must be consulted. No two specimens of any material ever give exactly similar results. The various brands of iron differ much; different specimens of steel differ still more; the strength is greater when the stress is applied along than when it is applied across the fibres. Iron or steel forged or drawn down to a small cross section is stronger than when in large masses ; the material in small castings is stronger than in large castings run from the same batch of metal; the skin is stronger than the rest of a casting. The variations to be expected in timber are still greater than those in metals, and the values for stones or bricks must in each case be specially determined by experiment on the special kind to be used. These warnings are applicable to the subsequent tables, which give the strength of materials to
resist other kinds of stress.
§5. Strength to resist Crushing.—The law given for tension applies to the compression of blocks, so that the strength f e of a material to resist crushing may also be measured in tons per square inch. Thus the ultimate strength P : of a block of the cross section S, subject to a uniform stress, is given in terms of / c the strength of the material per unit of section by the expression—
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This equation is not applicable to blocks or struts of iron in which the ratio of the shortest side of the cross section to the length is less than about 1 to 5, nor to struts of timber in which this ratio is less than about 1 to 10. When this limit is passed the strut bends before failing (vide 5 7), and whenever this occurs the essential condition that the stress shall be uniformly distributed no longer obtains. The flexure increases the stress on the inside of the curve assumed by the strut or pillar, and diminishes it on the outside ; but the strut will fail as soon as any part of the cross section is subject to a crushing stress of greater intensity than /.
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Name of Material. Tons per sq. inch. Wrought Iron ........................................ 15 to 18 Cast-iron ............................................... 37 to 65 Steel Plates ............................................ 90 Red Pine ............................................... 2 4 to 2 76 Larch ..................................................... 2 5 Oak ...................................................... 27 to 4-5 Teak ...................................... ................ 5 4 Bricks Lbs. per sq. inch. Portland Cement, 3 months old .............. 2460 9 ,, .............. . 3750 Gault Bricks.. ..................................... 710 to 930 Best Whites ........................................ 300 ,, poor quality ........................ 60 Best Reds ........................................... 490 Best Fire Bricks .................................. 930 Best Blue ........................................... 1260 Stones (specimens) Portland Stone (on bed) ....................... 2630 ,, ,, (against bed) ................... 2390 Bramley Fall (on bed) ........................... 5100 (againstbed) ...................... 2950 Yorkshire Landing (on bed) ................... 5380 ,, ,, (againstbed) ............... 5850 Granite .............................................. 5500 to 11, 000 Scotch Basalt ..................................... 8300 Greenstone ......................................... 17,200 Sandstones (ordinary) .......................... 3300 to 4000 Chalk ................................................ 330 to 500 Beton ............................................... 420 to 580
§6. Strength to resist Shearing.—Let a bar AD of any material be firmly supported on C, as shown in fig 1 , and let a strong tool B, say of steel, descend upon it in the direction of the arrow, with force sufficient to sever the part D from the part A, so that the surface dividing the two parts is in the plane of the face of C. This tool is said to shear the bar, and the resistance which the bar opposes to this stress is called its strength to resist shearing. The tools practically used to shear are not quite square at the edge, and therefore cut slightly, but for true shearing the lower face ought to be square, and the tool should come down close to the support, so that the inner face of the tool slides on the outer face of the support.
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Fig. 1.
Fig 2. represents two iron links joined by an iron pin. If the links are pulled asunder the pin will be shorn at two places, A and B, and the whole section shorn will be twice the cross section of the pin.
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Fig. 2.
Fig 3 shows a joint where the pin would be shorn in four places A, B, C, and D.
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Fig. 3.
The strength of a piece of any material to resist shearing is usually assumed by engineers to be proportional to the cross section to be shorn through, and each material may consequently be said to have a certain shearing strength per square inch; in other words, the ultimate shearing strength of the material is the intensity of stress required to shear it asunder. If, therefore, P x be the ultimate strength of a bar of cross section S to resist shearing in n places, and if /, be the ultimate strength of the material, we have the expression—
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not strictly correct ; indeed, the actual shearing described does not correspond with any simple homogeneous stress, and the form of the cross section shorn through must exer cise considerable influence on the strength of the piece to resist shearing. In a round pin the maximum intensity
of shearing stress is -? of the mean intensity, and in a rect-