Van Nostrand's eclectic engineering magazine . the common catenary, and all lines parallelto U V are evidently increased over thecorresponding ones of which they are the Fig. 13 (5).. parallel projections, in the same ratio thatU V exceeds 0 A. Laid down in the sameplane the two curves are CAB and C A B(Fig. 13 b). It is easy to pass from a given catenaryto a transformed catenary whose ordinatesshall be shorter instead of longer thanthose of the given curve, by erecting an ob- lique cylinder on the given catenary andsurface 0 Q T B, and cutting it by a planeless oblique than the base. So too,
Van Nostrand's eclectic engineering magazine . the common catenary, and all lines parallelto U V are evidently increased over thecorresponding ones of which they are the Fig. 13 (5).. parallel projections, in the same ratio thatU V exceeds 0 A. Laid down in the sameplane the two curves are CAB and C A B(Fig. 13 b). It is easy to pass from a given catenaryto a transformed catenary whose ordinatesshall be shorter instead of longer thanthose of the given curve, by erecting an ob- lique cylinder on the given catenary andsurface 0 Q T B, and cutting it by a planeless oblique than the base. So too, the hori-zontal dimensions can be changed insteadof the vertical, by making the cutting planemeet the base in a line parallel to 0 Y,instead of in one parallel to Q T. The equations of the curve G A! B (Fig. THEORY OF ARCHES. 103 13 5,) are tlius obtained. The abscissas arethe same as those in C A B, but the ordi-nates are changed, so that (if y = generalordinate of C A B and y^ = ^ 0, theordinate at the vertex A). y- y AO : A 0 2/0 y — ^ y^^y=y Vo : 2/0 In the equations of the common catenarysubstitute y for y and we have the equa-tions of C A B. From equation (6) m 2/
Size: 1559px × 1603px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, bookdecade1860, bookpubl, booksubjectengineering
