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Two upward loads are exerted on the small three dimensional truss. Reduce these two loads to a single force.couple system at point O. Show that R is perpendicular to Mo. Then determine the point in the x-z plane through which the resultant (single equivalent force) passes. 4.8 3.6 330 lb 200 lb Answer: Force-couple system at O. k) lb k) lb-ft Single equivalent force (x, z) ft

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Answer #1

F1 = 200j

F2 = 330j

R = 0i + 530j + 0k

Moment due to F1 at point O = 9.6i X 200j = 1920 k

Moment due to F2 at point O = -3.6k X 330j = 1188 i

M0 = 1188i + 0j + 1920k

R.M0 = (0i + 530j + 0k).(1188i + 0j + 1920k) = 0

Therefore, R is perpendicular to M0

(xi + zk) X 530j = 1188i + 0j + 1920k

=> (530x)k + (-530z)i = 1188i + 0j + 1920k

x = 1920/530 = 3.62

z = -1188/530 = -2.24

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