. The railroad engineer's practice . Trautwine gives for the thickness of the abutment at thespringing line, when the height above the ground of thisline is not more than 11- times the base, Rad. in ft. , rise in ft. , ^„ _ = —= + 2 feet. 5 10 ^ (See his Pocket Book for finding the thickness at thebase.) If the embankment over the arch is very high, or if thearch is the lining to a tunnel in earth, the proper form forthe intrados is a geostatic arch. Raukines approximateformula for this is : 42 X, -^x^—B-. 2/3 = Xq { oJ Xq ) In any given case x^ and y^ will be known, and we cancalculate ao by
. The railroad engineer's practice . Trautwine gives for the thickness of the abutment at thespringing line, when the height above the ground of thisline is not more than 11- times the base, Rad. in ft. , rise in ft. , ^„ _ = —= + 2 feet. 5 10 ^ (See his Pocket Book for finding the thickness at thebase.) If the embankment over the arch is very high, or if thearch is the lining to a tunnel in earth, the proper form forthe intrados is a geostatic arch. Raukines approximateformula for this is : 42 X, -^x^—B-. 2/3 = Xq { oJ Xq ) In any given case x^ and y^ will be known, and we cancalculate ao by trial ; x^ — Xo will then be the rise of thearch, which w^e shall call or. The geostatic arch willapproach a five-centre curve, which may be drawn asfollows : Calculate b = iy^ + gQ ^ Then ?„ = J. C = 1 + b8 \a^ 1 and ?i = B D = - 1 + &3 From these equations we obtain the centres C and J).About i> with a radius D E — ii — a describe a circulararc, and about C with a radius C E — a —?o describeanother arc; the intersection of these at E will be thethird centre. When brick is plentiful, circular culverts are often em-ployed. They require no foundation except for the facew^alls. For the thickness, one brick (nine inches) is suffi-cient for a span less than six feet. Add one more brickfor each six feet more of span up to thirty feet. 43 The following are two cheap forms of centering :
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