds of experiments, and include elevations and details of a very 

 consideralde number of important railway bridges. . . . . 



The Report commences with a notice of the contrariety of 

 opinions respecting the effects of tr.avelling weights on girders- 

 some engineers thinking one-third, and some no more than one- 

 tenth the statical breaking weight, the greatest _ load which the 

 structures could safelv bear. It is stated that in the course of 

 the inquirv, it appeared "that the eiiects ot heavy bodies moving 

 with -reat velocity upon structures had never been made the sub- 

 ject ol- direct scientific investigation." This may be true as regards 

 p,il>lication before the conuneucewcnt of the inquiry by the Com- 

 mission ■ but very shortly afterwards, and long before the publication 

 of the present volumes, the paper (which is noticed in it at page 

 213 by Professors Willis and Stokes, with approbation) on tlie 

 Dynamical Deflection and Strain of Railway Girders, appeared 

 in' the number of this Journal for September, 18t8. ., , , 



In theexijerimentsof the Commission, velocity liad considerable 

 eftect in increasing deflection. It is, however, important to know 

 tliat the conclusion is not extended to practice. 1 he results ot 

 the inquiry thoroushly confirm the conclusion stated in this Jounia/ 

 that ill reiil railwaV girders tlie deflection is incOHsulenib!,/ increased 

 bu the velodtij of the tnvusit of a train. The reason that the experi- 

 ments appai-en'tly vitiate this conclusion is admirably elucidated by 

 Professors Willis and Stokes. For tlie present, it is sufficient to 

 observe that the increase of deflection in the experiments arose 

 from the smallness of the mass of the beams compared with that 



of their loads. „ , » ri'i *• •).,, 



An apparent inaccuracy as to the history of the Laws of Elasticity 

 occurs in Appendix A, given in another part of this Journal- .•— 



" Dr Hooke's law, e.vpressed by him in the jihrase '■at tensw sw 

 vis: is not, perhaps, accurately true in any material. Its deviation 

 from truth in cast-iron, under every degree of strain, even the 

 smallest, was first shown by experiments made by tl>e author, and 

 reported in the sixth volume of the Transactions of the BrtUsh 

 Association for the Advancement of Science In his subsequent 

 researches on the elasticity of various materials, it was shown that 

 this defect was considerable in stone and other crystalline bodies 

 tried, and existed in a less_ degree in wrought-iron, steel, timber, 



and laminated substances." , , „ , . * ,a^ „„,.= 



The inexactness of "Hooke's law" was shown about 100 yeais 

 before any member of the Cmimission was born, and by no less a 

 person than James Bernouilli. In the Acta Eraditoram of Leipsic, 

 tor 1601 he gives investigations of the elastic curve— 1, generally 

 when the elastic forces "follow any law whatever; 2, when they 

 vary as any power of the extension; 3, when they are directly 

 proportional to the extension. The latter investigation heprefaces 

 by sayingt — 



■ " The common hypothesis, as I have just said is that the e.vten- 

 sions are proportional to the stretching forces, which was formerly 

 adopted l.v the celebrated Leibnitz, in his most mgeniuus research 

 resilecting the Resistance of Solids ; and by myself in the present 

 subject, before that I arrived at the general construction o the 

 uroblem 1 therefore consider it worth while to explain a little 

 n.ore particularly the nature and properties of our Curve on this 

 hynothesis; although I am very unwilling to contend for tl.e pre- 

 cise truth of this "hypothesis, or of any other, being persuaded 

 rather, that no constant law of tensions is observed in nature but 

 that it differs according to the different texture of bodies. J his is 

 seen to be abundantly confirmed, both by my own and other per- 

 sons experiments, of which a great part are industriously collected 

 by the author, whom I have already commended [I-ranciscus 1 er- 

 tius de Lanis] in the above quoted treatise, Mayistera natarw et 

 artis." ^_^_ 



t See Journal, page S6. 



« Vuli-aris f,.t modo tiixi) est hypothesis extensions viribus tendentib..s proporl.on- 

 ales«\se qua et usus olim cenlebefrimus l)r. Leibnilius in acuti.s.nna sua luc.braoonede 

 1 "isfenl.a S.fl.dorum ; et ip semet ego in presents materia, prru. qoam generalem pro. 

 blmA." eoustructijnem adveuissem. Qaapropter opera preuu.n eiisl.mo, naturam et 

 „r, Driat'S curvie n-sirs in hoe hypothesi pernio speciaiius exponere: quaoquam pro 

 FJsa"^ JpotheseoThnjus. sicut et pro cuju-ve'alterius. veritate nndtum m.l.tare nohm 

 ««,uarm potL b, beis, nullarn conslantec, tensioniin, l.gem in natura observari sed 

 ^am pro d vSL corporum texlura diversam existere, id quod expe.rmenta tun, tjostra, 

 tn" ^a™,ram[ abunde confirmare vid.ntur, quorum plurima prffila»datuB Author iudua- 

 tnU3 " Jlagistcril ualuia: cl attia " loto cit reteustt.-p. 2/0-1. 



There seems no reason to suppose that an e.xact mathematical 

 law of elastic tension can exist, or that a law which expresses the 

 extension by the first, or first and second, powers of the tension, 

 can he otherwise than approximate. With respect to many forces 

 existing in nature, there can be no such antecedent (dijeetion to 

 an exact mathematical law. For central forces, such as the sun s 

 attraction, we may readily supjiose « priori that the law may be 

 that of the inverse square, because if the attraction be supposed to 

 radiate into space, like light, the concentric spherical surfaces 

 over which it is diffused vary in magnitude as the square of then- 

 radii. But with regard to the cohesive force of particles in con- 

 tact, there can be no such regularity of operation. 1 he tensile 

 powers of a piece of stone or iron are afl^ected by its heterogeneity, 

 crystallisation, lamination, porosity, chemical affinities, tempera- 

 ture &c. Now, in discovering a law of tension from experiment, 

 all these irregularities are " lumped" together, and we strike an 

 average of their efi'ects. . ,-/r . 



If as in some of the experiments before us, twenty different 

 weights be applied to stretch in diiferent degrees the same rod a 

 theoretical law involving first and secund powers only, will slightly 

 disaeree with each of the twenty experimental results. \t e niu:n, 

 therefore, suppose either the law or the experiments, or both, tj. 

 be inexact. If the experiments exhibited perfect accuracy (though 

 this is never attainable), the law must not stop at the second 

 power but he continued to the twentieth; for there will be twenty 

 equations to determine twenty unknown quantities--namely, the 

 co-efficients of the twenty powers. A formula involving the first 

 four powers is given in a note, page 113. ^. , 



We observe with pleasure a notice of the efScient assistance 

 which Mr. Tredgold, son of the late celebrated writer of the 1 re;-:- 

 tiseonthe Steam-Engine,' rendered in the cmnse of this experi-- 

 mental inquiry. In addition to a great amount of numerical 

 computation and experimental observation, he pivpnred several 

 excellent drawings illustrative of the experiments, and appearing 

 with his name in the second volume. _ , . .v 



It will be remembered, that some surprise was occasioned by the 

 rublication in the recent edition of Dr. Gregory s .Mechanics 

 tor Practical Men,' of the results of some experiments giving 

 hio-her values for the tensile strength of cast-iron than have been 

 hitherto generally adopted. This subject has been again referred 

 to careful observation; and an explanation, which seems correct, is 

 .riven of the too high values of the tensile strength obtained by 

 Mr Thomas Cubitt— namely, that he used a hydraulic jn-ess to test 

 the iron, and that this machine is apt to give exaggerated results. 

 Experiments have also been made, to determine whether the ten- 

 sile strength be greater for cruciform than for circular or rect- 

 angular sections of the rod. It appears that the strength per square 

 indi of section is a little (but only a little) stronger for the cruci- 

 form section, the excess of strength being attributed to the metal 

 beinif harder in the thinner sections than others. We may here 

 remark, that for a similar reason the strength per square "'ch, of 

 circular sections for example, is probably somewhat aflected by the 

 magnitude of the section. On account of irregularities of casting 

 and cooling, it is probable that a circular rod 4 square inches iii 

 area, would not be exactly twice as strong as a similar rod of 2 



square inches area. . i „ i „„„ 



Only one beam exceeding IS feet in length appears to have been 

 used- and this was supplied not by government, but by private 

 persons. It was 48 feet long; and one of seveial girders in- 

 tended for a bridge across the river Irwcll. Lieutenant Galton, 

 the indefatigable secretary of the Commission, assisted at tb.s 

 experiment. . , ., 



in order to notice all the statical experiments together, we pro- 

 ceed to refer to experiments by trans%erse pressure on rectangular 

 beams, made by Captain James at Portsmouth. The mt.st ■■emar.;- 

 able of these experiments were on f-inch bars planed out of the 

 centresof 2-inch square ami 3-inch square bars. fl„„f„,. 



These experiments, like the preceding, show that the deflection 

 increases fi-'>m the commencement of each expcrraient somewhat 

 more rapidly tlian in pro] <u'tion to the transverse pressure. Expe- 

 riments'were also made by means of the hydraulic V';^^. °" * '"^ 

 efi-ect of tension bars attached along the under sides of the bottom 

 flange of cast-iron girders. The mean of severa experiments on 

 girders 9 feet between the supports, ga^ve t :e breaking weigh 

 lith the tension bar rather greater than without it ; and sim lar 

 results were obtained from girders with the upper «;'''f^e a ched 

 These experiments were n..t, however, followed out (from want 

 of time and limited means' again!) so far as was deemed desirable 



Our notice of other parts of the inqu ry we reserve for futuie 

 consideration. 



