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Tracts on vaults and bridges : containing observations on the various forms of vaults; on the taking down and rebuilding London Bridge : and on the principles of arches: illustrated by extensive tables of bridges : also containing the principles of pendent bridges, with reference to the properties of the catenary, applied to the Menai Bridge : and a theoretical investigation of the catenary / Samuel Ware
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63

CALCULATION-ARCH AND ABUTMENT PIER.

Fig. 12.

OG m x and put any angle ylm = gfh = <p.As ON:OL :: OL: OGn : OL :: OL : m xOL 2 x=.nm nx

OL rrr nm nxDK = EF + 2v/ nm nx

As KW : WY :: rad.: tang. <p

WY WY wv ,

Tang, f = WY = OL = n tang. f

As KW: KY :: rad. : sec. <p

Sec. p rz

KY _ KYKW n

KY r= n sec.

DK = EF + 2 n tang. <pAs fg :gh :: hi ( gh ): ik Vd Vwn: gh :: gh:m xgh 2 = nm nx

gh ~ y /nm nxdie = ef -{- 2 nm nxAsfg : gA :: rad.: tang. <p

Ta g . f =-

n

.*. gh n tang. <pAsJ^ - : fh :: rad.: sec. ?

Sec. f =/ 4 =&

.fg »

;.fh n sec. <pdk ef 4- 2 n tang. <pky -fh