. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. Rg. 7. Problem II.—Let a 6,fig. 7, be two points in the curve of equal hori- zontal thrust, in the arch A B ; required to find the point at which the curve intersects the joint 0 q, being the base of the abutment. Let G be the centre of gravity for the half arch A B, and g- that of the arch and abutment taken together. Through h, draw the horizontal line 6 r, and the vertical line b I; also through G and g, draw the vertical lines G h and g- k, intersecting br ia h and k ; jo
. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. Rg. 7. Problem II.—Let a 6,fig. 7, be two points in the curve of equal hori- zontal thrust, in the arch A B ; required to find the point at which the curve intersects the joint 0 q, being the base of the abutment. Let G be the centre of gravity for the half arch A B, and g- that of the arch and abutment taken together. Through h, draw the horizontal line 6 r, and the vertical line b I; also through G and g, draw the vertical lines G h and g- k, intersecting br ia h and k ; join a h and produce it to I, from k set offfcn equal to ft b, and through n draw the vertical line n m, making w »n to i 6 as the weight of the arch and abutment is to the weight of the arch A B ; join m k, and produce it, until it intersects « ^ ; p, the point of intersection, will be the point required. It is unnecessary to accompany these constructions with a demonstration, as it is evident, from the nature of the construction in either case, that the horizontal thrust of the portion A B, at the points a and b, is equal to that of 0 7 B, at the points p and 6.—For a loaded arch the construction remains the same ; the centre of gravity of the arch and load being taken, instead of that of the arch only. These constructions point out, not only the form of the curve of equal horizontal thrust in any given arch, but also the direction and amount of pressure at any joint. For as the perpendiculars of the several triangles represent the weights of the several parts, so the hypolhenuse of the seve- ral triangles represent the resultant pressures at any joint. From this it appears, that the actual pressure, tending to crush the material of which the arch is made, decreases towards the crown of the arch. Figs. 8, 9,10, 11, and 12 (Plate XI.), are drawings to scale, of ordinary forms of arches, showing the minimum thickness that will contain the curve of equal horizontal thrust, a
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