Barlow, Peter William; Barlow, Peter; Barlow, W. H.; Humber,'s A treatise on the strength of materials : with rules for PDF

By Barlow, Peter William; Barlow, Peter; Barlow, W. H.; Humber, William

ISBN-10: 0727750577

ISBN-13: 9780727750570

This finished paintings from the nineteenth century covers the energy of fabrics with reference to building of constructions, bridges and railways, and so on. and contains an appendix at the strength of locomotive engines and the influence of vulnerable planes and gradients.

summary: This entire paintings from the nineteenth century covers the power of fabrics in regards to building of structures, bridges and railways, and so forth. and contains an appendix at the energy of locomotive engines and the influence of susceptible planes and gradients

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Additional resources for A treatise on the strength of materials : with rules for application in architecture, the construction of suspension bridges, railways, etc., and an appendix

Example text

C B : D B : d' : ^77^7 = the element of deflection at D, as arising from the resistance at B ; d! denoting the deflec­ tion at C. But the point D has a further strain to sustain, and consequently a further deflection, arising from the weight of the part between C and D. Now this weight will be to the whole weight W a s C D to A B , or 2 G B ; that is, 2 CB : CD : : W : CD . W 2 C B Consequently, the deflection arising from this strain, as referred towards B, will be C B : C D x B D : : d! : 2 CD "R T) CB 2 d'.

Again, the beam F I T F', fig. 3, is similarly situated, at least as far as our present question is concerned, with regard to the strain upon it, and therefore to its deflections, as the equal beam F I F ' 1 ' , fig. 4 ; whether we consider the latter to rest against a fulcrum at C, and to be strained by the two weights W, W passing over the pulleys Q, Q ' ; or, as being supported on two fulcrums, F, F', and loaded in the middle with the weight P, equal to the two weights r w, w . Hence, then, we conclude, that the deflection of a beam fixed at one end in a wall, and loaded at the other, is equal to that of a beam of twice the length, supported at both ends, and loaded in the middle with a double weight; that is, the strain being the same in both cases : consequently, when the weights are the same, the deflection in the first instance is to that in the second as 2 : 1 .

In the same manner as in Art. 23, it may be shown, that if a beam be loaded with many weights, W, W', W", W , &c, as in //V 23 TRANSVERSE STRAIN. fig. ) . W. Hence, if the length of the beam be I, and the number of equal weights m, and the sum of all the weights W , then the above becomes , / = ' " rW m 2 / o + \ l m + 2 1 3 Z „ \ml\ — + — + &c. m m m / W x — ; or, m Z W / = — x (1 + 2 + 3 + 4, &c. 4 m) ; or, m ( | m + 1) \ m _ j I W m + j Z W m _ 2 ~ 2m * ' 2 X 2 - W + Z_W 4 m' Hence, when the weight is uniformly distributed through the whole length, the number of points of suspension, m, becoming infinite, the last term of the preceding expression, and there results vanishes; / = \ IW, for the strain on the centre of a beam, when the weight W is uniformly distributed throughout its length; which is half what it would be if it were all suspended from its middle point.

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A treatise on the strength of materials : with rules for application in architecture, the construction of suspension bridges, railways, etc., and an appendix by Barlow, Peter William; Barlow, Peter; Barlow, W. H.; Humber, William


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