Archives: Solution Manual

PROBLEM 9.96 Using Mohr’s circle, determine the moments of inertia and the product of inertia of the L152 102 12.7-mm angle cross section of Problem 9.78 with respect to new centroidal axes obtained by rotating the x and y axes […]

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 […]

PROBLEM 9.82 Determine the moments of inertia and the product of inertia of the area of Problem 9.75 with respect to new centroidal axes obtained by rotating the x and y axes 45 clockwise. SOLUTION From Problem 9.75: 4 471,040 […]

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 9.66* (Continued) : yP M xP xdP  Now (sin) sin x dP x y dA xydA      (sin) x y I   (Equation 9.12) Then (sin) Pxy x PI   or (sin) […]

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 9.53 A channel and a plate are welded together as shown to form a section that is symmetrical with respect to the y axis. Determine the moments of inertia of the combined section with respect to its centroidal x […]

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 9.40 Knowing that the shaded area is equal to 6000 mm2 and that its moment of inertia with respect to AA is 18  106 mm4, determine its moment of inertia with respect to BB for d1 = 50 […]

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 9.24 (Continued) Now 44 2 3 16 3 4 64 Pxy JII r           44 31.15545 316 rr       4 or 1.155 P J r […]

PROBLEM 9.19 (Continued) Find: and xx Ik We have 33 21 333 3 11 12 (2) sin 33 3 2 8(2)sin 32 xh dI y y dx x a h x dx aa hxa x a a    […]

PROBLEM 9.10 Determine by direct integration the moment of inertia of the shaded area with respect to the x axis. SOLUTION At 0, :xyb (1 0)bc or cb At ,0:xay 1/2 0(1 )bka 1/2 1 or ka  Then 1/2 […]

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 8.F1 Knowing that the coefficient of friction between the 25-kg block and the incline is  s = 0.25, draw the free-body diagram needed to determine both the smallest value of P required to start the block moving up […]

PROBLEM 8.136 (Continued) 0: (32 in.) (12 in.) (24 in.) 0 AB MPWN    8 3 6 0 0.25 0.3 P PW P W   tip ( 0.25 OK)PWP 0.25(120 lb)P or 30.0 lb P  (c) […]

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 8.121 A cable is placed around three parallel pipes. Two of the pipes are fixed and do not rotate; the third pipe is slowly rotated. Knowing that the coefficients of friction are 0.25 s   and 0.20, k […]

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 […]

Copyright © McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 8.104 A hawser is wrapped two full turns around a bollard. By exerting an 80-lb force on the free end of the hawser, a dockworker can resist a force […]

Copyright © McGraw-Hill Education. Permission required for reproduction or display. 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 […]

Copyright © McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 8.85 A scooter is to be designed to roll down a 2 percent slope at a constant speed. Assuming that the coefficient of kinetic friction between the 25-mm-diameter axles […]

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 8.68 Derive the following formulas relating the load W and the force P exerted on the handle of the jack discussed in Section 8.6. (a) P (Wr/a) tan (    s ), to raise the load; (b) […]

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 8.52 The elevation of the end of the steel beam supported by a concrete floor is adjusted by means of the steel wedges E and F. The base plate CD has been welded to the lower flange of the […]

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 8.39 Two rods are connected by a collar at B. A couple M A with a magnitude of 15 N·m is applied to rod AB. Knowing that the coefficient of static friction between the collar and the rod is […]

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 8.24 End A of a slender, uniform rod of length L and weight W bears on a surface as shown, while end B is supported by a cord BC. Knowing that the coefficients of friction are 0.40 s  […]

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 8.8 Considering only values of  less than 90, determine the smallest value of  required to start the block moving to the right when (a) 75 lb,W  (b) 100 lb.W SOLUTION FBD block (Motion impending): 1 tan […]

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 7.161 For the beam shown, draw the shear and bending–moment diagrams, and determine the magnitude and location of the maximum absolute value of the bending moment, knowing that (a) M = 0, (b) M = 24 kip ∙ ft. […]

PROBLEM 7.152* Determine the sag–to–span ratio for which the maximum tension in the cable is equal to the total weight of the entire cable AB. SOLUTION ( ) max 1 2 2 2 cosh 2 sinh 22 1 tanh 22 […]

PROBLEM 7.145 To the left of Point B the long cable ABDE rests on the rough horizontal surface shown. Knowing that the mass per unit length of the cable is 2 kg/m, determine the force F when a= 3.6 m. […]

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 7.125* Using the property indicated in Problem 7.124, determine the curve assumed by a cable of span L and sag h carrying a distributed load w=w0 cos ( π x/L), where x is measured from mid–span. Also determine the […]

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 7.108 The total mass of cable ACB is 20 kg. Assuming that the mass of the cable is distributed uniformly along the horizontal, determine (a) the sag h, (b) the slope of the cable at A. SOLUTION Free body: […]

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 7.92* (Continued) (b) Load diagram Shear diagram At A: 2.26 kips A VA = = + To determine Point G where 0,V= we write GC VV w µ −=− 0 (1.22 kips) (0.25 kip/ft) µ −=− 4.88 ft µ […]

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 7.78 For the beam and loading shown, (a) draw the shear and bending– moment diagrams, (b) determine the magnitude and location of the maximum absolute value of the bending moment. SOLUTION 0: (8.75)(1.75) (2.5) 0 A MBΣ= − = […]

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 7.59 (Continued) We set 2 2 22 1 11 111 | | | |: 2 82 282 AC M M wa wL wLa wa wL wLa= −=− +=− 22 0.25 0a La L+− = 22 22 max 11 ( […]

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 7.48 (Continued) Copyright © McGraw–Hill Education. Permission required for reproduction or display. For 3m:x= 0,V= 9.00 kN mM=−⋅  For 4.5 m:x= 6 kN, D V= + 4.50 kN m D M=−⋅  At B: 0 BB VM= = […]

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 7.37 (Continued) max Copyright © McGraw–Hill Education. Permission required for reproduction or display. Just to the right of E: 4 0: 4.5 0 y FVΣ= − = 44.5 kipsV= +  44 0: (4.5)2 0MM Σ= − − = […]