. Concrete bridges and culverts, for both railroads and highways . e foundthat any i>art of it falls without the middle third,a new position must then be assumed for the pointS. Through c draw the horizontal line EF, inter-secting CS prolonged at F. The line FC will repre-sent truly to scale the amount of the crown R lay off on a horizontal line through R, thedistance RP, equal to FE, and join P with the pointsa, h, L\ d and c. From R draw the line of resistancewith sides parallel to the lines Pa, Vh, etc. If anypart of this line of resistance falls outside of themiddle third of
. Concrete bridges and culverts, for both railroads and highways . e foundthat any i>art of it falls without the middle third,a new position must then be assumed for the pointS. Through c draw the horizontal line EF, inter-secting CS prolonged at F. The line FC will repre-sent truly to scale the amount of the crown R lay off on a horizontal line through R, thedistance RP, equal to FE, and join P with the pointsa, h, L\ d and c. From R draw the line of resistancewith sides parallel to the lines Pa, Vh, etc. If anypart of this line of resistance falls outside of themiddle third of the arch ring, a new position mustthen be assumed for the point S, and another lineof resistance drawn, falling entirely within the mid-dle third. If no such line of resistance can bedrawn, then either the form of the arch or its thick-ness must be changed until a line of resistance canbe drawn lying entirely within the middle third. Line of Resistance—Partial Loading. Consider next the case of a maximum live loadover half the span, acting in conjunction with. COXCRFTF. ARCH BRIDGFS. 47 the inaximiiiii dead load. Botli lialves of the archmust then be considered. As before, the portionof the bridge above the intrados is divided intovertical strips, and the vertical and conjugate load-ings written down in their respective places. Aload line, ABC, is drawn, and any trial pole, P,assumed. With this position of pole, the funicularpolygon shown in dotted lines is drawn. By usinga little care, the })oint .r may be selected, so thecurve on the left will fall within the middle third,or tangent to it. It will be seen that this line ofresistance shown dotted, falls outside of the middlethird in two places and intersects the outer verticalthrough c at 3. This curve cuts the center lineof arch at /. See if it is possible to draw anotherline of resistance, so that it will cut the center ofthe span at the point / and pass through the point P draw a line parallel to / y inters
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