## A Practical and Theoretical Essay on Oblique Bridges |

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acute quoin adjusted angle angle ACB angle DCK angle of obliquity applied arris axis breadth brick bridge centre CF in fig CHAPTER constructed convenient number corresponding cot Sec curve cylinder described DESCRIPTIVE GEOMETRY determine dimensions Direct span distance divisions draw drawn at right drawn parallel eccentricity elevation engineer equation extrado face formulae given half heading joints heading spiral horizontal internal angle intrado intradosal angle laggings lines drawn method mutual intersections number of equal number of voussoirs numbers in Column oblique arch observed parallel rule parallel to AC parallelogram perpendicular plate points principles projection proper radiate radius Railway right angles secant semicircle ABC semicircular arch semicylindrical shown in fig side similar triangles sine soffit spiral line spiral surface stone straight edge suppose tangent template thickness twisting rule Watford

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Page 6 - After having had several drawings of the faces of oblique arches made on a large scale and projected with great exactitude, we observed that the following remarkable property exists. If the lines, which are the chords of the small curves forming the joints in the face of the arch, be produced, they will all meet in one point 0, below the axis of the cylinder ; and this property was found to hold even when the obliquity is so great as to depress the point 0 out of the cylinder altogether.

Page 12 - The mode of obtaining such winding beds is familiar to workmen, and is done by placing two rules, one of which has its edges parallel, and the other diverging, at a determinate distance, and then each is sunk into a draft in the stone until their upper edges are in one plane, when the under edges will be in the intended winding surface or bed ; this being done, the superfluous parts of the stone on the other parts of the bed are to be dressed off until a straight-edge applied from one draft to the...

Page 18 - Let AaB be the half of a semicircular arch, the obliquity of which is BDC, and suppose it is required to produce the development DeE by means of ordinates obtained by calculation. " Let the arc AB be divided into a convenient number of parts and its development, BE, into the same number. Suppose a to be one of the divisions of the arc and b its corresponding division in the development, such that E6 — Aa.

Page 14 - CE (Fig. 16) will exactly coincide with the spiral bed of the stone which has been already worked by the twisting rules, and the stone being placed with its soffit uppermost, let this template be inverted, and applied with its blades BD and CE to the worked bed, the strip BC (Figs.

Page 19 - Thus having found a sufficient number of distances, fe, corresponding to divisions of the arc AB or to its development BE, and consequently to DE also, let DE be divided into the same number of parts as shown in Fig. 65. "At each of the divisions draw the ordinates fe, Fig. 65, making all the angles, Dfe, each equal to the complement of BED, which is the intradosal angle being treated of,, and upon these ordinates set off the distances fe, as previously calculated; then the curve...

Page 14 - AC, fig. 14, and this line so drawn will be at right angles to the axis of the cylinder. Let another line be drawn by the side AB, and this line will be parallel to the axis of the cylinder. Remove the template, and let chisel drafts be sunk in the soffit on the line CA, to fit the curve of the stock of the template, and also on the line AB, (which will be...

Page 4 - ... draw the lines EF, EG, each equal to one-fourth of the circumference of the circle, ACBD, or equal to one-fourth of the circumference of the revoloid. Divide these lines into any numLP PM her of equal parts, as 1, 2, 3, 4, &c., on the line EF. In like manner divide each quadrant of the circumference into the same number of equal parts, 1. 2, 3, 4, &c. ; through the divisions on the circumference draw lines from 1, 2, 3, &c., parallel to DC, and through the divisions on the line EFdraw lines both...

Page 24 - ... corresponding to groups on the development. A convenient form for the arrangement of these calculations is as follows: Column 1 contains the different assumed values of the arcs whose ordiuates have to be found. Column 2 contains the corresponding logarithmic sines of the angles in column 1. Column 3. The numbers in this column are the logarithms of the lines be, Fig. 66, and are obtained by adding log R log cot 0 to each of the numbers in column 2. In this case log R = log 16.25 = 1.210853,...

Page 5 - B B' being the most concave, and the others diminishing in concavity as they approach the vertex, where it disappears altogether. If a third development were made at half the thickness of the arch, we should have a middle series of points, and thus three points in the curve would be obtained.