![]() Sample 3/6 A 200-N force is applied to the handle of the hoist in the direction shown. Thrust-bearing “initially properly aligned” The 6 force reactions developed by the bearing, hinge and ball are sufficient for maintaining the equilibrium, so the couple reactions will not be developed at the bearing and hinge. Properly Alignment and Moment Support “properly aligned” The couple reactions are developed to make the object in equilibrium The 4 force reactions developed at bearing A and tension T are not sufficient to maintain the equilibrium of the body. Properly Alignment and Moment Support “initially properly aligned”Įven though the line of pipe is initially placed without pretorsion or properly aligned. 6 unknown reactions with 6 independent equations. The 6 force reactions developed by the bearings are sufficient for maintaining the equilibrium since they prevent the shaft from rotating about any of the coordinate axes. “Properly Alignment” If the line of pipe is initially placed without pre-torsion, the 6 couple reactions are not necessary to maintain equilibrium, and then can be considered as not existing. Properly Alignment and Moment Support A,B,C: journal bearings At D, support is provided in y-direction only - Find the tensions, T1 and T2 - Find total force supported at C and the lateral force R supported at D. Support at C can be treated as a ball-andsocket joint. You can use other rE and rB (Solve as 2D problem)ģ/90 Sign has a mass of 100 kg, center of mass at the center of the sign. Assume that the bearing at A is capable of exerting force components only in the z and y directions (since it is properly aligned on the shaft). Use only one equilibrium equation to obtain a direct solution for the tension in cable BC. Technique: Finding unknown in 1 equation The bent rod is supported at A by a journal bearing, at D by a ball-and-socket joint, at B by means of cable BC. rBA T1 rBA T2 rBM P 0 component x, component z Calculate tension in each cable resulting from the 20-kN force acting in the horizontal plane at the midpoint M of the boom. Az Bz TC 300 981 0 20īoom AB lies in vertical y-z plane, is supported by a balland-socket joint at B and by 2 cables at A. If it is supported in the horizontal plane by means of a roller at A, a balland-socket joint at B, and a cord at C, determine the components of reaction at the supports. The homogeneous plate shown has a mass of 100 kg and is subjected to a force and couple moment along its edges. Vector Cross Product is useful in 3D Problem Write force name Use (at least) 3 different colors No axis No system isolation (surrounding still exists) Caution: In some slides using in this class, FBD may be drawn wrongly according to the rule introduced, DO NOT IMITATE this style in your homework or examination. Find the force exerted by the walls and the floor on the ends of the shaft. The ball end B rests against the smooth vertical walls. nˆ Forces which interest or parallel with axis, do not cause the moment in that axis 15Įxample 3/5 The uniform 7m steel shaft has a mass of 200kg and is supported by a ball-and-socket joint at A in the horizontal floor. Position vector: from any point on line to any point on tline of action of the force. Not in this class, but be careful about the moment equations, things get very complicated if the body is not spinning in a single plane! Each of the equation may be applied independently e.g., an accelerating car on a flat surface may be treated as in equilibrium in the vertical direction. Position (where the axis pass) also matters.ĭirection of moment axis has a affect on solving problem. The 3 axises need not interesect at one point Fx= 0 Fy= 0 Fz= 0 Mx= 0 My= 0 Mz= 0Īny but only three independent (perpendicular) axis For some problem, the couples in both case should be treated as zero to provide statical determinacy ![]()
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