Essentials in the theory of framed structures . f twoof the forces P and Q are 520 lb. and 340 lb. respectively. What are the direc-tions of P and Q? 4. Four concurrent forces are in equilibrium (Fig. 9). The magnitude ofQ is 300 lb. Find the magnitude of P and the direction of Q. 24 THEORY OF FRAMED STRUCTURES Chap. I 5. In Fig. 10 the moments of all the forces are balanced about the two pointsA and B, , ZMa = oand ZMb = o yet the system is not in equilibrium because neither the horizontal nor the verticalmagnitudes are balanced. Explain. 6. In Fig. II, AB represents the mast of a derrick
Essentials in the theory of framed structures . f twoof the forces P and Q are 520 lb. and 340 lb. respectively. What are the direc-tions of P and Q? 4. Four concurrent forces are in equilibrium (Fig. 9). The magnitude ofQ is 300 lb. Find the magnitude of P and the direction of Q. 24 THEORY OF FRAMED STRUCTURES Chap. I 5. In Fig. 10 the moments of all the forces are balanced about the two pointsA and B, , ZMa = oand ZMb = o yet the system is not in equilibrium because neither the horizontal nor the verticalmagnitudes are balanced. Explain. 6. In Fig. II, AB represents the mast of a derrick 40 ft. long. The boomAC is 60 ft. long. The length of the cable BC can be varied to place the boomin any desired angle. The load at C is 2,000 lb. Three forces at C are in equi-librium. What is the force acting along the direction AC? Sec. V. CoPLANAR Parallel Forces 20. General Considerations.—In a concurrent system thelocation of each force is known and we are interested in theelements of magnitude and direction only; in a parallel system. the direction of each force is known and we have the elementsof magnitude and location for our consideration. If a body is subject to the action of a system of parallelforces which have vertical directions, the condition IH = o is satisfied whether the body is in equilibrium or not. Conse-quently this equation lends no aid in finding the unknownelements for the equilibrium of such a system. We have theequation IV = oand equations of the type ZM = o for the algebraic solution of a system of vertical forces. Let us examine the expressions for Z V and ZMp in connec-tion with Figs. 12a and 12& and note the difference. Sec. V EQUILtBRIUM OF COPLANAR FORCES 25 The algebraic sum of the magnitudes of the three forces inFig. 12a (indicating magnitudes of upward sense as positive) is ZF = +5 - 12 - 2 = -gib., , the resultant of the three forces has a magnitude of 9 downward. The algebraic sum of the moments of thethree forces about t
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