Solved: A slender rod AB, of weight W, is attached to

Two crates, each of mass 350 kg, are placed as shown in the bed of a 1400-kg pickup truck. Determine the reactions at each of the two (a) rear wheels A, (b) front wheels B.

Solve Prob. 4.1, assuming that crate D is removed and that the position of crate C is unchanged.

A T-shaped bracket supports the four loads shown. Determine the reactions at A and B (a) if a = 10 in., (b) if a = 7 in.

For the bracket and loading of Prob. 4.3, determine the smallest distance a if the bracket is not to move.

A hand truck is used to move two kegs, each of mass 40 kg. Neglecting the mass of the hand truck, determine (a) the vertical force P that should be applied to the handle to maintain equilibrium when \(a=35^{\circ}\), (b) the corresponding reaction at each of the two wheels.

Solve Prob. 4.5 when \(a=40^{\circ}\).

A 3200-lb forklift truck is used to lift a 1700-lb crate. Determine the reaction at each of the two (a) front wheels A, (b) rear wheels B.

For the beam and loading shown, determine (a) the reaction at A, (b) the tension in cable BC.

For the beam and loading shown, determine the range of the distance a for which the reaction at B does not exceed 100 lb downward or 200 lb upward.

The maximum allowable value of each of the reactions is 180 N. Neglecting the weight of the beam, determine the range of the distance d for which the beam is safe.

Three loads are applied as shown to a light beam supported by cables attached at B and D. Neglecting the weight of the beam, determine the range of values of Q for which neither cable becomes slack when P = 0.

Three loads are applied as shown to a light beam supported by cables attached at B and D. Knowing that the maximum allowable tension in each cable is 4 kN and neglecting the weight of the beam, determine the range of values of Q for which the loading is safe when P = 0.

For the beam of Prob. 4.12, determine the range of values of Q for which the loading is safe when P = 1 kN.

For the beam of Sample Prob. 4.2, determine the range of values of P for which the beam will be safe, knowing that the maximum allowable value of each of the reactions is 30 kips and that the reaction at A must be directed upward.

The bracket BCD is hinged at C and attached to a control cable at B. For the loading shown, determine (a) the tension in the cable, (b) the reaction at C.

Solve Prob. 4.15, assuming that a = 0.32 m.

The lever BCD is hinged at C and attached to a control rod at B. If P = 100 lb, determine (a) the tension in rod AB, (b) the reaction at C.

The lever BCD is hinged at C and attached to a control rod at B. Determine the maximum force P that can be safely applied at D if the maximum allowable value of the reaction at C is 250 lb.

Two links AB and DE are connected by a bell crank as shown. Knowing that the tension in link AB is 720 N, determine (a) the tension in link DE, (b) the reaction at C.

Two links AB and DE are connected by a bell crank as shown. Determine the maximum force that can be safely exerted by link AB on the bell crank if the maximum allowable value for the reaction at C is 1600 N.

Determine the reactions at A and C when (a) a = 0, (b) \(a=30^{\circ}\).

Determine the reactions at A and B when (a) a = 0, (b) \(a=90^{\circ}\), (c) \(a=30^{\circ}\).

Determine the reactions at A and B when (a) h = 0, (b) h = 200 mm.

A lever AB is hinged at C and attached to a control cable at A. If the lever is subjected to a 75-lb vertical force at B, determine (a) the tension in the cable, (b) the reaction at C.

For each of the plates and loadings shown, determine the reactions at A and B.

For each of the plates and loadings shown, determine the reactions at A and B.

A rod AB hinged at A and attached at B to cable BD supports the loads shown. Knowing that d = 200 mm, determine (a) the tension in cable BD, (b) the reaction at A.

A rod AB hinged at A and attached at B to cable BD supports the loads shown. Knowing that d = 150 mm, determine (a) the tension in cable BD, (b) the reaction at A.

A force P of magnitude 90 lb is applied to member ACE, which is supported by a frictionless pin at D and by the cable ABE. Since the cable passes over a small pulley at B, the tension may be assumed to be the same in portions AB and BE of the cable. For the case when a = 3 in., determine (a) the tension in the cable, (b) the reaction at D.

Solve Prob. 4.29 for a = 6 in.

Neglecting friction, determine the tension in cable ABD and the reaction at support C.

Neglecting friction and the radius of the pulley, determine (a) the tension in cable ADB, (b) the reaction at C.

Rod ABC is bent in the shape of an arc of circle of radius R. Knowing the \(\mathrm{u}=30^{\circ}\), determine the reaction (a) at B, (b) at C.

Rod ABC is bent in the shape of an arc of circle of radius R. Knowing the \(\mathrm{u}=60^{\circ}\), determine the reaction (a) at B, (b) at C.

A movable bracket is held at rest by a cable attached at C and by frictionless rollers at A and B. For the loading shown, determine (a) the tension in the cable, (b) the reactions at A and B.

A light bar AB supports a 15-kg block at its midpoint C. Rollers at A and B rest against frictionless surfaces, and a horizontal cable AD is attached at A. Determine (a) the tension in cable AD, (b) the reactions at A and B.

A light bar AD is suspended from a cable BE and supports a 50-lb block at C. The ends A and D of the bar are in contact with frictionless vertical walls. Determine the tension in cable BE and the reactions at A and D.

A light rod AD is supported by frictionless pegs at B and C and rests against a frictionless wall at A. A vertical 120-lb force is applied at D. Determine the reactions at A, B, and C.

Bar AD is attached at A and C to collars that can move freely on the rods shown. If the cord BE is vertical (a = 0), determine the tension in the cord and the reactions at A and C.

Solve Prob. 4.39 if the cord BE is parallel to the rods \(\left(a=30^{\circ}\right)\).

The T-shaped bracket shown is supported by a small wheel at E and pegs at C and D. Neglecting the effect of friction, determine the reactions at C, D, and E when \(\mathrm{u}=30^{\circ}\).

The T-shaped bracket shown is supported by a small wheel at E and pegs at C and D. Neglecting the effect of friction, determine (a) the smallest value of u for which the equilibrium of the bracket is maintained, (b) the corresponding reactions at C, D, and E.

Beam AD carries the two 40-lb loads shown. The beam is held by a fixed support at D and by the cable BE that is attached to the counterweight W. Determine the reaction at D when (a) W = 100 lb, (b) W = 90 lb.

For the beam and loading shown, determine the range of values of W for which the magnitude of the couple at D does not exceed \(40\mathrm{\ lb}\cdot\mathrm{ft}\).

An 8-kg mass can be supported in the three different ways shown. Knowing that the pulleys have a 100-mm radius, determine the reaction at A in each case.

A tension of 20 N is maintained in a tape as it passes through the support system shown. Knowing that the radius of each pulley is 10 mm, determine the reaction at C.

Solve Prob. 4.46, assuming that 15-mm-radius pulleys are used.

The rig shown consists of a 1200-lb horizontal member ABC and a vertical member DBE welded together at B. The rig is being used to raise a 3600-lb crate at a distance x = 12 ft from the vertical member DBE. If the tension in the cable is 4 kips, determine the reaction at E, assuming that the cable is (a) anchored at F as shown in the figure, (b) attached to the vertical member at a point located 1 ft above E.

For the rig and crate of Prob. 4.48, and assuming that the cable is anchored at F as shown, determine (a) the required tension in cable ADCF if the maximum value of the couple at E as x varies from 1.5 to 17.5 ft is to be as small as possible, (b) the corresponding maximum value of the couple.

A 6-m telephone pole weighing 1600 N is used to support the ends of two wires. The wires form the angles shown with the horizontal and the tensions in the wires are, respectively, \(T_1=600\mathrm{\ N}\) and \(T_2=375\mathrm{\ N}\). Determine the reaction at the fixed end A.

A vertical load P is applied at end B of rod BC. (a) Neglecting the weight of the rod, express the angle u corresponding to the equilibrium position in terms of P, l, and the counterweight W. (b) Determine the value of u corresponding to equilibrium if P = 2W.

A vertical load P is applied at end B of rod BC. (a) Neglecting the weight of the rod, express the angle u corresponding to the equilibrium position in terms of P, l, and the counterweight W. (b) Determine the value of u corresponding to equilibrium if P = 2W.

A slender rod AB, of weight W, is attached to blocks A and B, which move freely in the guides shown. The blocks are connected by an elastic cord that passes over a pulley at C. (a) Express the tension in the cord in terms of W and u. (b) Determine the value of u for which the tension in the cord is equal to 3W.

Rod AB is acted upon by a couple M and two forces, each of magnitude P. (a) Derive an equation in u, P, M, and l that must be satisfied when the rod is in equilibrium. (b) Determine the value of u corresponding to equilibrium when \(M=150\mathrm{\ N}\cdot\mathrm{m}\), P = 200 N, and l = 600 mm.

Solve Sample Prob. 4.5, assuming that the spring is unstretched when \(\mathrm{u}=90^{\circ}\).

A slender rod AB, of weight W, is attached to blocks A and B that move freely in the guides shown. The constant of the spring is k, and the spring is unstretched when u = 0. (a) Neglecting the weight of the blocks, derive an equation in W, k, l, and u that must be satisfied when the rod is in equilibrium. (b) Determine the value of u when W = 75 lb, l = 30 in., and k = 3 lb/in.

A vertical load P is applied at end B of rod BC. The constant of the spring is k, and the spring is unstretched when \(\mathrm{u}=60^{\circ}\). (a) Neglecting the weight of the rod, express the angle u corresponding to the equilibrium position in terms of P, k, and l. (b) Determine the value of u corresponding to equilibrium if \(P=\frac{1}{4} k l\).

A collar B of weight W can move freely along the vertical rod shown. The constant of the spring is k, and the spring is unstretched when u = 0. (a) Derive an equation in u, W, k, and l that must be satisfied when the collar is in equilibrium. (b) Knowing that W = 300 N, l = 500 mm, and k = 800 N/m, determine the value of u corresponding to equilibrium.

Eight identical \(500 \times 750-\mathrm{mm}\) rectangular plates, each of mass m = 40 kg, are held in a vertical plane as shown. All connections consist of frictionless pins, rollers, or short links. In each case, determine whether (a) the plate is completely, partially, or improperly constrained, (b) the reactions are statically determinate or indeterminate, (c) the equilibrium of the plate is maintained in the position shown. Also, wherever possible, compute the reactions.

The bracket ABC can be supported in the eight different ways shown. All connections consist of smooth pins, rollers, or short links. For each case, answer the questions listed in Prob. 4.59, and, wherever possible, compute the reactions, assuming that the magnitude of the force P is 100 lb.

Determine the reactions at A and B when a = 150 mm.

Determine the value of a for which the magnitude of the reaction at B is equal to 800 N.

Using the method of Sec. 4.7, solve Prob. 4.22b.

A 500-lb cylindrical tank, 8 ft in diameter, is to be raised over a 2-ft obstruction. A cable is wrapped around the tank and pulled horizontally as shown. Knowing that the corner of the obstruction at A is rough, find the required tension in the cable and the reaction at A.

For the frame and loading shown, determine the reactions at A and C.

For the frame and loading shown, determine the reactions at C and D.

Determine the reactions at B and D when b = 60 mm.

Determine the reactions at B and D when b = 120 mm.

A T-shaped bracket supports a 300-N load as shown. Determine the reactions at A and C when \(a=45^{\circ}\).

A T-shaped bracket supports a 300-N load as shown. Determine the reactions at A and C when \(a=60^{\circ}\).

A 40-lb roller, of diameter 8 in., which is to be used on a tile floor, is resting directly on the subflooring as shown. Knowing that the thickness of each tile is 0.3 in., determine the force P required to move the roller onto the tiles if the roller is (a) pushed to the left, (b) pulled to the right.

One end of rod AB rests in the corner A and the other end is attached to cord BD. If the rod supports a 40-lb load at its midpoint C, find the reaction at A and the tension in the cord.

A 50-kg crate is attached to the trolley-beam system shown. Knowing that a = 1.5 m, determine (a) the tension in cable CD, (b) the reaction at B.

Solve Prob. 4.73, assuming that a = 3 m.

Determine the reactions at A and B when \(b=50^{\circ}\).

Determine the reactions at A and B when \(b=80^{\circ}\).

Knowing that \(u=30^{\circ}\) determine the reaction (a) at B, (b) at C.

Knowing that \(u=60^{\circ}\) determine the reaction (a) at B, (b) at C.

Using the method of Sec. 4.7, solve Prob. 4.23.

Using the method of Sec. 4.7, solve Prob. 4.24.

Member ABC is supported by a pin and bracket at B and by an inextensible cord attached at A and C and passing over a frictionless pulley at D. The tension may be assumed to be the same in portions AD and CD of the cord. For the loading shown and neglecting the size of the pulley, determine the tension in the cord and the reaction at B.

Member ABC is supported by a pin and bracket at B and by an inextensible cord attached at A and C and passing over a frictionless pulley at D. The tension may be assumed to be the same in portions AD and CD of the cord. For the loading shown and neglecting the size of the pulley, determine the tension in the cord and the reaction at B.

A thin ring of mass 2 kg and radius r = 140 mm is held against a frictionless wall by a 125-mm string AB. Determine (a) the distance d, (b) the tension in the string, (c) the reaction at C.

A uniform rod AB of length 2R rests inside a hemispherical bowl of radius R as shown. Neglecting friction, determine the angle u corresponding to equilibrium.

A slender rod BC of length L and weight W is held by two cables as shown. Knowing that cable AB is horizontal and that the rod forms an angle of \(40^{\circ}\) with the horizontal, determine (a) the angle u that cable CD forms with the horizontal, (b) the tension in each cable.

A slender rod of length L and weight W is attached to a collar at A and is fitted with a small wheel at B. Knowing that the wheel rolls freely along a cylindrical surface of radius R, and neglecting friction, derive an equation in u, L, and R that must be satisfied when the rod is in equilibrium.

Knowing that for the rod of Prob. 4.86, L = 15 in., R = 20 in., and W = 10 lb, determine (a) the angle u corresponding to equilibrium, (b) the reactions at A and B.

Rod AB is bent into the shape of an arc of circle and is lodged between two pegs D and E. It supports a load P at end B. Neglecting friction and the weight of the rod, determine the distance c corresponding to equilibrium when a = 20 mm and R = 100 mm.

A slender rod of length L is attached to collars that can slide freely along the guides shown. Knowing that the rod is in equilibrium, derive an expression for the angle u in terms of the angle b.

An 8-kg slender rod of length L is attached to collars that can slide freely along the guides shown. Knowing that the rod is in equilibrium and that \(b=30^{\circ}\), determine (a) the angle u that the rod forms with the vertical, (b) the reactions at A and B.

A 200-mm lever and a 240-mm-diameter pulley are welded to the axle BE that is supported by bearings at C and D. If a 720-N vertical load is applied at A when the lever is horizontal, determine (a) the tension in the cord, (b) the reactions at C and D. Assume that the bearing at D does not exert any axial thrust.

Solve Prob. 4.91, assuming that the axle has been rotated clockwise in its bearings by \(30^{\circ}\) and that the 720-N load remains vertical.

A \(4 \times 8-\mathrm{ft}\) sheet of plywood weighing 40 lb has been temporarily propped against column CD. It rests at A and B on small wooden blocks and against protruding nails. Neglecting friction at all surfaces of contact, determine the reactions at A, B, and C.

Two tape spools are attached to an axle supported by bearings at A and D. The radius of spool B is 1.5 in. and the radius of spool C is 2 in. Knowing that \(T_B=20\mathrm{\ lb}\) and that the system rotates at a constant rate, determine the reactions at A and D. Assume that the bearing at A does not exert any axial thrust and neglect the weights of the spools and axle.

Two transmission belts pass over a double-sheaved pulley that is attached to an axle supported by bearings at A and D. The radius of the inner sheave is 125 mm and the radius of the outer sheave is 250 mm. Knowing that when the system is at rest, the tension is 90 N in both portions of belt B and 150 N in both portions of belt C, determine the reactions at A and D. Assume that the bearing at D does not exert any axial thrust.

Solve Prob. 4.95, assuming that the pulley rotates at a constant rate and that \(T_B=104\mathrm{\ N}\), \(T_{B}^{\prime}=84\mathrm{\ N}\), and \(T_C=175\mathrm{\ N}\).

Two steel pipes AB and BC, each having a mass per unit length of 8 kg/m, are welded together at B and supported by three vertical wires. Knowing that a = 0.4 m, determine the tension in each wire.

For the pipe assembly of Prob. 4.97, determine (a) the largest permissible value of a if the assembly is not to tip, (b) the corresponding tension in each wire.

The 45-lb square plate shown is supported by three vertical wires. Determine the tension in each wire.

The table shown weighs 30 lb and has a diameter of 4 ft. It is supported by three legs equally spaced around the edge. A vertical load P of magnitude 100 lb is applied to the top of the table at D. Determine the maximum value of a if the table is not to tip over. Show, on a sketch, the area of the table over which P can act without tipping the table.

An opening in a floor is covered by a \(1 \times 1.2-\mathrm{m}\) sheet of plywood of mass 18 kg. The sheet is hinged at A and B and is maintained in a position slightly above the floor by a small block C. Determine the vertical component of the reaction (a) at A, (b) at B, (c) at C.

Solve Prob. 4.101, assuming that the small block C is moved and placed under edge DE at a point 0.15 m from corner E.

The rectangular plate shown weighs 80 lb and is supported by three vertical wires. Determine the tension in each wire.

The rectangular plate shown weighs 80 lb and is supported by three vertical wires. Determine the weight and location of the lightest block that should be placed on the plate if the tensions in the three wires are to be equal.

A 2.4-m boom is held by a ball-and-socket joint at C and by two cables AD and AE. Determine the tension in each cable and the reaction at C.

Solve Prob. 4.105, assuming that the 3.6-kN load is applied at point A.

A 10-ft boom is acted upon by the 840-lb force shown. Determine the tension in each cable and the reaction at the ball-and-socket joint at A.

A 12-m pole supports a horizontal cable CD and is held by a ball and socket at A and two cables BE and BF. Knowing that the tension in cable CD is 14 kN and assuming that CD is parallel to the x axis (f = 0), determine the tension in cables BE and BF and the reaction at A.

Solve Prob. 4.108, assuming that cable CD forms an angle \(f=25^{\circ}\) with the vertical xy plane.

A 48-in. boom is held by a ball-and-socket joint at C and by two cables BF and DAE; cable DAE passes around a frictionless pulley at A. For the loading shown, determine the tension in each cable and the reaction at C.

Solve Prob. 4.110, assuming that the 320-lb load is applied at A.

A 600-lb crate hangs from a cable that passes over a pulley B and is attached to a support at H. The 200-lb boom AB is supported by a ball-and-socket joint at A and by two cables DE and DF. The center of gravity of the boom is located at G. Determine (a) the tension in cables DE and DF, (b) the reaction at A.

A 100-kg uniform rectangular plate is supported in the position shown by hinges A and B and by cable DCE that passes over a frictionless hook at C. Assuming that the tension is the same in both parts of the cable, determine (a) the tension in the cable, (b) the reactions at A and B. Assume that the hinge at B does not exert any axial thrust.

Solve Prob. 4.113, assuming that cable DCE is replaced by a cable attached to point E and hook C.

The rectangular plate shown weighs 75 lb and is held in the position shown by hinges at A and B and by cable EF. Assuming that the hinge at B does not exert any axial thrust, determine (a) the tension in the cable, (b) the reactions at A and B.

Solve Prob. 4.115, assuming that cable EF is replaced by a cable attached at points E and H.

A 20-kg cover for a roof opening is hinged at corners A and B. The roof forms an angle of \(30^{\circ}\) with the horizontal, and the cover is maintained in a horizontal position by the brace CE. Determine (a) the magnitude of the force exerted by the brace, (b) the reactions at the hinges. Assume that the hinge at A does not exert any axial thrust.

The bent rod ABEF is supported by bearings at C and D and by wire AH. Knowing that portion AB of the rod is 250 mm long, determine (a) the tension in wire AH, (b) the reactions at C and D. Assume that the bearing at D does not exert any axial thrust.

Solve Prob. 4.115, assuming that the hinge at B is removed and that the hinge at A can exert couples about axes parallel to the y and z axes.

Solve Prob. 4.118, assuming that the bearing at D is removed and that the bearing at C can exert couples about axes parallel to the y and z axes.

The assembly shown is welded to collar A that fits on the vertical pin shown. The pin can exert couples about the x and z axes but does not prevent motion about or along the y axis. For the loading shown, determine the tension in each cable and the reaction at A.

The assembly shown is used to control the tension T in a tape that passes around a frictionless spool at E. Collar C is welded to rods ABC and CDE. It can rotate about shaft FG but its motion along the shaft is prevented by a washer S. For the loading shown, determine (a) the tension T in the tape, (b) the reaction at C.

The rigid L-shaped member ABF is supported by a ball-and-socket joint at A and by three cables. For the loading shown, determine the tension in each cable and the reaction at A.

Solve Prob. 4.123, assuming that the load at C has been removed.

The rigid L-shaped member ABC is supported by a ball-and-socket joint at A and by three cables. If a 1.8-kN load is applied at F, determine the tension in each cable.

Solve Prob. 4.125, assuming that the 1.8-kN load is applied at C.

The assembly shown consists of an 80-mm rod AF that is welded to a cross consisting of four 200-mm arms. The assembly is supported by a ball-and-socket joint at F and by three short links, each of which forms an angle of \(45^{\circ}\) with the vertical. For the loading shown, determine (a) the tension in each link, (b) the reaction at F.

The uniform 10-kg rod AB is supported by a ball-and-socket joint at A and by the cord CG that is attached to the midpoint G of the rod. Knowing that the rod leans against a frictionless vertical wall at B, determine (a) the tension in the cord, (b) the reactions at A and B.

Three rods are welded together to form a “corner” that is supported by three eyebolts. Neglecting friction, determine the reactions at A, B, and C when P = 240 lb, a = 12 in., b = 8 in., and c = 10 in.

Solve Prob. 4.129, assuming that the force P is removed and is replaced by a couple \(\mathbf{M}=+(600\ \mathrm{lb}\cdot\mathrm{in.})\mathbf{j}\) acting at B.

In order to clean the clogged drainpipe AE, a plumber has disconnected both ends of the pipe and inserted a power snake through the opening at A. The cutting head of the snake is connected by a heavy cable to an electric motor that rotates at a constant speed as the plumber forces the cable into the pipe. The forces exerted by the plumber and the motor on the end of the cable can be represented by the wrench \(\mathbf{F}=-(48\mathrm{\ N})\mathbf{k},\mathbf{\ M}=-(90\mathrm{\ N}\cdot\mathrm{m})\mathbf{k}\). Determine the additional reactions at B, C, and D caused by the cleaning operation. Assume that the reaction at each support consists of two force components perpendicular to the pipe.

Solve Prob. 4.131, assuming that the plumber exerts a force F = -(48 N)k and that the motor is turned off (M = 0).

The 50-kg plate ABCD is supported by hinges along edge AB and by wire CE. Knowing that the plate is uniform, determine the tension in the wire.

Solve Prob. 4.133, assuming that wire CE is replaced by a wire connecting E and D.

Two rectangular plates are welded together to form the assembly shown. The assembly is supported by ball-and-socket joints at B and D and by a ball on a horizontal surface at C. For the loading shown, determine the reaction at C.

Two \(2 \times 4-\mathrm{f t}\) plywood panels, each of weight 12 lb, are nailed together as shown. The panels are supported by ball-and-socket joints at A and F and by the wire BH. Determine (a) the location of H in the xy plane if the tension in the wire is to be minimum, (b) the corresponding minimum tension.

Solve Prob. 4.136, subject to the restriction that H must lie on the y axis

The frame ACD is supported by ball-and-socket joints at A and D and by a cable that passes through a ring at B and is attached to hooks at G and H. Knowing that the frame supports at point C a load of magnitude P = 268 N, determine the tension in the cable.

Solve Prob. 4.138, assuming that cable GBH is replaced by a cable GB attached at G and B.

The bent rod ABDE is supported by ball-and-socket joints at A and E and by the cable DF. If a 60-lb load is applied at C as shown, determine the tension in the cable.

Solve Prob. 4.140, assuming that cable DF is replaced by a cable connecting B and F.

A gardener uses a 60-N wheelbarrow to transport a 250-N bag of fertilizer. What force must she exert on each handle?

The required tension in cable AB is 200 lb. Determine (a) the vertical force P that must be applied to the pedal, (b) the corresponding reaction at C.

A lever AB is hinged at C and attached to a control cable at A. If the lever is subjected to a 500-N horizontal force at B, determine (a) the tension in the cable, (b) the reaction at C.

A force P of magnitude 280 lb is applied to member ABCD, which is supported by a pin at A and by the cable CED. Neglecting friction and considering the case when a = 3 in., determine (a) the tension in the cable, (b) the reaction at A.

Two slots have been cut in plate DEF, and the plate has been placed so that the slots fit two fixed, frictionless pins A and B. Knowing that P = 15 lb, determine (a) the force each pin exerts on the plate, (b) the reaction at F.

Knowing that the tension in wire BD is 1300 N, determine the reaction at the fixed support C of the frame shown.

The spanner shown is used to rotate a shaft. A pin fits in a hole at A, while a flat, frictionless surface rests against the shaft at B. If a 60-lb force P is exerted on the spanner at D, find the reactions at A and B.

Rod AB is supported by a pin and bracket at A and rests against a frictionless peg at C. Determine the reactions at A and C when a 170-N vertical force is applied at B.

The 24-lb square plate shown is supported by three vertical wires. Determine (a) the tension in each wire when a = 10 in., (b) the value of a for which the tension in each wire is 8 lb.

Frame ABCD is supported by a ball-and-socket joint at A and by three cables. For a = 150 mm, determine the tension in each cable and the reaction at A.

The pipe ACDE is supported by ball-and-socket joints at A and E and by the wire DF. Determine the tension in the wire when a 640-N load is applied at B as shown.

A force P is applied to a bent rod ABC, which may be supported in four different ways as shown. In each case, if possible, determine the reactions at the supports.