1830] 



THE CIVIL EXGINEER AND ARCHITECT'S JOURNAL 



S7 



d= wCAf—r—^ 

 V p r{v 



sure, and w = a weight equivalent to the resistance of the beam, 

 from its inertia. 



If the resistance of the body struck had been uniform, the right 

 side of the equation would have been tw ice as great, or ;; p ; but in 

 a beam, tlie resistance to flexure is nothing in the commencement, 

 and it increases in proportion to the flexure. 



The preceding formula gives the impact, in terms of the height 

 fallen through by the ball or striking body; but, in the experi- 

 ments, the deflections are given in terms of the chord of the arc of 

 impact, and the following formula would represent them. 



e 

 (w + w) 



where d = the deflection of the beam, c =^ the chord of the arc, r 

 = the radius, from the point of suspension to the centre of the 

 ball, // := any pressure applied to bend the beam, e =: the deflec- 

 tion caused by that pressure, and the rest as before. 



The value of w depends upon the weight of the beam, and as a 

 mean, it may be taken at one half of the weight of the beam 

 between tlie supports, as was shown by the experiments in the 

 Report above-mentioned. 



Objects of the Tables of Experiments, with some of the Results 

 arrived at. 

 Tensile and Crushing Strength of Cast-iron. — Tables I . to V. These 

 experiments were made to ascertain the direct tensile and crushing 

 strengths of several denominations of cast-iron in common use, 

 but of which these properties had not been at all determined, or 

 very imperfectly. The irons of which the tensile force was deter- 

 mined, were 17, and the crushing force of all these irons was also 

 obtained. — (See Abstract, No. I.) 



Tranverse Pressure on Bars, very long and flexible. — Tables I. to 

 VI. contain results on the tran.n-erse strength and resistance of very 

 thin flexible bars, by forces acting horizontally, the ends of the bars 

 being supported on friction rollers. The experiments were made 

 to exhibit very fully the deflections and sets of cast-iron, and the 

 defect of its elasticity; in order to throw light on the great devia- 

 tions in this metal, from computations according to the theories in 

 common use; and to explain anomalies in some of the results of 

 the other parts of this inquiry. Thus, by showing that defect of 

 elasticity, the cause of these anomalies, n-as nearly as the s(ji,are of 

 the defection, it was rendered probable that the value of the weight 

 might be expressed in terms of the difl"erence between the 1st and 

 2nd powers of the deflection, instead of the 1st power alone, on 

 which it had been assumed by previous authors to depend. This 

 being tried, was found to give results diff'ering but little from 

 those of the experiments, as may be seen by turning to the tables. 

 Formulae for the weights and sets, in terms of deflections, were 

 obtained. 



Long-continued Impact upon Bars of Cast-Iron. — Tables I to IV. 

 are on the eff'ects of long-continued impact, applied horizontally, 

 upon the middle of the beams, to ascertain to what degree beams 

 or beam bridges might be successively deflected, by impacts and 

 vibrations, to resist fracture for any length of time. As an abstract 

 of the results of these experiments is given, they will not be fur- 

 ther noticed here, except to mention that it is scarcely safe to bend 

 beams constantly to one-third of their ultimate deflection, and that 

 they ought not to he loaded to more than one-sixth of their breaking 

 weight laid on rapidly. — (See Abstract, No. II.) 



Horizontal Impact upon Bars of Cast-Iron. — Tables I. to III. 

 show that bars of various forms of section, but of equal weight, 

 off'er the same resistance to impact when struck by the same ball. 

 Thus a bar 6X1^ inches in section, placed on supports 13 feet 6 

 inches asunder, required the same magnitude of blows to break it 

 in the middle, whether it was struck on the broad side or the nar- 

 row one; and these blows were required to break a bar, the section 

 of which was 3x3 and the length the same. The main object of 

 these experiment was to furnish data for a correct theory of the 

 resisting power of bars to impact. — (See Abstract, No. III.) 



Impact on Bars of Wrought-Iron. — Another course of experiments 

 was tried, to ascertain the eff'ects of horizontal impacts upon bars of 

 wrought-iron, to compare together the results from pressure and 

 impact, and to obtain the resistance of the bar from its own weight. 

 In these the deflections produced by a ball suspended with a con- 

 stant radius, were nearly as the chord of the arc through which it 

 was allowed to fall, to strike the beam at the bottom of the arc. 

 In other words the deflection of the beam was nearly as the velocity of 

 impact, since the velocity varies as the arc. The deflection in cast- 

 iron bars is greater than in proportion to the velocity. 



Vertical Impact on Loaded Bars. — On the effsct of vertical 

 impacts on loaded bars of cast-iron. 



These experiments show, that beams loaded to a certain degi-ee, 

 with weights attached to them, and spread over their whole length, 

 so as not to prevent the flexure of the beam, resisted greater 

 impacts from the same body falling on them, than when the beams 

 were unloaded, in the ratio of 2 to 1. For other particulars, and 

 a property connecting the velocities of impact and deflections, 

 see Abstract, No. IV. 



On the Extension of Cast-iron Bars.— The experiments of this 

 class were made on bars one inch area of section nearly, and 50 feet 

 long. They were suspended vertically from the top of a high 

 building, arid had weights attached to the bottom; the weights wtre 

 varied by small increments, until the bar broke; the extension and 

 set, with every change of weight, were obtained with great car';. 

 The results being afterwards reduced to what they would have 

 been, if the length had been 10 feat, and the area of a section 1 

 square inch. 



From these, formulae were obtained connecting the weights with 

 the extensions. 



On the Compression of Cast-iron Bars. — Tables I. to VI. contain 

 results of experiments on the compressions of bars of the same 

 irons, 10 feet long and I inch square; together with formula; con- 

 necting the weights and the compressions produced by them. 



The results, both of extension and compression of cast-iron, have 

 been adapted to any length / at pleasure, in order that they miglit 

 be applied to determining the transverse strength of a beam of cast- 

 iron, on more correct principles than those hitherto used, and they 

 have also been adapted to the formulae for the strength of beams 

 given in a work formerly published by the author, entitled, ' Expe- 

 rimental Researches on the Strength and other Properties of Cast- 

 iron.' — (See Abstract, No. V.) 



On the Compression of Short Cylinders of Cast-Iron of Various 

 Kinds. — These experiments contain the decrements in parts of the 

 length, with difl'erent weights, up to the crushing weight. 



Transverse Strength of Bars and Beams. — Tables I. to X. are on 

 the transverse strength of square bars of Blaenavon Iron, No. S, 

 of which the lengths were 15 feet, 10 feet, and 5 feet, and the sides 

 of the squaie 3, 2, 1 inches respectively; with some other bars of 

 different kinds of iron. — (See Abstract, No. VI.) 



Table XI. The experiment in this Table, is on the strength of 

 a large beam of cast-iron, the distance between the supports of 

 which was 45 feet, and the depth 28^ inches; the breaking weight 

 being 54 tons nearly. 



The great labour of an inquiry of this nature, both in making 

 the experiments and in adapting them to their intended purpose, 

 requires the union of much time and many hands; and the author 

 has great pleasure in acknowledging the efficient services derived 

 from one who has been engaged in the matter nearly from the 

 commencement, Mr. Thomas Tredgold, the son of the late eminent 

 writer on these subjects. 



Abstract No. I. 

 Tensile and Crushing Strength op Cast-Iron. 

 Results op Experiments to determine the ultimate Tensile and Com- 

 pressive, or Crushing Forces, of various denominations of Cast-iron 

 in common use; these qualities not having been previously obtained in 

 the Irons tried. 



The experiments are given at large in Tables I., IV., and V. In 

 obtaining the tensile strength in Table I. the form of the castings 



was that of a cross; or that which had been employed in all the 

 published experiments of the author. And to show that this was 



