. Stereotomy : Problems in stone cutting. In four classes. I. Plane-sided structures. II. Structures containing developable surfaces. III. Structrues containing warped surfaces. IV. Structures containing double-curved surfaces. For students of engineering and architecture . be wrought by the straight edge,No. 1, held in the direction of elements of the surface, andthese will be found by transferring their extremities as k andA, M and B, from the drawings to the stone. THE OBLIQUE ARCH. 60. This, the most extended of all the problems in StoneCutting, is usually made the subject of a separate tr
. Stereotomy : Problems in stone cutting. In four classes. I. Plane-sided structures. II. Structures containing developable surfaces. III. Structrues containing warped surfaces. IV. Structures containing double-curved surfaces. For students of engineering and architecture . be wrought by the straight edge,No. 1, held in the direction of elements of the surface, andthese will be found by transferring their extremities as k andA, M and B, from the drawings to the stone. THE OBLIQUE ARCH. 60. This, the most extended of all the problems in StoneCutting, is usually made the subject of a separate treatise ; forwhich its many and marked varieties, as well as its complexity,make it sufficient. Yet, by the full and careful exhibition ofall the essential features of its usual form, the student can beprepared both to design and superintend the construction ofan oblique arch as commonly built, and to read the works inwhich the subject is treated more elaborately. Preliminary Mechanics of the Arch. 61. Let ABC be an ordinary semi-cylindrical arch, of whichwe will first consider only one half, as ABTa, Fig. 4. Let G 54 STEEEOTOMY. represent the centre of gravity of this half, and GH its weight,acting vertically downward. The half ABT, as a whole, and. -£■ Fig. 4. thus actuated by its unresisted weight, would fall, by turningabout a as a centre. As it would prevent the use of the archto oppose GH by props underneath, it is counteracted by a hori-zontal force acting, as at T, at any point of BT, and this hor-izontal force consists in the reaction of the other half, BTC, ofthe arch and its immovable backing. This understood, as aforce may be considered as acting at any point on its ownproper line of direction, the pressure at T, and the weight con-centrated at G, may be considered as both acting at g ; the for-mer at gt, the latter at gh, whence gR, would be their it is necessary for the stability of the half arch that gHshould intersect the base o
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