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Theory of Steel-Concrete Arches and of Vaulted Structures

Theory of Steel-Concrete Arches and of Vaulted Structures


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Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: Therefore, T CONDITIONS FOR EQUILIBRIUM FOR ARCH WITH NO HINGES. 12. The neutral line, for the case where the steel bars are symmetrically placed with respect to the centre line of the arch ring, is the centre line itself and can at once be laid off. For an unsymmetrical cross-section, points in the neutral line must be found and laid off by aid of (5), and a curve traced through them. In either case, let a b c, Fig. o, represent the neutral line of an unstrained arch with fixed end tangents, and let s represent a length of the neutral line whose centre is at b. When the arch is loaded either with its own weight only or in addition with a live load, the neutral line changes shape, and it was agreed in Art. 8, to regard the change in the inclination of the end tangents to the neutral arc s, as given by the formula, Fig. 5. where n and E, are constant and M, I, and I, are taken at b, the middle of arc s. Regard the end c temporarily free, then the bending in s alone will cause a rotation of the arc be about b equal to 0, so that a line be will rotate through an infinitesimal distance ce, taken as perpendicular to be. Take c as origin, ca the axis of x and axis of y vertical and callthe co-ordinates of b, x and y. Draw ed perpendicular to ca; then from similarity of triangles, C6 a T ce cd = -=- y = y v, ue? -x = xv. bcy y be The exact result would of course be found by dividing s into infinitesimal lengths Js, and regarding the rotation to take place about the end of each littlo portion in turn, x and y thus having values above and below the means taken for b (the middle of s). Wo assume, therefore, in the graphical treatment to follow that if M, I, 1, a-, y are all taken at the mid-point of arc s, as a sort of average, that the horizontal and vertic...


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Product Details
  • ISBN-13: 9780217901376
  • Publisher: General Books
  • Publisher Imprint: General Books
  • Height: 246 mm
  • No of Pages: 108
  • Spine Width: 6 mm
  • Width: 189 mm
  • ISBN-10: 0217901379
  • Publisher Date: 14 Jan 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 209 gr


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