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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1920 Excerpt: ...arch rib is one which has a parabola for an axis, the vertex being at the crown. The formula for II gives its value for bending only and assumes a rib of uniform material but with a moment of inertia varying from a minimum at the crown to a maximum at the skewback hinges', the moment of inertia at any section equals that at the crown times the secant of the angle the arch axis makes with the horizontal at that section. Vl-W(i-t) K,-Wk _ s,Wl,,,, 1.6A 8A i + k-f Effect of Temperature on Arch Ribs with Solid Webs. A rise in the temperature tends to increase the span length and a fall in temperature to decrease it. If the span cannot change, a horizontal reaction is exerted on the arch at each support, and temperature stresses are produced within the rib. For the general case. Fig. 148, the horizontal reaction is H-Eljil I (' fdx For A Parabolic Rib. Fig. 149, with solid web thus equation" for horizontal reaction becomes H » 15 F,Itc% /8 A3. The temperature range t is frequendy taken as ± 750 Fahr. from the mean temperature of 500 Fahr. For a rise in temperature above normal, ( is positiv and the reactions H act inwardly and for a fall in temperature below normal, / is negativ and the reactions H act outwardly. The bending moment at any section due to temperature is Hyt being positiv for a fall and negativ for a rise in temperature. / is here assumed to increase from the crown towards the abutments. Rib Shortening in Arch Ribs with Solid Webs. The compression of the rib due to the thrust acting along the arch axis shortens the arch axis and produces outward horizontal reactions at the supports. The horizontal reaction is For general case (Fig. 148) H--SI J I £ fdx For the parabolic rib (Fig. 149) H--15 SI„/S h Rib shortening is simila...
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