. Concrete bridges and culverts, for both railroads and highways . 27 111 Figure 5, let FB be the half span and FA therise of the proposed arch. ]Make AC=;°, andBDz:=r, the radius of curvature at the crown andspringing as calculated from the above C will be one of the centers and D D, with the radius DE, describe a circularare, and about 0, with radius CF. describe another circular arc. LetE be the point ofintersection o fthese ares. Thepoints D, E and Cwill be the re-quired centers. Many semi-ellip-tic arches ap-proach very near-ly the form of ahydrostatic c
. Concrete bridges and culverts, for both railroads and highways . 27 111 Figure 5, let FB be the half span and FA therise of the proposed arch. ]Make AC=;°, andBDz:=r, the radius of curvature at the crown andspringing as calculated from the above C will be one of the centers and D D, with the radius DE, describe a circularare, and about 0, with radius CF. describe another circular arc. LetE be the point ofintersection o fthese ares. Thepoints D, E and Cwill be the re-quired centers. Many semi-ellip-tic arches ap-proach very near-ly the form of ahydrostatic comparison be-tween Rankines approximate curve and the true oneaie shown in Figure 6. The upper or outside curveis the approximate curve as given by Rankine. Thecenter curve is the true hydrostatic arch plottedfrom a succession of radii, and the inside curve is atrue ellipse. Selection of the Most Suitable Form. Full centered arches, either circular or elliptical,produce the least overturning moment on the piers,and will generally require less pier masonry than. 28 CONCRETE BRIDGES AND CULVERTS. segmental arches. If the arch thrusts against nat-ural rock skewbacks or abutments, the amount ofsuch thrust is then a matter of little importance asfar as the abutment is concerned. The attachmentof segmental arches to piers usually requires tiltedbeds to bring the joints at right angles to the lineof pressure. This is a condition that does not occurin full centered arches. In flat ellipses the pierthrust is greater than with semicircular arches, theposition of thrust approaching more nearly that ofa segmental arch. It has already been shown that,for arch culverts carrying heavy earth banks, thesegmental form of arch will be more effective andless expensive. It produces heavy thrusts on theabutments, which thrusts counteract the inwardpressure of the earth on the side retaining the same time there is a shorter length of curvedwork to build than with a semi-circular form. Theco
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