COHESIVE STRENGTH.] 



APPLIED MECHANICS. 



797 



area required to break or tear the bars asunder. The 

 numbers in the last column are calculated by a simple 

 proportion ; thus, taking the bar 1 inch in diameter, the 

 area of which is 0'7854 square inches, and the breaking- 

 weight 17 tons, we say 



So in. Sq. in. Tons. Tone. 



07854 : 1 : : 17 : 21 '645; 

 the weight that would be required to break the bar were 

 it one inch square. 



TABLE L Experiments on Cohesive Strength of Cylin- 

 drical Copper Bars. 



Diameter of bar : 



inches. 



Area : 



q. inches. 



0-9940 

 07854 

 0-6013 

 0-4417 



Breaking-weight : 

 tons. 



22 

 17 

 12-8 

 9 



Breakinu-weiirht 



reduced to 1 



sq. inch : 



tons. 

 22-133 

 21-645 

 21-287 

 20-376 



Mean 21 '36 tons. 



It will be seen that, although the sectional areas of 

 the bars differ very considerably, the breaking-weights, 

 reduced to one square inch of area, do not vary greatly 

 from their mean value. 



Table II. contains the results of experiments on best 

 hempen bower cables used in the navy. The first column 

 contains the circumferences, or girths, of the cables in 

 inches (the dimensions of cables being generally stated 

 in terms of their girths) ; the second column contains 

 their sectional areas in square inches ; the third expresses 

 the number of threads in each ; the fourth column marks 

 the actual breaking-weights ; the fifth the breaking- 

 weights per square inch of sectional area ; and the sixth 

 the breaking-weights per thread. 



TABLE IL Experiments on the Cohesive Strengths of Best 

 Hempen Bower Cables. 



_, . ,. M . , Breaking- Break, wght. Break, wght 

 tire.: sect, art >o. MI i_i..r iJ^^ ., . 



inch*. 



1AJIIB. wVHV. J 



a 



88 



Mean 2-5 nearly 87 



The strengths in these cases also are very nearly as the 

 sectional areas or numbers of threads. We shall finally 

 quote the results of some experiments on the strength 

 of wrought-iron bars of various qualities, as marked in 

 Table III., where the breaking-weights per square inch 

 are given as calculated from the experiments. The first 

 column contains the description of bar, the second 

 contains the dimensions, the third gives the amounts 

 in inches which each foot of the bars stretched, and the 

 fourth gives the breaking-weights per square inch of 

 sectional area. 



TABLE III. Experiments on the Cohesive Strengths and 

 Extension of Wrought Iron Bars. 



Extension 



28 

 18 



42 



26 

 17 



2786 

 1656 

 1080 



tons. 

 114 



68 



40 



tons. 

 2-714 

 2 tJl 

 2853 



Description 

 and form. 



Dimension before 

 extension : 



inclit*. 



Bonth Wales, cylindrcl. 

 Ditto, ditto. 



Stafford, square 



Ditto, ditto 



Welsh, square 



Scrap, square 



Common, cylindrical.. 

 Stafford, square 



1 > diam. 



(I 7'.-, -ilic. 

 108 ,. 

 100 

 100 



2 00 diam. 

 1-00 side. 



per foot : 

 inches. 



1-81 

 1-86 

 1-22 

 1-24 

 238 

 2-50 

 1-50 

 MO 



section: 

 tons. 

 298 

 29-8 

 272 

 27-5 

 290 

 29-0 

 31-8 

 81-0 



Mean 29 -3 



By numerous experiments, such as those quoted, data 

 have been determined from which we can readily calcu- 

 late the dimensions of a bar of any material required to 

 carry a given weight, or conversely, the weight which a 

 given bar of material will carry. These data have been 

 determined by the actual breakage of the bars tested ; 

 but in practice, where durability and adequate strength 

 to meet contingencies of strain are required, it is neces- 

 sary to give the materials we employ, considerably greater 

 diiuenxipns than such as would merely preserve them 

 from breakage, or to load them with considerably less 

 weights than those which would tear them asunder. 



Farther, it is found in practice, that materials subjected 

 to considerable strains for long periods of time gradually 

 lose their tenacity ; and this degradation of quality must 

 be provided against when permanence and stability are 

 required. 



In the case of metal bars, it is advisable not to load 

 them beyond one-third of their actual breaking strain ; 

 or, in other words, to provide them of three times the 

 strength sufficient to resist tearing asunder. In the case 

 of ropes, timber, and such other materials as are of less 

 uniform consistency than metals generally are, or are 

 more liable to degradation, it is advisable to provide at 

 least four times the breaking strength. 



Table IV. contains data for the strength of a number 

 of materials on which experiments have been made ; and 

 the numbers given may be safely used in calculation, as 

 they are reduced to one-third or one-fourth of the break- 

 ing strength. 



TABLE IV. Data for Calculating the Cohesive Strength of 

 Bars of different Materials, determined from the Ave- 

 rages of numerous experiments. The numbers are given 

 roundly, as no material error will arise in practice 

 from their use. 



The strengths are given in square inches, and also in 

 circular inches for convenience of calculation ; and the 

 following are the rules for calculating the strength of a 

 given bar, or the dimensions required to bear a given load. 



I . Given, the dimensions of a bar of any material to 

 find its cohesive strength, or the constant load it will 

 safely bear in the direction of its length. 



1. When the bar is square. 



Rule. Multiply the number of inches in the side by 

 itself : that is, square the number, and then multiply by 

 the number opposite the given material in column 2 of 

 Table IV. 



Example L Required the cohesive strength of a 

 square bar of English wrought-iron of which each side 

 measures 2J inches. 



- i expressed decimally . 



Multiplied by itself ; . 



Multiply by tons in table 



5-0625 

 8-3 



151875 

 405000 



42-01875 

 Neglecting the decimal fraction, we find that we may 



safely load the bar with a weight of 42 tons. 



2. When the bar is oblong, or qf some other form hav-r 



ing straight sides. 



