Essentials in the theory of framed structures . except for illustration, to draw the location-direction AC; forthe location-direction diagram could have been closed at e aswell as at any other point/ on the location-direction AC. Complete the magnitude-direction diagram, and comparethese results with the two algebraic solutions. 4. The body in Fig. 24a, carrying a vertical load of 15 tons,is supported by a vertical reaction of 50 tons; and three other so THEORY OF FRAMED STRUCTURES Chap. I forces p, q and 5 having known locations and the magnitudes p, q and s if the wei
Essentials in the theory of framed structures . except for illustration, to draw the location-direction AC; forthe location-direction diagram could have been closed at e aswell as at any other point/ on the location-direction AC. Complete the magnitude-direction diagram, and comparethese results with the two algebraic solutions. 4. The body in Fig. 24a, carrying a vertical load of 15 tons,is supported by a vertical reaction of 50 tons; and three other so THEORY OF FRAMED STRUCTURES Chap. I forces p, q and 5 having known locations and the magnitudes p, q and s if the weight of the body isneglected. Algebraic Method.—Make the sketch (Fig. 246) and assumeH- and F-components for the inclined forces ^and q. Theunknown quantities a, b and s may be determined by writingand solving three independent static equations. There is,however, a very simple and more direct method whereby anyone of the unknown magnitudes may be determined independ-. ently of the other two. The method of procedure is asfollows: balance the moments of all the forces about the pointF, thereby eliminating the two unknown magnitudes p and qand the load of 15 tons. Only two magnitudes remain—thereaction of 50 tons and the magnitude s—and their momentsabout F must balance for equilibrium; for the other magnitudescannot help or hinder rotation about the point F. Themoment of the reaction about F is 3,000 clockwise; andthe body will rotate clockwise about F unless the magnitude s,acting through a distance of 40 ft. and to the right or away fromthe body, is 75 the point G, where the directions of q and 5 intersect, Sec. VI EQUILIBRIUM OF COPLANAR FORCES 51 resolve the magnitude q into H- and F-components 3a and the point if in a vertical line with G, resolve the magnitudep into H- and F-components 6b and h. Balance the momentsof all the forces about G, thereby eliminating the unknownmagnitudes s, q and h. The Zf-component
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