14 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



[Janiary, 



pxtremity, ami loaded at tlie other, lieeomes a lever, at the ex- 

 treme end (if which acts the vveiirht teiidiiisr ti> heiul and break tlie 

 material, by turning it round tlie iioint of support ; while tlie 

 power of resistance, residin;:^ in the section of fracture at the 

 support, acts in the middle of that section, and at a distance 

 from the centre of motion equal only to half the depth of the 

 beam. The same is the case with a beam supported at the two 

 extremities and loaded in the middle ; the beam, in that case, 

 dividing itself in the centre into two levers, and half tlie weight 

 acting at the extremity of each ; wliile the strength of the beam 

 acts, as before, in the centre of resistance, which is in tlie middle 

 section of the beam. The notion of tlie beam turning round the 

 point of sup|)ort and distending or stretching all the particles in 

 the section of fracture, which was that of Galileo, is not correct ; 

 the centre of rotation is in a point somewhere near the middle of 

 the beam, and all the particles below this point are distended, 

 while all the particles above this point are compressed or crushed 

 together, while in the centre they are neither compressed nor dis- 

 tended, and hence this point has been termed the neutral axis. 

 Much discussion has arisen regarding the exact position of this 

 neutral axis — the limit between the tensile and compressive forces 

 — a nice question, and one of abstruse and difficult investigation ; 

 and the probability is, after all, that it is not a fixed point, but is 

 liable to vary with the nature and intensity of the strains. Be 

 that as it may, it fortunately happens that the practical result as 

 to the strength of the beam is almost exactly the same, whether 

 the axis be supposed, with Galileo, at the point of support, or, 

 with succeeding philosophers, at a point near the centre. In every 

 case the strength depends, as formerly explained, on the length and 

 depth of the beam, combined with its area at the section of frac- 

 ture ; and by these three elements the strength can be calculated 

 in every case, provided we ascertain fty experiment the actual 

 strength of a beam or beams of given dimensions. Numerous 

 exjieriments have been made with this view, and particularly on 

 cast-iron, by Messrs. Hodgkinson and Fairhairu, and other ob- 

 servers. These were made on beams of various dimensions as to 

 length, breadth, and thickness, but the calculation is simplified if 

 we reduce them all to a unit or standard of 1 cubic inch ; taking, 

 for example, a bar 1 inch square, resting on supports 1 inch 

 apart and loaded in the middle, and the average result of all the 

 different experiments is, that such a bar of cast-iron would bear a 

 weight of 24,400 lb., or very nearly U tons. The strongest spe- 

 cimen was of No. 3, cold blast, which gave 31,212 lb., or nearly 

 14 tons ; and the weakest being one of No. 2, hot blast, gave only 

 1.1,278 lb., or better than Si tons. The difference as to strength 

 between the hot and cold blast appears to be trifling. The follow- 

 ing are the .strengths of some of the irons, given by Mr. Hodgkin- 

 son : — 



Carron, No, 3, hot blast 



llo., do., cold blast 



Do., No. 2, hot blast 



L)o., do., cold blast 



Low Hloor, No. *J, cold blast 



Wuirkirk. No. 1, hot blast 



Buffery, No. 1, hot blast 



12 7 tons, 

 109 

 111 

 11'5 



11-4 

 lll-l 



llr.'j 



Every other beam, then, will bear in this average proportion of 

 1 1 tons, in respect of the three elements above mentioned — namely, 

 1st, the section of fracture ; 2nd, tlie depth of the beam ; anil, 

 .Srd, the length or distance between the sujiports ; and the rule is, 

 to multiply this average unit of strength of 11 tons, 1st, by the 

 section of fracture; 2nd, by the depth ; and, 3rdly, divide the pro- 

 duct by tlie length. This is an universal rule, and one of most 

 extensive application, and is here given in a somewhat simpler 

 form than is generally found in elementary works. He then 

 .sliowed the effect, by experiment, on a cast-iron beam, one inch 

 square, siipporteil at the extremities at two feet apart, and loaded 

 in the middle till it broke. Bv the above calculation of 11 tons 

 for the unit, the strength would be I,0(iH lb. ; and it first deflected 

 greatly, and then broke, all of a sudden, with a weight of 

 1,140 lb. ; and as the exact area of the bar is about l-lotli more 

 than an inch, this gives a unit of strength very nearly that of the 

 average above mentioned. This specimen of iron was from 

 Broughton Foundry, and he understood was of Summerlee iron, ■ 

 No. 2. 



Form of the beam. — The sim])le rectangular beam is not the one 

 best fitted for strength in proportion to the weight of the ma- 

 terial emidoyed. In the first place, the centre being the weak 

 Jioint, the mass at the ends may be redui^ed and accumulated in 

 the centre, giving the beam a curved shape on the upper or under 

 or on both sides ; and this is the form generally adopted in large 

 beams or girders. The ends may be safely reduced to half or 

 two-thirds of the depth in the middle; and' for a load uniformly 



distributed over the beam, the surface should be formed to an 

 elliptic curve, and for a load at the centre, to a parabidic curve. 

 But, 2ndly, the cross section of the beam, instead of being rect- 

 angular, can be modified with great advantage by removing the 

 material from the central parts, and accumulating it, in the form 

 of projections or flanges either at the top or bottom, or both. If 

 the flange be at the top, the cross section or the figure of the 

 beam looking endways is that of the letter j ; and if the flange be 

 at the top and bottom, the figure is that of the letter I, with the 

 head and tail extended. Originally the j form vvith the head or 

 flange downmost was adojited in large manufactories or buihlings 

 for carrying brick arches, chiefly for the convenience of obtaining 

 a bearing from which the arches on each side might be sprung. 

 Afterwards the 1 or double t form was recommended, on no less an 

 authority than Tredgold. But the knowledge and consideration 

 of the property of cast-iron, already described, in possessing a 

 compressive strength much superior to the tensile, has given an 

 entirely new view to the subject, and led to very important practi- 

 cal results. This is a discovery due to Mr. Hodgkinson, and the 

 experiments and investigations which he has undertaken, in con- 

 junction with Mr, Fairbairn, have rendered most essential service 

 in this branch of practical mechanics. The upper part of the 

 beam being compressed by the application of a weight, and the 

 under part distended, and the tensile resistance being three or 

 four times less than the compressive, it is evident that the ma- 

 terial of the beam ought to be accumulated much more at the 

 bottom than at the top ; and in order to ascertain practically how- 

 far this principle might be carried, Mr, Hodgkinson made a variety 

 of trials of different forms, beginning with the flanges equal at 

 top and bottom, or the letter I form, then increasing the bottom 

 flange by ten or twelve difterent steps, till he found at last the 

 greatest strength was attained vvhen the bottom flange (as in this 

 figure X) was si.x times greater than the top ; and some very curi- 

 ous results arose from these investigations. The strength of the 

 beams, formed according to these views, is easily calculated on the 

 principle already explained ; for, whatever be the form, it will be 

 found that the strength is still very nearly proportional to the 

 three elements — length, depth, and section of fracture; but the 

 unit of strength or standard for each beam is diff^erent. For rect- 

 angular beams of cast-iron, this unit, as explained, is at an ave- 

 rage 11 tons. For the equal flange beam, which was formerly con- 

 sidered a model, the unit is no greater, but rather, if anything, 

 less ; but when the bottom flange is increased beyond the top in 

 the ratio of 4^ to 1, the unit of strength of every inch of the 

 beam is increased to fifteen tons ; and when the bottom flange is 

 farther increased in the ratio of 6 to 1, the strength is increased 

 to nineteen tons. He then showed by experiment the strength of 

 a cast-iron beam 2 feet by 2 inches deep, bottom flange five times 

 greater than the top, and area of fracture 1 inch. If rectangular, 

 it should have broke with 2,280 lb., but it carried 3,750 lb., and then 

 gave way, showing an increase of strength equal to 4,170 lb. gained 

 by this form of the section. Since these experiments of Mr. 

 Hodgkinson, others have been lately made by Bramah and others, 

 particularly those under the sanction of government, in reference 

 to the fall of the cottou-mlll at t)ldham, by Sir Henry de la Beche 

 and Mr, Thomas C'ubitt, These are important, as being made on 

 a larger scale than the others. They entirely confirm the views 

 and results of Hodgkinson, but the beams experimented on not 

 being of the same forms, do not give the same degree of strength. 

 On the whole, therefore, the results given above may be relied on; 

 but the strains for perfect security ought on no account to be car- 

 ried beyond one-fourth or one-third of the breaking weight. 



Now, that the nature of the transverse strain has been so tho- 

 roughly investigated, an important consideration arises, — how far 

 improvements may not still be made by the introduction of mal- 

 leable iron in conjunction with cast-iron, so as to form beams of a 

 compound nature, having all tlie parts liable to compression of 

 cast-iron, and all the parts liable to tension of malleable iron. 

 This has already been adopted, in some cases with success, by the 

 introduction of what are called tension-rods of malleable iron ; 

 but it is extremely doubtful if the best combination of the two 

 metals has yet been ascertained. The great point is to keep the 

 two metals clearly and distinctly to their different offices of re- 

 sisting compression and tension, and unless this be done there is 

 difficulty and risk of bringing the one or other of them into 

 action ; and neither of them, in such cases, sustaining its proper 

 share of the load or pressure, the most serious consequences may 

 result from the combination. Owing to this, the use of tension- 

 rods has been rather condemned by engineers, and not without 

 reason ; but Mr. Buchanan thought the objections were not so much 

 to the use of the tension-rods, as to the injudicious manner in 



