Essentials in the theory of framed structures . the location of Q. Cases (i), (4) and (12) are more frequently encountered inthe theory of framed structures than any or aU of the cases are indeterminate under certain (i) is in this class when P, Q and S have the same location,or are parallel. Other cases are partially indeterminate, forthey may have several solutions or none. Any problem whichinvolves a force having a known magnitude and an unknowndirection is in this class. The most difficult problems are tobe found in cases (2) and (7). 35. Illustrative Problem
Essentials in the theory of framed structures . the location of Q. Cases (i), (4) and (12) are more frequently encountered inthe theory of framed structures than any or aU of the cases are indeterminate under certain (i) is in this class when P, Q and S have the same location,or are parallel. Other cases are partially indeterminate, forthey may have several solutions or none. Any problem whichinvolves a force having a known magnitude and an unknowndirection is in this class. The most difficult problems are tobe found in cases (2) and (7). 35. Illustrative Problems.—i Determine the unknown ele-ments necessary for equilibrium (Fig. 21a). (a) Algebraic^ Method.—The three elements of each of the The term algebraic is used simply for the purpose of distinguishing themethod of computing by the use of numerals or letters, from the graphic method Sec. VI EQUILIBRIUM OF COPLANAR FORCES 39 four forces shown are given. The elements necessary forequilibrium are the magnitude, direction and location of a fifth. force. The problem is one of case (12). Make a sketch () and transfer to it the horizontal and vertical componentsof the four known forces properly located. in which quantities are represented by the length, direction and location of writers refer to the two methods as the analytic and graphic; but this ismanifestly incorrect, since both methods are analytic. The frequent use how-ever, of the word algebraic should be discouraged. It is true that algebraicequations have been used in the discussions which have preceded, but in theactual solution of problems their use is often a hindrance rather than a the first place, if the equations are not written, the problem can frequentlybe solved more quickly and easily; and the computations can be arranged in amore convenient form for checking. But a more important reason for discardingthe equation whenever possible is the fact that by so doing, the attenti
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