By Barlow, Peter William; Barlow, Peter; Barlow, W. H.; Humber, William
This accomplished paintings from the nineteenth century covers the power of fabrics with reference to development of constructions, bridges and railways, and so forth. and contains an appendix at the energy of locomotive engines and the impact of vulnerable planes and gradients.
summary: This finished paintings from the nineteenth century covers the energy of fabrics in regards to building of structures, bridges and railways, and so on. and comprises an appendix at the energy of locomotive engines and the impression of vulnerable planes and gradients
Read Online or Download A treatise on the strength of materials : with rules for application in architecture, the construction of suspension bridges, railways, etc., and an appendix PDF
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Extra 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
Let A F and R X be the radii of curvature at the points A and R, then the triangles A a b and A a F, as also E s r and R r X , are similar; and therefore, since A a = R r, we have rs : E r : : R r : E X a&:Aa::Aa:AF; therefore r s : a b : : A F : R X ; but r s : a b : : C L : C G, and consequently, C L : C G : : A F : R X ; whence again, C L . R X = C G . A F , a con sf ant quantity — A. 38 STRENGTH OF T I M B E R . In order now to trace the property of the curve, let C L = x, R L = y, and R C = z; then, as is shown by writers on the diffe rential calculus, the radius of curvature 2 dz* d x ,d R X = 2 2 (d x + d y ) | —dx .
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.
Strain; that is, as I W : therefore, again, the deflection varies as 3 3 I W I w -g—; or, denoting the deflection m D by 6, we have - y y = E, a constant quantity, the same result as before. 4 9 . The same may be otherwise demonstrated as follows : In the above investigation it is shown that D m, which is sup posed to represent the deflection, is expressed by the equation ^ 2 _ \ ra =*It m + 1 + t t and that in any other beam of which the number of parts are m', the deflection is also from which we conclude, that when m is infinite, the deflections are as 2 2 dm 2 2 : cZ'm' ; or as eZ Z : d' Z ' ; where Z and V denote the two lengths.