Essentials in the theory of framed structures . Group 4.—Suppose that in Fig. 17 = o (i) ZMo = o (2) and 2Mo = o (6) then UMp - IMo = {h X 2F) - (Jb X Zff) = o (7) and IMo - IMo = (s X 2F) - {p X IE) = o (8)If the three points O, P and Q are in a straight line s p and Eqs. (7) and (8) are identical and not independent (see Example 4). Eliminate ZF in (7) and (8) kX IE ^ pX IH h s Sec. VI or EQUILIBRIUM OF COPLANAR FORCES kX IH kX ZH 37(9) 5 p If the three points O, P and Q are not in a straight line, then - does not equal —s P in which case Eqs. (7) and (8) are independent; and IH inEq. (
Essentials in the theory of framed structures . Group 4.—Suppose that in Fig. 17 = o (i) ZMo = o (2) and 2Mo = o (6) then UMp - IMo = {h X 2F) - (Jb X Zff) = o (7) and IMo - IMo = (s X 2F) - {p X IE) = o (8)If the three points O, P and Q are in a straight line s p and Eqs. (7) and (8) are identical and not independent (see Example 4). Eliminate ZF in (7) and (8) kX IE ^ pX IH h s Sec. VI or EQUILIBRIUM OF COPLANAR FORCES kX IH kX ZH 37(9) 5 p If the three points O, P and Q are not in a straight line, then - does not equal —s P in which case Eqs. (7) and (8) are independent; and IH inEq. (9)must equal zero (see Example 5). But if IH = othen from Eq. (7) or (8) ZF = o 31. Hence in any case where the moments of all the forcesin a non-concurrent non-parallel system are balanced aboutany three points not in a straight line, the horizontal magni-tudes are balanced, the vertical magnitudes are balanced, andthe H- and F-equations will be dependent upon the threeM-equations. 32. One Unknown Location.—In Fig. 20 the unknown loca-. PlG. 20. tions of two forces are represented by the quantities b and the horizontal magnitude A represent a third unknownelement. All the vertical magnitudes are known and magnitude A, determined by balancing the horizontalmagnitudes, equals 6 lb., and acts to the right. Since themagnitudes are now balanced horizontally and vertically, it ispossible to have only one independent If-equation for thesolution of b and c, and a single solution is impossible. 38 THEORY OF FRAMED STRUCTURES Chap. I 33. Show that a similar condition is encountered when theunknown elements are two locations and one direction. Therecan be only one unknown location if a single solution ispossible. 34. Combinations.—The unknown elements which can bewholly or partially determined in a coplanar non-concurrentnon-parallel system of forces will appear in one of the followingcombinations; where P, Q and S represent any forces whichhave unknown element
Size: 1893px × 1319px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1920, booksubjectstructu, bookyear1922
