Get 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 entire paintings from the nineteenth century covers the power of fabrics in regards to building of constructions, bridges and railways, and so on. and comprises an appendix at the strength of locomotive engines and the impact of vulnerable planes and gradients.

summary: This entire paintings from the nineteenth century covers the energy of fabrics with reference to building of structures, bridges and railways, and so forth. and comprises an appendix at the strength 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

This, however, supposes the section to be rectangular, or that the number of fibres in each horizontal lamina is the same. When the beam is triangular, cylindrical, or has any other than a rect­ angular section, the several small weights must be made propor­ tional to the breadth of the section at the point where each is supposed to act : the illustration, however, is equally obvious. Since, then, the whole resistance to fracture is made up of the sum of the resistance of every particle or fibre, acting at different distances on the lever C A, which is supposed to turn upon C as a fulcrum, there must necessarily be some point in that lever, in which, if all the several forces were united, their resistance to the weight W would be exactly the same as in the actual operation ; and this point is the centre of gravity of the section represented fcyAC.

It should be observed, however, that Mr. Hodgkinson, in the experiments he has described in the article above referred to, finds the ratio to be nearly 4 to 4, instead of 3 to 5 ; and unquestionably there must be considerable irregularities in the position of this line in different specimens of timber, even of the same kind, and much more in woods of different kinds. Without, therefore, attempting to determine this point, we may at all events assume, from what has been above stated, that there is necessarily such a point in the area of fracture in all beams ; and this is sufficient for our present purpose, as it is intended in the first instance to speak here only of rectangular beams.

D = a'd' d = a" d" d = a'" d"> &c. 40 STRENGTH OF TIMBER. Also, according to our supposition, nm — m x a d = m d n o — (m — 1) a d = d m ( o p = ( m - 2 ) a" d" = &c. &c. m ~ m 2 ) 2 d, &c. Whence the whole deflection m D will be expressed by the series 2 2 2 m D = ~ - { m + (m - I ) + (m - 2 ) + &c. I 2 ]• . . (1), or by the summation of the series, 3 2 _ c£ [ m m D = — j — m C 3 m m ) + — • + — \ . ; but when m is infinite, then the two latter terms vanish, as being inconsiderable with regard to the first; and we have m D = - ^ - ^ .

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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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