Essentials in the theory of framed structures . Example 2.—Use the equa-tions of group 2 and see if asolution is possible by choos-ing any other two points, OandP: (a) In a vertical line. (6) Not in a vertical line. Example 3.—Use the equations of group 3 and see if a solution Fig. 18. S tI. Fig. 19. is possible by choosing any two points, 0 and P:(a) In a horizontal line.(6) Not in a horizontal 4.—Find the magnitudes A and B and the distance a Sec. VI EQUILIBRIUM OF COPLANAR FORCES 35 (Fig. 19) for equilibrium using the equations of group 4 andchoosing three points, 0, P and Q in
Essentials in the theory of framed structures . Example 2.—Use the equa-tions of group 2 and see if asolution is possible by choos-ing any other two points, OandP: (a) In a vertical line. (6) Not in a vertical line. Example 3.—Use the equations of group 3 and see if a solution Fig. 18. S tI. Fig. 19. is possible by choosing any two points, 0 and P:(a) In a horizontal line.(6) Not in a horizontal 4.—Find the magnitudes A and B and the distance a Sec. VI EQUILIBRIUM OF COPLANAR FORCES 35 (Fig. 19) for equilibrium using the equations of group 4 andchoosing three points, 0, P and Q in a straight line. IMp = 80 - 100 + sA — So + aB = o (i) IMo = 20 — (16 — a)B + 384 — 120 — 176 — 11^ = o (2)IMq = 180 - 150 + 88 + isA - 130 + (8 + a)B -192 = o (3) Multiply Eq. (3) by 2, add Eq. (2), and divide the sum by quotient is Eq. (i). Only two independent equations arerepresented, since any one of th6 three may be derived from theother two, and a solution of the problem as stated is impossible. Example 5.—Choose three points 0, P and Q not in a straightline and see if a solution is possible. It has been shown that under certain conditions the threeequations in each of the last three groups represent but twoindependent equations, and are insufficient for
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