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PROBLEM 10.88 Collar A can slide freely on the semicircular rod shown. Knowing that the constant of the spring is k and that the unstretched length of the spring is equal to the radius r, determine the value of  […]

CHAPTER 10 PROBLEM 10.1 Determine the vertical force P that must be applied at C to maintain the equilibrium of the linkage. SOLUTION Assume A y  2 CA yy   DA yy   11 22 EDA yyy […]

PROBLEM 10.99* Two rods of negligible weight are attached to drums of radius r that are connected by a belt and spring of constant k. Knowing that the spring is undeformed when the rods are vertical, determine the range of […]

PROBLEM 10.20 For the linkage shown, determine the force Q required for equilibrium when 18 in.,l 600 lb in.,M and 70 .   SOLUTION 1 2cos l C    Virtual Work: 0:U   0MQC   […]

PROBLEM 10.52 Knowing that the coefficient of static friction between the block attached to rod ACE and the horizontal surface is 0.15, determine the magnitude of the largest and smallest force Q for which equilibrium is maintained when 30 , […]

PROBLEM 10.71 Two uniform rods AB and CD, of the same length l, are attached to gears as shown. Knowing that rod AB weighs 3 lb and that rod CD weighs 2 lb, determine the positions of equilibrium of the […]

PROBLEM 10.36 A load W of magnitude 72 lb is applied to the mechanism at C. Neglecting the weight of the mechanism, determine the value of  corresponding to equilibrium. The constant of the spring is 20 lb/in.,k and the […]

PROBLEM 2.98 For the boom and loading of Problem. 2.97, determine the magnitude of the load P. PROBLEM 2.97 The boom OA carries a load P and is supported by two cables as shown. Knowing that the tension in cable […]

PROBLEM 2.136 A container of weight W is suspended from ring A. Cable BAC passes through the ring and is attached to fixed supports at B and C. Two forces P=Pi and Q Q=k are applied to the ring to […]

PROBLEM 2.79 Determine the magnitude and direction of the force F = (240 N)i – (270 N)j + (680 N)k. SOLUTION 222 222 (240 N) ( 270 N) ( 680 N) xyz F FFF F = ++ = +− +− […]

PROBLEM 2.59 For the situation described in Figure P2.48, determine (a) the value of α for which the tension in rope BC is as small as possible, (b) the corresponding value of the tension. SOLUTION Free–Body Diagram Force Triangle To […]

PROBLEM 2.111 A transmission tower is held by three guy wires attached to a pin at A and anchored by bolts at B, C, and D. If the tension in wire AB is 840 lb, determine the vertical force P […]

PROBLEM 2.19 Two forces P and Q are applied to the lid of a storage bin as shown. Knowing that P = 48 N and Q = 60 N, determine by trigonometry the magnitude and direction of the resultant of […]

PROBLEM 2.39 For the collar of Problem 2.35, determine (a) the required value of α if the resultant of the three forces shown is to be vertical, (b) the corresponding magnitude of the resultant. SOLUTION (100 N)cos (150 N)cos( 30 […]

PROBLEM 2.124 Knowing that the tension in cable AE of Prob. 2.123 is 75 lb, determine (a) the magnitude of the load P, (b) the tension in cables BAC and AD. PROBLEM 2.123 Cable BAC passes through a frictionless ring […]

CHAPTER 2 PROBLEM 2.1 Two forces are applied as shown to a hook. Determine graphically the magnitude and direction of their resultant using (a) the parallelogram law, (b) the triangle rule. SOLUTION (a) Parallelogram law: (b) Triangle rule: We measure: […]

PROBLEM 3.131 A concrete foundation mat of 5-m radius supports four equally spaced columns, each of which is located 4 m from the center of the mat. Determine the magnitude and the point of application of the resultant of the […]

CHAPTER 3 PROBLEM 3.1 A crate of mass 80 kg is held in the position shown. Determine (a) the moment produced by the weight W of the crate about E, (b) the smallest force applied at B that creates a […]

PROBLEM 3.58 In Problem 3.57, determine the moment about the diagonal AD of the force exerted on the frame by portion BG of the cable. PROBLEM 3.57 The frame ACD is hinged at A and D and is supported by […]

PROBLEM 3.149 A small boat hangs from two davits, one of which is shown in the figure. The tension in line ABAD is 82 lb. Determine the moment about C of the resultant force RA exerted on the davit at […]

PROBLEM 3.142* (Continued) Substituting ? 160 ( 42 18 8 ) ( 3 ) 0 11 − + − ⋅ −− + =i j k ij k or ? 160 [( 42)( 1) (18)( 1) ( 8)(3)] 0 11 − […]

PROBLEM 3.19 Determine the moment about the origin O of the force F = 4i − 3j + 5k that acts at a Point A. Assume that the position vector of A is (a) r = 2i + 3j − […]

PROBLEM 3.113 A truss supports the loading shown. Determine the equivalent force acting on the truss and the point of intersection of its line of action with a line drawn through Points A and G. SOLUTION We have (240 lb)(cos70 […]

PROBLEM 3.78 Replace the two couples shown with a single equivalent couple, specifying its magnitude and the direction of its axis. SOLUTION Replace the couple in the ABCD plane with two couples P and Q shown: 160 mm (50 N) […]

Copyright © McGraw–Hill Education. Permission required for reproduction or display. PROBLEM 3.96 To keep a door closed, a wooden stick is wedged between the floor and the doorknob. The stick exerts at B a 175–N force directed along line AB. […]

PROBLEM 3.39 Knowing that the tension in cable AC is 280 lb, determine (a) the angle between cable AC and the boom AB, (b) the projection on AB of the force exerted by cable AC at point A. SOLUTION (a) […]

PROBLEM 4.68 (Continued) Force Triangle Law of sines: 150 lb sin 29.745 sin116.565 sin 33.690 CD   270.42 lb, 167.704 lb C D   270 lbC 56.3 ; 167.7 lbD26.6  Copyright © McGraw-Hill Education. Permission required for […]

PROBLEM 4.35 Bar AC supports two 400-N loads as shown. Rollers at A and C rest against frictionless surfaces and a cable BD is attached at B. Determine (a) the tension in cable BD, (b) the reaction at A, (c) […]

CHAPTER 4 PROBLEM 4.1 A gardener uses a 60-N wheelbarrow to transport a 250-N bag of fertilizer. What force must she exert on each handle? SOLUTION Free-Body Diagram:   0: (2 )(1 m) (60 N)(0.15 m) (250 N)(0.3 m) […]

PROBLEM 4.134 (Continued) // (0.5 m) ; (1 m) ; (268 N) BA CA ririPj To eliminate the reactions at A and D, we shall write // / 0: ( ) ( ) ( ) 0 AD AD B A […]

PROBLEM 4.85 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   30, determine (a) the angle  that the […]

PROBLEM 4.124 Solve Problem 4.123, assuming that the 1.8- kN load is applied at C. PROBLEM 4.123 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 […]

PROBLEM 4.53 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 […]

PROBLEM 4.148 Determine the reactions at A and B when a  150 mm. SOLUTION Free-Body Diagram: Force triangle 80 mm 80 mm tan 150 mm 28.072 a     320 N sin 28.072 A 680 NA28.1  […]

PROBLEM 4.113 (Continued) 0.90 0.88182(19.6203 N) 0; 19.2240 N xx AA  j: 0.90 44.145 0.180(19.6203 N) 0; 45.123 N yy AA i: 19.62 N CD F (19.22N) (45.1 N)  Aij  0: cos11.5370 0 19.2240 19.6203cos11.5370 0 0 […]

PROBLEM 4.19 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. SOLUTION At B: 0.18 m 0.24 m […]

PROBLEM 5.136 (Continued) Then 50 30 00 11 1 44550 EL x x dV x z dx dz      30 2 50 32 00 50 0 50 2 0 4 19 650 42 10937.5 ft zz […]

PROBLEM 5.66 For the beam and loading shown, determine (a) the magnitude and location of the resultant of the distributed load, (b) the reactions at the beam supports. SOLUTION I II 1 ( ) (400 N/m) (6 m) 2 1200 […]

PROBLEM 5.83 The base of a dam for a lake is designed to resist up to 120 percent of the horizontal force of the water. After construction, it is found that silt (that is equivalent to a liquid of density […]

PROBLEM 5.113 (Continued) 2 ,mmA ,mm x ,mm y 3 ,mmxA 3 ,mmyA 1 (74)(60) 4440 0 43 0 190,920 2 565.49 2.1803 2.1803 1233 1233 3 (30)(60) 1800 21 0 37,800 0 4 565.49 39.820 2.1803 22,518 1233 5 […]

CHAPTER 5 PROBLEM 5.1 Locate the centroid of the plane area shown. SOLUTION Area 1: Rectangle 72 mm by 45 mm. Area 2: Triangle b = 27 mm, h = 45 mm. 2 ,mmA ,mm x ,mm y 3 ,mmxA […]

PROBLEM 5.98 (Continued) (b) ?when 0.4 hYa a Substituting into Eq. (1) 2 3 (0.4)4 4 8 hh aa aa                or 2 33.20.80 hh aa […]

PROBLEM 5.128* Locate the centroid of the volume generated by revolving the portion of the sine curve shown about the x-axis. SOLUTION First, note that symmetry implies 0y  0z  Choose as the element of volume a disk of […]

PROBLEM 5.48* Determine by direct integration the centroid of the area shown. SOLUTION We have 22 cos cos 33 22 sin sin 33 EL EL xr ae yr ae       and 22 11 ()( ) […]

PROBLEM 5.18 Determine the x coordinate of the centroid of the trapezoid shown in terms of h1, h2, and a. SOLUTION Area 1: A x x A 1 1 1 2ha 1 3a 2 1 1 6ha 2 2 1 […]

PROBLEM 5.35 Determine by direct integration the centroid of the area shown. Express your answer in terms of a and h. SOLUTION At (, ),ah 2 1 :yhka or 2 h ka  2 :yhma or h ma  Now […]

PROBLEM 6.10 (Continued) Free body: Joint B:  11 0: 7.07 0 22 yBD FF   7.07 kN BD FT   11 0: 5 (7.07) 7.07 0 22 xBA FF     5.00 kN BA FC […]

CHAPTER 6 PROBLEM 6.1 Using the method of joints, determine the force in each member of the truss shown. State whether each member is in tension or compression. SOLUTION Free body: Entire truss: 0: 0 0 yy y FB  […]

PROBLEM 6.45 Determine the force in members BD and CD of the truss shown. SOLUTION 45 kipsH  We pass a section through members BD, CD, and CE and use the free body shown. 0: (7.5 ft) (27 kips)(10 ft) […]

PROBLEM 6.78 Determine the components of all forces acting on member ABCD of the assembly shown. SOLUTION Free body: Entire assembly: 0: (6 in.) (120 lb)(4 in.) 0 B MD   80.0 lb D  0: 120 lb 0 […]

PROBLEM 6.65 The diagonal members in the center panels of the power transmission line tower shown are very slender and can act only in tension; such members are known as counters. For the given loading, determine (a) which of the […]

PROBLEM 6.91 Knowing that each pulley has a radius of 250 mm, determine the components of the reactions at D and E. SOLUTION Free body: Entire assembly: 0: (4.8 kN)(4.25 m) (1.5 m) 0 Ex MD   13.60 kN […]

PROBLEM 6.164 Using the method of joints, determine the force in each member of the truss shown. State whether each member is in tension or compression. SOLUTION Reactions: 0: 16 kN Cx M A 0: 9 kN yy F A […]

PROBLEM 6.21 Determine the force in each of the members located to the left of FG for the scissors roof truss shown. State whether each member is in tension or compression. SOLUTION Free Body: Truss: 0: 0 xx F A […]

PROBLEM 6.118 (Continued) Member AFB: 0: 0 y FFABP  80 33 EE FP           3FP E (3) 0: ( ) (3 ) 0 A MFaBa   8 (3)() (3)0 […]

PROBLEM 6.151 Since the brace shown must remain in position even when the magnitude of P is very small, a single safety spring is attached at D and E. The spring DE has a constant of 50 lb/in. and an […]

PROBLEM 6.104 Solve Problem 6.103 assuming that the 360-lb load has been removed. PROBLEM 6.103 For the frame and loading shown, determine the components of all forces acting on member ABD. SOLUTION Free body diagram of entire frame. 0: (12 […]

PROBLEM 6.33 For the given loading, determine the zero-force members in each of the two trusses shown. SOLUTION Truss (a): Note: Reaction at F is vertical (0). x F Joint :G 0,F 0 DG F  Joint :D 0,F 0 […]

PROBLEM 6.133 The Whitworth mechanism shown is used to produce a quick-return motion of Point D. The block at B is pinned to the crank AB and is free to slide in a slot cut in member CD. Determine the […]

PROBLEM 6.174 A couple M of magnitude 1.5 kN  m is applied to the crank of the engine system shown. For each of the two positions shown, determine the force P required to hold the system in equilibrium. SOLUTION […]

PROBLEM 7.135 A counterweight D is attached to a cable that passes over a small pulley at A and is attached to a support at B. Knowing that L= 45 ft and h= 15 ft, determine (a) the length of […]

PROBLEM 7.100 Determine (a) the distance dC for which portion BC of the cable is horizontal, (b) the corresponding components of the reaction at E. SOLUTION Free body: Portion CDE 0: 2(2 kips) 0 4 kips yy y FE EΣ= […]

CHAPTER 7 PROBLEM 7.1 Determine the internal forces (axial force, shearing force, and bending moment) at Point J of the structure indicated. Frame and loading of Problem 6.76. SOLUTION From Problem 6.76: 720 lb x=C 140 lb y =C Copyright […]

PROBLEM 7.151* A cable has a mass per unit length of 3 kg/m and is supported as shown. Knowing that the span L is 6 m, determine the two values of the sag h for which the maximum tension is […]

PROBLEM 7.68 Using the method of Section 7.6, solve Problem 7.34. PROBLEM 7.34 For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute values of the shear and bending moment. SOLUTION Free […]

PROBLEM 7.43 Assuming the upward reaction of the ground on beam AB to be uniformly distributed and knowing that P =wa, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute values of the shear and bending moment. […]

PROBLEM 7.54 Solve Problem 7.53 when 60 . θ = ° PROBLEM 7.53 Two small channel sections DF and EH have been welded to the uniform beam AB of weight W 3 kN= to form the rigid structural member shown. […]

PROBLEM 7.87 For the beam and loading shown, (a) write the equations of the shear and bending-moment curves, (b) determine the magnitude and location of the maximum bending moment. SOLUTION (a) We check that beam is in equilibrium ( ) […]

PROBLEM 7.116 Cable ACB supports a load uniformly distributed along the horizontal as shown. The lowest Point C is located 9 m to the right of A. Determine (a) the vertical distance a, (b) the length of the cable, (c) […]

PROBLEM 7.16 Knowing that the radius of each pulley is 200 mm and neglecting friction, determine the internal forces at Point K of the frame shown. SOLUTION Free body: frame and pulleys 0: (1.8 m) (360 N)(0.2 m) (360 N)(2.6 […]

PROBLEM 7.30 For the beam and loading shown, (a) draw the shear and bending- moment diagrams, (b) determine the maximum absolute values of the shear and bending moment. SOLUTION Copyright © McGraw–Hill Education. Permission required for reproduction or display. 2 […]

PROBLEM 8.127 (Continued) Eq. (3): 17.5056 ln 4.9742 rad 2 1.3225 4.9742 s    0.2659  Eq. (4): sin 75 7.5056 cos 75 0.96953 7.2468 s       0.1333  We choose the larger […]

PROBLEM 8.15 A uniform crate with a massof 30 kg must be moved up along the 15° incline without tipping. Knowing that force P is horizontal, determine (a) the largest allowable coefficient of static friction between the crate and the […]

PROBLEM 8.33 A pipe of diameter 60 mm is gripped by the stillson wrench shown. Portions AB and DE of the wrench are rigidly attached to each other, and portion CF is connected by a pin at D. If the […]

PROBLEM 8.138 The hydraulic cylinder shown exerts a force of 3 kN directed to the right on Point B and to the left on Point E. Determine the magnitude of the couple M required to rotate the drum clockwise at […]

PROBLEM 8.75 The ends of two fixed rods A and B are each made in the form of a single-threaded screw of mean radius 6 mm and pitch 2 mm. Rod A has a right-handed thread and rod B has […]

PROBLEM 8.46 Two slender rods of negligible weight are pin-connected at C and attached to blocks A and B, each of weight W. Knowing that 80    and that the coefficient of static friction between the blocks and […]

PROBLEM 8.60 The spring of the door latch has a constant of 1.8 lb/in. and in the position shown exerts a 0.6-lb force on the bolt. The coefficient of static friction between the bolt and the strike plate is 0.40; […]

PROBLEM 8.114 Solve Problem 8.113 assuming that the belt is looped around the pulleys in a figure eight. PROBLEM 8.113 A flat belt is used to transmit a couple from pulley A to pulley B. The radius of each pulley […]

CHAPTER 8 PROBLEM 8.1 Determine whether the block shown is in equilibrium and find the magnitude and direction of the friction force whenP 150 N. SOLUTION Assume equilibrium: 0: (500 N)sin 20 (150 N) cos 20 0 x FF  […]

PROBLEM 8.95* Assuming that bearings wear out as indicated in Problem 8.94, show that the magnitude M of the couple required to overcome the frictional resistance of a worn-out collar bearing is 1 12 2 () k MPRR   […]

PROBLEM 9.115 A piece of thin, uniform sheet metal is cut to form the machine component shown. Denoting the mass of the component by m , determine its mass moment of inertia with respect to ( a ) the x […]

PROBLEM 9.60* The panel shown forms the end of a trough that is filled with water to the line AA. Referring to section 9.2, determine the depth of the point of application of the resultant of the hydrostatic forces acting […]

PROBLEM 9.75 Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to the centroidal x and y axes. SOLUTION We have 123 ()() () xy xy xy xy II I I Now symmetry implies […]

PROBLEM 9.46 Determine the polar moment of inertia of the area shown with respect to (a) Point O, (b) the centroid of the area. SOLUTION Determination of centroid C of entire section: Section Area, in2 ,in.x 3 ,inxA 1 2 […]

PROBLEM 9.169 Determine the mass moment of inertia of the machine component of Problems 9.136 and 9.155 with respect to the axis through the origin characterized by the unit vector (4 8 )/9.  λijk SOLUTION From the solutions to […]

PROBLEM 9.31 Determine the moment of inertia and the radius of gyration of the shaded area with respect to the x axis. SOLUTION First note that 123 2 2 2 [(24)(6) (8)(48) (48)(6)] mm (144 384 288) mm 816 mm […]

PROBLEM 9.138 A section of sheet steel 0.03 in. thick is cut and bent into the sheet metal machine component shown. Determine the mass moment of inertia of the component with respect to each of the coordinate axes. (The specific […]

PROBLEM 9.19 (Continued) Find: and xx Ik We have 33 21 3 33 3 11 12 (2) sin 33 3 2 8(2)sin 32 x h dI y y dx x a h x dx aa hxa x a a  […]

PROBLEM 9.180 For the component described in Problem 9.165, determine (a) the principal mass moments of inertia at the origin, (b) the principal axes of inertia at the origin. Sketch the body and show the orientation of the principal axes […]

PROBLEM 9.127 (Continued) and 22 22 22 2 62 2 2 11 1ft (769.80) 1 10 lb s /ft in 82 144 in              92 62 (84.628 62.191 […]

PROBLEM 9.146 (Continued) 24 35 12345 2 32 2 () (), () () () () () () () 1 ft [(8.5857 10 lb s /ft)(16 in.) ] 12 in. yy yy yy y y y y II II II I […]

PROBLEM 9.101 Using Mohr’s circle, determine for the area indicated the orientation of the principal centroidal axes and the corresponding values of the moments of inertia. Area of Problem 9.74. SOLUTION From Problem 9.83: 4 4 0.390 in 1.09 in […]

CHAPTER 9 PROBLEM 9.1 Determine by direct integration the moment of inertia of the shaded area with respect to the y axis. SOLUTION At  2 0, : 0xybbka  2 b ka  then  2 2 ; b […]

PROBLEM 9.185 Determine by direct integration the moments of inertia of the shaded area with respect to the x and y axes. SOLUTION 33456 3456 0 34 5 6 7 3456 0 33 64 33 3 64 1 3 1 […]

PROBLEM 9.158 Thin aluminum wire of uniform diameter is used to form the figure shown. Denoting by m the mass per unit length of the wire, determine the mass products of inertia I xy , I yz , and I […]

PROBLEM 9.91 Using Mohr’s circle, determine for the quarter ellipse of Problem 9.67 the moments of inertia and the product of inertia with respect to new axes obtained by rotating the x and y axes about O (a) through 45 […]