"The weights were laid gradually and slowly on, and the beam had borne within a little of its breaking weight a considerable time, perhaps half an hour." "The form of the fracture and wedge is represented in the Fig. 6, where enf is the wedge, ef=5.1 inches, tn=3.9 inches, angle enf 82°." It is extremely probable, from this fracture, that the neutral point was at n, the vertex of the wedge, and therefore at ths the depth of the beam, since 3.9=x5 nearly." The relative dimensions above given were arrived at by "constantly making small additions" to the bottom flanch, until a point was reached where resistance to compression could no longer be sustained. The beams of this form, in all previous experiments, having yielded by the bottom flanch tearing asunder. "The great strength of this form of cross section is an indisputable refutation of that theory which would make the top and bottom ribs of a cast iron beam equal." "The form of cross section" (as above)" is the best which we have arrived at for the beam to bear an ultimate strain. If we adopt the form of beam (as above) I think we may confidently expect to obtain the same strength with a saving of upwards of 4th of the metal." 365. Rules for determining the Ultimate Strength of Cast Iron Beams of the above Forms. From the results of his experiments, Mr. Hodgkinson has deduced the following very simple formulæ, for determining the breaking weight, in tons, when applied at the middle of a beam. Call the breaking weight in tons, W. Call the area of the cross section of the bottom flanch, taken at the middle of the beam, a. Call the depth of the beam at the middle point, d. Call the distance between the supports, l. when the beam has been cast with the bottom flanch upward and W=24ad when the beam has been cast on its side. The working strain on cast iron beams subjected to direct compression is placed by most authorities at from 4th to th of the crushing weight, when the beam, a column for exam ple, is not subjected to violent vibrations or shocks. In the contrary case, particularly in beams subjected to a transverse strain, it is recommended to reduce the working strain to th the crushing strain. 366. Effect of Horizontal Impact upon Cast Iron Bars. The following tables of experiments on this subject, and the results drawn from them, are taken from a paper by Mr. Hodgkinson, published in the Fifth Report of the British Association. The bars under experiment were impinged upon by a weight suspended freely in such a position that, hanging vertically, it was in contact with the side of the bar. The blow was given by allowing the weight to swing through different arcs. The bars were so confined against lateral supports, that they could take no vertical motion. Table of experiments on a cast iron bar, 4 ft. 6 in. long, 1 in. broad, in. thick, weighing 7 lbs., placed with the broadside against lateral supports 4 ft. asunder, and impinged upon by cast iron and lead balls weighiny 8 lbs., swinging through arcs of the radius 12 feet. "Before the experiments on impact were made upon this bar, it was laid on two horizontal supports 4 feet asunder, and weights gently laid on the middle bent it (in the same direction that it was afterwards bent by impact) as below: 28 lbs, bent it .37 inch. 56 lbs. 66 .77 inch. Elasticity a little injured.” tion of bar in Observed deflec inches. Table of experiments on a cast iron bar 7 ft. long, 1.08 in. broad and 1.05 in. thick, weighing 23 lbs., placed, as in preceding experiments, against supports 6 ft. 6 in. asunder, and bent by impacts in the middle. Impinging ball of cast iron weighing 20 lbs. Radius of arcs 16 feet. The results in the 3d and 4th columns of the above table were derived from allowing the ball to impinge against a weight of 56 lbs., hung so as to be in contact with the bar. "Before the experiments on impact, the beam was laid on two supports 6 ft. 6 in. asunder, and was bent .78 in. by 123 lbs. (including the pressure from its own weight), applied gently in the middle.” Tables of experiments on two cast iron bars, 4 ft. 6 in. long, full inch square, weighing 14 lbs. 10 oz. nearly, placed against supports 4 feet apart, and impinged upon by a cast iron ball weighing 44 lbs. Radius 16 ft. The results in the 1st of the above tables are from bars struck in the middle, those in the 2d table are from bars struck at the middle point between the centre and extremity of the bar. From the above and other experiments the conclusion is drawn," that a uniform beam will bear the same blow, whether struck in the middle or half way between that and one end." "From all the experiments it appears that the deflection is nearly as the chord of the arc fallen through, or as the velocity of impact." The following conclusions are drawn from the experiments. (1.) "If different bodies of equal weight, but differing considerably in hardness and elastic force, be made to strike horizontally against the middle of a heavy beam supported at its ends, all the bodies will recoil with velocities equal to one another." (2.) "If, as before, a beam supported at its ends be struck horizontally by bodies of the same weight, but different hardness and elastic force, the deflection of the beam will be the same whichever body be used." (3.) "The quantity of recoil in a body, after striking against a beam as above, is nearly equal to (though somewhat below) what would arise from the full varying pressure of a perfectly elastic beam, as it recovered its form after deflection." Note. This last conclusion is drawn from a comparison of the results of experiment with those obtained from calculation, in which the beam is assumed as perfectly elastic. (4.) "The effect of bodies of different natures striking against a hard, flexible beam, seems to be independent of the elasticities of the bodies, and may be calculated, with trifling error, on a supposition that they are inelastic." (5.) "The power of a uniform beam to resist a blow given horizontally, is the same in whatever part it is struck." 367. From the results of the experiments of Messrs. Fairbairn and Hodgkinson, on the properties of cold and hot blast iron, it appears that the ratio of their resistances to impact is 1000 to 1226.3, the resistance of cold blast being represented by 1000 the resistance, or power of the beam to bear a hori zontal impact, being measured by the product of its breaking weight from a transverse strain at the middle of the beam and its ultimate deflection. This measure, Mr. Hodgkinson remarks, "supposes that all cast iron bars of the same dimensions, in our experiments, are of the same weight, and that the deflection of a beam up to the breaking weight would be as the pressure. Neither of these is true; they are only approximations; but the difference in the weights of cast iron bars of equal size is very little, and, taking them as the same, it may be inferred from my paper on Impact upon Beams (Fifth Report of the British Association) that the assumption above gives results near enough for practice." VI. STRENGTH OF WROUGHT IRON. THIS material, from its very extensive applications in structures where a considerable tensile force is to be resisted, as in suspension bridges, iron ties, etc., has been the subject of a very great number of experiments. Among the many may be cited those of Telford and Brown in England, Duleau in France, and the able and extensive series upon plate iron for steam boilers, made under the direction of the Franklin Institute, and published in the 19th and 20th vols. (New Series) of the Journal of the Institute. 368. Resistance to Tensile Strain. The tables on the next page exhibit the tensile strength of this material under ordinary temperatures, and in the different states in which it is used for structures. It is remarked, in the Report of the Sub-committee, "that the inherent irregularities of the metal, even in the best specimens, whether of rolled or hammered iron, seldom fall short of 10 or 15 per cent. of the mean strength." From the same series of experiments, it appears that the strength of rolled plate lenghthwise is about 6 per cent. greater than its strength crosswise. In the Tenth Report of the British Association in 1840, Mr. Fairbairn has given the results of experiments on plate iron by Mr Hodgkinson, from which it appears that the mean strength of iron plates lengthwise is 22.52 tons. Crosswise" 23.04 66 Single-riveted plates "18,590 lbs. 70. Representing the strength of the plate by 100. 56. |