Solved: The uniform rod has a length l and weight W. It is

Draw the free-body diagram for the following problems. a) The cantilevered beam in Prob. 5–10. b) The beam in Prob. 5–11. c) The beam in Prob. 5–12. d) The beam in Prob. 5–14.

Draw the free-body diagram for the following problems. a) The truss in Prob. 5–15. b) The beam in Prob. 5–16. c) The man and load in Prob. 5–17. d) The beam in Prob. 5–18.

Draw the free-body diagram for the following problems. a) The man and beam in Prob. 5–19. b) The rod in Prob. 5–20. c) The rod in Prob. 5–21. d) The beam in Prob. 5–22.

Draw the free-body diagram for the following problems. a) The beam in Prob. 5–25. b) The crane and boom in Prob. 5–26. c) The bar in Prob. 5–27. d) The rod in Prob. 5–28.

Draw the free-body diagram for the following problems. a) The boom in Prob. 5–32. b) The jib crane in Prob. 5–33. c) The smooth pipe in Prob. 5–35. d) The beam in Prob. 5–36.

Draw the free-body diagram for the following problems. a) The jib crane in Prob. 5–37. b) The bar in Prob. 5–39. c) The bulkhead in Prob. 5–41. d) The boom in Prob. 5–42.

Draw the free-body diagram for the following problems. a) The rod in Prob. 5–44. b) The hand truck and load when it is lifted in Prob. 5–45. c) The beam in Prob. 5–47. d) The cantilever footing in Prob. 5–51.

Draw the free-body diagram for the following problems. a) The beam in Prob. 5–52. b) The boy and diving board in Prob. 5–53. c) The rod in Prob. 5–54. d) The rod in Prob. 5–56.

Draw the free-body diagram for the following problems. a) The beam in Prob. 5–57. b) The rod in Prob. 5–59. c) The bar in Prob. 5–60.

Determine the components of the support reactions at the fixed support A on the cantilevered beam.

Determine the reactions at the supports

Determine the horizontal and vertical components of reaction at the pin A and the reaction of the rocker B on the beam.

Determine the reactions at the supports

Determine the reactions at the supports

Determine the reactions at the supports

Determine the tension in the cable and the horizontal and vertical components of reaction of the pin A. The pulley at D is frictionless and the cylinder weighs 80 lb

The man attempts to support the load of boards having a weight W and a center of gravity at G. If he is standing on a smooth floor, determine the smallest angle \(\theta\) at which he can hold them up in the position shown. Neglect his weight.

Determine the components of reaction at the supports A and B on the rod.

The man has a weight W and stands at the center of the plank. If the planes at A and B are smooth, determine the tension in the cord in terms of W and \(\theta\).

A uniform glass rod having a length L is placed in the smooth hemispherical bowl having a radius r. Determine the angle of inclination \(\theta\) for equilibrium.

The uniform rod AB has a mass of 40 kg. Determine the force in the cable when the rod is in the position shown. There is a smooth collar at A.

If the intensity of the distributed load acting on the beam is w = 3 kN/m, determine the reactions at the roller A and pin B.

If the roller at A and the pin at B can support a load up to 4 kN and 8 kN, respectively, determine the maximum intensity of the distributed load w, measured in kN/m, so that failure of the supports does not occur.

The relay regulates voltage and current. Determine the force in the spring CD, which has a stiffness of k = 120 N/m, so that it will allow the armature to make contact at A in figure (a) with a vertical force of 0.4 N. Also, determine the force in the spring when the coil is energized and attracts the armature to E, figure (b), thereby breaking contact at A

Determine the reactions on the bent rod which is supported by a smooth surface at B and by a collar at A, which is fixed to the rod and is free to slide over the fixed inclined rod.

The mobile crane is symmetrically supported by two outriggers at A and two at B in order to relieve the suspension of the truck upon which it rests and to provide greater stability. If the crane boom and truck have a mass of 18 Mg and center of mass at \(G_{1}\), and the boom has a mass of 1.8 Mg and a center of mass at \(G_{2}\), determine the vertical reactions at each of the four outriggers as a function of the boom angle \(\theta\) when the boom is supporting a load having a mass of 1.2 Mg. Plot the results measured from \(\theta=0^{\circ}\) to the critical angle where tipping starts to occur.

Determine the reactions acting on the smooth uniform bar, which has a mass of 20 kg.

A linear torsional spring deforms such that an applied couple moment M is related to the spring’s rotation \(\theta\) in radians by the equation \(M=(20 \theta) \mathrm{N} \cdot \mathrm{m}\). If such a spring is attached to the end of a pin-connected uniform 10-kg rod, determine the angle \(\theta\) for equilibrium. The spring is undeformed when \(\theta=0^{\circ}\).

Determine the force P needed to pull the 50-kg roller over the smooth step. Take \(\theta=30^{\circ}\

Determine the magnitude and direction \(\theta\) of the minimum force P needed to pull the 50-kg roller over the smooth step.

The operation of the fuel pump for an automobile depends on the reciprocating action of the rocker arm ABC, which is pinned at B and is spring loaded at A and D. When the smooth cam C is in the position shown, determine the horizontal and vertical components of force at the pin and the force along the spring DF for equilibrium. The vertical force acting on the rocker arm at A is \(F_{A}\) = 60 N, and at C it is \(F_{C}\) = 125 N.

Determine the magnitude of force at the pin A and in the cable BC needed to support the 500-lb load. Neglect the weight of the boom AB.

The dimensions of a jib crane, which is manufactured by the Basick Co., are given in the figure. If the crane has a mass of 800 kg and a center of mass at G, and the maximum rated force at its end is F = 15 kN, determine the reactions at its bearings. The bearing at A is a journal bearing and supports only a horizontal force, whereas the bearing at B is a thrust bearing that supports both horizontal and vertical components.

The dimensions of a jib crane, which is manufactured by the Basick Co., are given in the figure. The crane has a mass of 800 kg and a center of mass at G. The bearing at A is a journal bearing and can support a horizontal force, whereas the bearing at B is a thrust bearing that supports both horizontal and vertical components. Determine the maximum load F that can be suspended from its end if the selected bearings at A and B can sustain a maximum resultant load of 24 kN and 34 kN, respectively.

The smooth pipe rests against the opening at the points of contact A, B, and C. Determine the reactions at these points needed to support the force of 300 N. Neglect the pipe’s thickness in the calculation.

The beam of negligible weight is supported horizontally by two springs. If the beam is horizontal and the springs are unstretched when the load is removed, determine the angle of tilt of the beam when the load is applied.

The cantilevered jib crane is used to support the load of 780 lb. If x = 5 ft, determine the reactions at the supports. Note that the supports are collars that allow the crane to rotate freely about the vertical axis. The collar at B supports a force in the vertical direction, whereas the one at A does not.

The cantilevered jib crane is used to support the load of 780 lb. If the trolley T can be placed anywhere between 1.5 ft \(\leq\) x \(\leq\) 7.5 ft, determine the maximum magnitude of reaction at the supports A and B. Note that the supports are collars that allow the crane to rotate freely about the vertical axis. The collar at B supports a force in the vertical direction, whereas the one at A does not.

The bar of negligible weight is supported by two springs, each having a stiffness k = 100 N/m. If the springs are originally unstretched, and the force is vertical as shown, determine the angle \(\theta\) the bar makes with the horizontal, when the 30-N force is applied to the bar.

Determine the stiffness k of each spring so that the 30-N force causes the bar to tip \(\theta\) = \(15^{\circ}\) when the force is applied. Originally the bar is horizontal and the springs are unstretched. Neglect the weight of the bar.

The bulk head AD is subjected to both water and soil- backfill pressures. Assuming AD is “pinned” to the ground at A, determine the horizontal and vertical reactions there and also the required tension in the ground anchor BC necessary for equilibrium. The bulk head has a mass of 800 kg.

The boom supports the two vertical loads. Neglect the size of the collars at D and B and the thickness of the boom, and compute the horizontal and vertical components of force at the pin A and the force in cable CB. Set \(F_{1}\) = 800 N and \(F_{2}\) = 350 N.

The boom is intended to support two vertical loads, \(F_{1}\) and \(F_{2}\). If the cable CB can sustain a maximum load of 1500 N before it fails, determine the critical loads if \(F_{1}\) = 2\(F_{2}\). Also, what is the magnitude of the maximum reaction at pin A?

The 10-kg uniform rod is pinned at end A. If it is also subjected to a couple moment of \(50 \mathrm{~N} \cdot \mathrm{m} \text {, }\) determine the smallest angle \(\theta\) for equilibrium. The spring is unstretched when \(\theta\) = 0, and has a stiffness of k = 60 N/m.

The man uses the hand truck to move material up the step. If the truck and its contents have a mass of 50 kg with center of gravity at G, determine the normal reaction on both wheels and the magnitude and direction of the minimum force required at the grip B needed to lift the load.

Three uniform books, each having a weight W and length a, are stacked as shown. Determine the maximum distance d that the top book can extend out from the bottom one so the stack does not topple over.

Determine the reactions at the pin A and the tension in cord BC. Set F = 40 kN. Neglect the thickness of the beam.

If rope BC will fail when the tension becomes 50 kN, determine the greatest vertical load F that can be applied to the beam at B. What is the magnitude of the reaction at A for this loading? Neglect the thickness of the beam.

The rigid metal strip of negligible weight is used as part of an electromagnetic switch. If the stiffness of the springs at A and B is k = 5 N/m and the strip is originally horizontal when the springs are unstretched, determine the smallest force F needed to close the contact gap at C.

The rigid metal strip of negligible weight is used as part of an electromagnetic switch. Determine the maximum stiffness k of the springs at A and B so that the contact at C closes when the vertical force developed there is F = 0.5 N. Originally the strip is horizontal as shown.

The cantilever footing is used to support a wall near its edge A so that it causes a uniform soil pressure under the footing. Determine the uniform distribution loads, \(w_{A}\) and \(w_{B}\), measured in lb/ft at pads A and B, necessary to support the wall forces of 8000 lb and 20 000 lb.

The uniform beam has a weight W and length l and is supported by a pin at A and a cable BC. Determine the horizontal and vertical components of reaction at A and the tension in the cable necessary to hold the beam in the position shown.

A boy stands out at the end of the diving board, which is supported by two springs A and B, each having a stiffness of k = 15 kN/m. In the position shown the board is horizontal. If the boy has a mass of 40 kg, determine the angle of tilt which the board makes with the horizontal after he jumps off. Neglect the weight of the board and assume it is rigid.

The 30-N uniform rod has a length of l = 1 m. If s = 1.5 m, determine the distance h of placement at the end A along the smooth wall for equilibrium.

The uniform rod has a length l and weight W. It is supported at one end A by a smooth wall and the other end by a cord of length s which is attached to the wall as shown. Determine the placement h for equilibrium.

The uniform rod of length L and weight W is supported on the smooth planes. Determine its position u for equilibrium. Neglect the thickness of the rod.

The beam is subjected to the two concentrated loads. Assuming that the foundation exerts a linearly varying load distribution on its bottom, determine the load intensities \(w_{1}\) and \(w_{2}\) for equilibrium if P = 500 lb and L = 12 ft.

The beam is subjected to the two concentrated loads. Assuming that the foundation exerts a linearly varying load distribution on its bottom, determine the load intensities \(w_{1}\) and \(w_{2}\) for equilibrium in terms of the parameters shown.

The rod supports a weight of 200 lb and is pinned at its end A. If it is also subjected to a couple moment of \(100 \mathrm{lb} \cdot \mathrm{ft}\), determine the angle \(\theta\) for equilibrium. The spring has an unstretched length of 2 ft and a stiffness of k = 50 lb/ft.

Determine the distance d for placement of the load P for equilibrium of the smooth bar in the position \(\theta\) as shown. Neglect the weight of the bar.

If d = 1 m, and \(\theta\) = \(30^{\circ}\), determine the normal reaction at the smooth supports and the required distance a for the placement of the roller if P = 600 N. Neglect the weight of the bar

The uniform load has a mass of 600 kg and is lifted using a uniform 30-kg strongback beam BAC and four ropes as shown. Determine the tension in each rope and the force that must be applied at A.

Due to an unequal distribution of fuel in the wing tanks, the centers of gravity for the airplane fuselage A and wings B and C are located as shown. If these components have weights \(W_{A}\) = 45 000 lb, \(W_{B}\) = 8000 lb, and \(W_{C}\) = 6000 lb, determine the normal reactions of the wheels D, E, and F on the ground.

Determine the components of reaction at the fixed support A. The 400 N, 500 N, and 600 N forces are parallel to the x, y, and z axes, respectively.

The 50-lb mulching machine has a center of gravity at G. Determine the vertical reactions at the wheels C and B and the smooth contact point A.

The smooth uniform rod AB is supported by a balland-socket joint at A, the wall at B, and cable BC. Determine the components of reaction at A, the tension in the cable, and the normal reaction at B if the rod has a mass of 20 kg.

The uniform concrete slab has a mass of 2400 kg. Determine the tension in each of the three parallel supporting cables when the slab is held in the horizontal plane as shown.

The 100-lb door has its center of gravity at G. Determine the components of reaction at hinges A and B if hinge B resists only forces in the x and y directions and A resists forces in the x, y, z directions

Determine the tension in each cable and the components of reaction at D needed to support the load.

The stiff-leg derrick used on ships is supported by a ball-and-socket joint at D and two cables BA and BC. The cables are attached to a smooth collar ring at B, which allows rotation of the derrick about z axis. If the derrick supports a crate having a mass of 200 kg, determine the tension in the cables and the x, y, z components of reaction at D.

Determine the components of reaction at the balland-socket joint A and the tension in each cable necessary for equilibrium of the rod.

Determine the components of reaction at the balland-socket joint A and the tension in the supporting cables DB and DC.

The bent rod is supported at A, B, and C by smooth journal bearings. Determine the components of reaction at the bearings if the rod is subjected to the force F = 800 N. The bearings are in proper alignment and exert only force reactions on the rod.

The bent rod is supported at A, B, and C by smooth journal bearings. Determine the magnitude of F which will cause the positive x component of reaction at the bearing C to be \(C_{x}\) = 50 N. The bearings are in proper alignment and exert only force reactions on the rod.

Member AB is supported by a cable BC and at A by a square rod which fits loosely through the square hole in the collar fixed to the member as shown. Determine the components of reaction at A and the tension in the cable needed to hold the rod in equilibrium.

The member is supported by a pin at A and cable BC. Determine the components of reaction at these supports if the cylinder has a mass of 40 kg.

The member is supported by a square rod which fits loosely through the smooth square hole of the attached collar at A and by a roller at B. Determine the components of reaction at these supports when the member is subjected to the loading shown.

The bent rod is supported at A, B, and C by smooth journal bearings. Compute the x, y, z components of reaction at the bearings if the rod is subjected to forces \(F_{1}\) = 300 lb and \(F_{2}\) = 250 lb. \(F_{1}\) lies in the y–z plane. The bearings are in proper alignment and exert only force reactions on the rod.

The bent rod is supported at A, B, and C by smooth journal bearings. Determine the magnitude of \(F_{2}\) which will cause the reaction Cy at the bearing C to be equal to zero. The bearings are in proper alignment and exert only force reactions on the rod. Set \(F_{1}\) = 300 lb.

The bar AB is supported by two smooth collars. At A the connection is with a ball-and-socket joint and at B it is a rigid attachment. If a 50-lb load is applied to the bar, determine the x, y, z components of reaction at A and B.

The rod has a weight of 6 lb/ft. If it is supported by a ball-and-socket joint at C and a journal bearing at D, determine the x, y, z components of reaction at these supports and the moment M that must be applied along the axis of the rod to hold it in the position shown.

The sign has a mass of 100 kg with center of mass at G. Determine the x, y, z components of reaction at the ball-and-socket joint A and the tension in wires BC and BD.

Both pulleys are fixed to the shaft and as the shaft turns with constant angular velocity, the power of pulley A is transmitted to pulley B. Determine the horizontal tension T in the belt on pulley B and the x, y, z components of reaction at the journal bearing C and thrust bearing D if \(\theta\) = 0. The bearings are in proper alignment and exert only force reactions on the shaft.

Both pulleys are fixed to the shaft and as the shaft turns with constant angular velocity, the power of pulley A is transmitted to pulley B. Determine the horizontal tension T in the belt on pulley B and the x, y, z components of reaction at the journal bearing C and thrust bearing D if \(\theta\) = \(45^{\circ}\). The bearings are in proper alignment and exert only force reactions on the shaft.

Member AB is supported by a cable BC and at A by a square rod which fits loosely through the square hole at the end joint of the member as shown. Determine the components of reaction at A and the tension in the cable needed to hold the 800-lb cylinder in equilibrium.