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 . thesame plane, the composition of forces in space cannot befurther simplified. Still we can give any value we please to P, one of the forces of the couple G, calculate the correspond-enting arm a = -p, then transfer G until one of the jPs has the same point of application as R, and combine them by theparallelogram of forces. We thus have the whole systemequivalent to two forces, viz., the second P, and the re
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 . thesame plane, the composition of forces in space cannot befurther simplified. Still we can give any value we please to P, one of the forces of the couple G, calculate the correspond-enting arm a = -p, then transfer G until one of the jPs has the same point of application as R, and combine them by theparallelogram of forces. We thus have the whole systemequivalent to two forces, viz., the second P, and the resultantof R and the first P. These two forces are not in the sameplane, and therefore cannot be replaced by a single resultant. 39. Problem. (Non-concurrent forces in space.)—Given allgeometrical elements (including <*, /?, y, angles of JP), also theweight of Q, and weight of apparatus G; A being a hinge whosepin is in the axis Y, G a ball-and-socket joint: required theamount of P (lbs.) to preserve equilibrium, also the pressures STATICS OF A RIGID BODY. 41 (amount anc* direction) at A and 0 ; no friction. Replace Pby its X, .F, and Z components. The pressure at A will have. Fig. 44. Z and X components ; that at 0, X, Yy and Z components. The body is now free, and there are six , 2 Y, and 2Z give, respectively, P cos a + Xx + X0 = 0; P cos ft + Y0 = 0; and Z, + Z0 — Q — G -P cos y = 0. As for moment-equations (see note in last paragraph), project-ing the system upon YZ and putting 2(Pa) about (9 = 0,we have - ZJ+ Qd+Ge + (P cos y)b + (Pcos ft)o = 0 ;projecting it upon XZ, and putting 2(Pa) about 0 = 0, wehave Qr — (P cos a)c — (P cos y)a = 0 ; projecting on XI7^ moments about (9 give XXZ + (P cos a)b - (P cos /?> = 0. From these six equations we may obtain the six unknowns,T3, X0, Y0, Z0, Xa, and Zx. If for any one of these a negativeresult is obtained, it shows that its direction in Fig. 44 shouldbe reversed. 42 MECHANICS OF ENGINEERING. CHAPTER IV.
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