Archives: Solution Manual

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 9.169 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 9.158 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 9.146 (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 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 8.114 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 […]

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 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 8.60 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 8.75 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 8.33 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 8.15 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 […]

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 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 7.135 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 7.116 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 7.100 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= […]

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 7.43 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 7.30 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 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 […]

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 7.54 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 7.68 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 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 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 6.151 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 6.133 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 6.118 (Continued) Member AFB: 0: 0 y FFABP  80 33 EE FP           3FP E (3) 0: ( ) (3 ) 0 A MFaBa   8 (3)() (3)0 […]

PROBLEM 6.104 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 6.78 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 6.45 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 6.33 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 6.91 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 6.21 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 6.10 (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 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 5.128* 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 5.113 (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 […]

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 5.83 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 5.66 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 5.48* 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 5.35 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 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 […]

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 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 […]