Determine the mass m, the compressive force AB and the tension force in cable BC.
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- The structure ABCD (shown below) is designed to support a finite mass hanging from a cable, DF, attached to the structure at point D. x=8m, y=6 m, and z-15 m. The structure is mounted to the ground by a hinge at B and a roller at C and is also supported by a horizontal cable, AE, attached to the wall. The mass of the object hanging from cable DF is 500 kg. The tension in the support cable AE is 1.000 × 10³ N. Determine the force in each member and the reaction forces. E DA block of mass m hangs from the end of bar AB that is 8 meters long and connected to the wall in the xz plane. The bar is supported at A by a ball joint such that it carries only a compressive force along its axis. The bar is supported at end B by cables BD and BC that connect to the xz plane at points C and D respectively with coordinates given in the figure. Cable BD is elastic and can be modeled as a linear spring with a spring constant k 500 N/m and unstretched length of 6.81 - meters. Determine the mass m, the compressive force in beam AB and the tension force in cable BC. Z C (a, 0, b). e D (c, 0, d) α b с d A Variable Value 6.7 m 4.8 m 2.4 m 5.3 m 3.1 m 4.3 m e f f B X Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. m y Cci❀O BY NC SA 2016 Eric DavishahlA block of mass m hangs from the end of bar AB that is 5.6 meters long and connected to the wall in the az plane. The bar is supported atA by a ball joint such that it carries only a compressive force along its axis. The bar is supported at end B by cables BD and BC' that connect to the xz plane at points C and D respectively with coordinates given in the figure. Cable BD is elastic and can be modeled as a linear spring with a spring constant k = 300 N/m and unstretched length of 5.16 meters. Determine the mass m, the compressive force in beam AB and the tension force in cable BC. D (c, 0, d) C (a, 0, b), В A у f m e Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value a 5.8 m b 4.9 m 1.3 m d 3.6 m e 2.5 m f 4.3 m The mass of the block is kilograms. The compressive force in bar AB is Newtons. The tension in cable BC is Newtons.
- Answer FOUR questions ONLY selecting TWO questions from SECTION A. 1. (a) The vertical structure ABCD shown in Figure 1(a) is subjected to a system of coplanar forces and a moment. The structure is simply supported at D with a frictionless pin and is roller-supported at A. i Sketch the free body diagram (FBD). Take moments about D and hence find the reaction force at support A. ii. 35 AN 23m 60 100 km Osm Figure 1(a) (b) An assembly of a steel bar enclosed within an aluminium alloy tube is shown in Figure 1(b). The tube and the bar are of the same initial length. The combination is compressed between two rigid parallel plates by a force of 500 kN. The diameter of the steel bar is 40 mm, and the inside and outside diameters of the alloy tube are 60 mm and 100 mm respectively. The Young's moduli for steel and aluminium alloy respectively are Est = 200 GNM2, EA = 70 GNm?. Find the stresses generated in the steel bar and the aluminium alloy tube. Sael he -Rid pl Figure 1(b)As shown, an L-shaped bar is supported by a pin at joint A. The bar's dimensions are aaa = 620 mmmm and bbb = 400 mmmm , and the bar is subjected to a force with magnitude FFF = 5.05 kNkN at joint B. Ignoring the bar's weight, find the actual orientation of the applied force. What is the value of the angle θθtheta?A block of mass m hangs from the end of bar AB that is 5.5 meters long and connected to the wall in the az plane. The bar is supported atA by a ball joint such that it carries only a compressive force along its axis. The bar is supported at end B by cables BD and BC that connect to the az plane at points Č and D respectively with coordinates given in the figure. Cable BD is elastic and can be modeled as a linear spring with a spring constant k = 600 N/m and unstretched length of 4.78 meters. Determine the mass m, the compressive force in beam AB and the tension force in cable BC. D (с, 0, d) C (a, 0, b), В A y f m e Cc 090 BY NC SA 2016 Eric Davishahl Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value a 6.3 m 6.2 m 3.4 m d 6.9 m e 4.9 m f 4.6 m The mass of the block is kilograms. The compressive force in bar AB is Newtons. The tension in cable BC is Newtons.
- The rigid body is supported by a hinge at A and a cable at C. The hinge resists 5.5m translation in all three coordinate directions and rotation in the x and y directions. The 260 N force is in the -x direction and acts at the center of the 3m body. Find the tension in the cable and the components of the support C 2.5m 260N reactions at A. Your answer should include a properly Ilm annotated FBD. B 3.ImThe bar AC is supported by a joint at A and a pin B that is free to slide in the same direction (alpha) of the bar. A bar is connected at C and a force is applied in the theta direction. Consider that L1 = 2.7 m, L2 = 1.7 m, alpha = 13 °, theta = 25 °, and P = 68 kN. Determine the magnitude of the force (kN) on pin B.Two smooth spheres of weight W and radius r each are in equilibrium in a horizontal channel of A and B vertical sides as shown in the figure. Find the force exerted by each sphere on the other. Calculate these values, if r=250mm, b=900mm and W=100N.
- 4. The access door in Fig. P6-13 is held in the position by cable AB. If the magnitude of tension T in the cable is 50 pound force, find the rectangular components of T acting at A. 10 in. B 10 in. 12 in. 6 in. 20° FIGURE P6-13Th lamp , mass = 10 Kg, is suspended in the position shown. The undeformed length of spring AB is 0.84 m and the spring has a stiffness of K = 784 N/m. For L= 2.8 m find Tension in cable AC , Internal force in spring AB, length of ACThe lamp shown in the figure is supported by a pole AO and cables AC and AB. Each cable can sustain a 1.5 m B maximum tension of 500 N, and pole can withstand a maximum compression of 300 N. Note that the force in pole AO acts along its axis. 4 m The coordinates of the points are: O (0, 0, 0); A (2, -1.5, 6); B (-4, 1.5, 0); C (0, 1.5, 0) Determine the maximum weight of the lamp that can be supported. 2 m 6 m / /1.5 m Draw all necessary FBD's to solve this problem. Put 1.5 m units on your answers.