12

THE PRINCIPLES OF BRIDGES.

TRACT I.

PROP. III.

>

Let there be any number of lines, or bars, or beams, ab, pc,cd, de, kc. all in the same vertical plane, connected togetherand freely moveable about the joints or angles a, b, c, d, k,&’c, and kept in equilibria by their own weights, or by weightsonly kid on the angles: It is required to assign the proportionof those weights; as also the force or push in the direction ofthe said lines; and the horizontal thrust at every angle.

Solution .—Through any point,as d, draw a verti-cal line aT>ng, &c :to which, from anypoint, as c, drawlines in the direction

a

of, or parallel to, the given lines or beams, viz, c a parallel toab, and c b parallel to bc, and ce to de, and cf to ef, and egto fg, &c; also ch parallel to the horizon, or perpendicularto the vertical line ang, in which also all these parallels ter-

minate.

r l hen will all those lines he exactly proportional to theforces acting or exerted in the directions to which thev arcparallel, and of all the three kinds, viz. vertical, horizontal,and oblique. That is, the oblique forces or thrusts in direc-tion of the bars. ab, bc, cd, de, ef, fg,

are proportional to their parallels .. ca, cb, cd, ce, cf, eg",and the vertical weights on the angles b, c, d, e, f, &c,are as the parts of the vertical .... ab, bn, nc, if, fg,and the weight of the whole frame arcdefg,is proportional to the sum ol all the verticals, or to ag;also the horizontal thrust, at every angle, is every where thesame constant quantity, and is expressed by the constant ho-

/• W