Mechanics of engineeringComprising statics and dynamics of solids: and the mechanics of the materials of constructions, or strength and elasticity of beams, columns, arches, shafts, etc . but a = the half-chord, hence, finally, x = -tajp • Peoblem 6.—Trapezoid; thin plate, etc.,by the method in the corollary of § 23; equa-tions (3). Kequired the distance x from thebase AB. Join DB, thus dividing the trape-zoid ABCD into two triangles ADB = Fxand DBG = F„ whose gravity xJs are, re-spectively, xx = -JA and a?2 = fh. Also, Fx= ihbx, F7 = -JA52, and F (area of trape-zoid) = ±h(bx + 52). Eq. (3) of
Mechanics of engineeringComprising statics and dynamics of solids: and the mechanics of the materials of constructions, or strength and elasticity of beams, columns, arches, shafts, etc . but a = the half-chord, hence, finally, x = -tajp • Peoblem 6.—Trapezoid; thin plate, etc.,by the method in the corollary of § 23; equa-tions (3). Kequired the distance x from thebase AB. Join DB, thus dividing the trape-zoid ABCD into two triangles ADB = Fxand DBG = F„ whose gravity xJs are, re-spectively, xx = -JA and a?2 = fh. Also, Fx= ihbx, F7 = -JA52, and F (area of trape-zoid) = ±h(bx + 52). Eq. (3) of § 23 givesFxj= Fxxx -f- i^2a?2; hence, substituting,^ -j-b,)x=ibxh+% Fig. 21. -_h (ft, + 26,) • w — « • t ; t « The line joining the middles of bx and b2 is a line of gravity, andis divided in such a ratio by the centre of gravity that the fol-lowing construction for finding the latter holds good : Prolongeach base, in opposite directions, an amount equal to the otherbase; join the two points thus found: the intersection withthe other line of gravity is the centre of gravity of the trape-zoid. Thus, Fig. 21, with BF= ba and DF= bx, join FF,etc. 24 MECHANICS OF ENGINEERING. Problem 7. Homogeneous oblique cone or pyramid.—Take the origin at the vertex, and the axis Xperpendicular tothe base (or bases, if a frustum). In finding x we may putd V = volume of any lamina parallel to YZ, F being the baseof such a lamina, each point of the lamina having the same , (equations (2), § 23), but and = \fxdV, V=fdV=fFdx; F:F%::«?:h;., .:F=fix, h. q ~L 4 7 4 For a frustum, x — —. ~-% ~; while for a pyramid, hlt be- — 3ing = 0, x = -rh. Hence th
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
