Essentials in the theory of framed structures . rtion are balanced by the forces p, q and s asillustrated in Figs. 426 and c. The left portion (Fig. 426)represents a coplanar system of five non-concurrent forceshaving three unknown magnitudes; corresponding to the firstcombination listed in Article 34. An algebraic and graphicsolution for this system is given in Article 35, Problem 4. Sec. I APPLICATION OF PRINCIPLES OF EQUILIBRrUM 69 The algebraic solution when performed by writing andsolving three simultaneous equations is known as Rankines^Method of Sections. The corresponding graphic solut
Essentials in the theory of framed structures . rtion are balanced by the forces p, q and s asillustrated in Figs. 426 and c. The left portion (Fig. 426)represents a coplanar system of five non-concurrent forceshaving three unknown magnitudes; corresponding to the firstcombination listed in Article 34. An algebraic and graphicsolution for this system is given in Article 35, Problem 4. Sec. I APPLICATION OF PRINCIPLES OF EQUILIBRrUM 69 The algebraic solution when performed by writing andsolving three simultaneous equations is known as Rankines^Method of Sections. The corresponding graphic solutionis the work of Culmann.^ The algebraic solution, wherebyany one of the three unknown magnitudes is determined bybalancing the moments of all the forces about the intersectionof the other two forces having unknown magnitudes, is knownas Ritters* Methods of Moments. In order to determine thestress by Ritters method, we balance the moments of all theexternal forces about C (Figs. 426 or c) thereby eliminating thetwo unknown magnitudes p and Moments about CFig. 42660 X S° = 3.°°° Fig. 42c30 X 8 = 240 180 X 73 = 13,14060 X 20 = 1,200 10,14° 90 X 40 = 3,600 3,000 120 X 30 = 3,600 ISO X 10 = 1,500 10,140 1 Applied Mechanics. 2 Die Graphische Statik. 1886. Dach- und Brucken constnictionen. 1862. 70 THEORY OF FRAMED STRUCTURES Chap. II The sum of the moments about C of the known forces actingon the left-hand portion is 3,000 clockwise; hence, theforce 5 acting at a distance of 40 ft. from C must have a magni-tude of 75 tons toward the right or away from the joint G tobalance the moments. The sum of the moments about C ofthe known forces acting on the right-hand portion is also 3,, but counter-clockwise; hence, the force 5 acting at adistance of 40 ft. from C must have a magnitude of 75 tonstoward the left, or away from the joint H to balance themoments. The fact that the sum of the moments about C of the knownexternal forces is the same (3,000 ) f
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