Archives: Solution Manual

Problem 10.55 The cable supports a railway bridge between two tunnels. The distributed load is wD 1 MN/m, and hD40 m. (a) What is the maximum tension in the cable? (b) What is the length of the cable? 36 m […]

Problem 9.145 The 20-lb homogenous object is supported at Aand B. The distance hD4 in, friction can be neglected at B, and the coefficient of static friction at Ais 0.4. Determine the largest force Fthat can be exerted without causing […]

Problem 9.122* The “Morse taper” is used to support the workpiece on a machinist’s lathe. The taper is driven into the spindle and is held in place by friction. If the spindle exerts a uniform pressure pD15 psi on the […]

Problem 9.92 Member BE of the frame has a turn- buckle. (See Problem 9.90.) The threads have pitch pD 1 mm, their mean radius is rD6 mm, and the coeffi– cient of static friction between the threads and the mating […]

Problem 9.61 The direction cosines of the crane’s cable are cos xD0.558,cos yD0.766,cos zD 0.260. The yaxis is vertical. The stationary caisson to which the cable is attached weights 2000 lb and rests on horizontal ground. If the coefficient of […]

Problem 9.34 The coefficient of static friction bet- ween the blades of the shears and the object they are gripping is 0.36. What is the largest value of the angle ˛for which the object will not slip out? Neglect the […]

Problem 9.1 In Active Example 9.1, suppose that the coefficient of static friction between the 180-lb crate and the ramp is sD0.3. What is the magnitude of the smallest horizontal force the rope must exert on the crate to prevent […]

Problem 8.136 The thick plate consists of steel of density D15 slug/ft3. Determine its moment of inertia about the zaxis. 4 in 2 in 2 in x yy z Solution: Divide the object into three parts: Part (1) the rectangle […]

Problem 8.115 Determine the moment of inertia of the bar in Problem 8.114 about the z0axis through its center of mass. Solution: In the solution of Problem 8.114, it is shown that the Problem 8.116 The rocket is used for […]

Problem 8.83 If the beam in Fig. a is subjected to couples of magnitude Mabout the xaxis (Fig. b), the beam’s longitudinal axis bends into a circular are whose radius Ris given by RDEIx M, where Ixis the moment of […]

Problem 8.48 Determine JOand kO. Solution: For the rectangle, JO1D6.656 ð107mm4 A1Dbh D9600 mm2 J0 O2D2.513 ð105mm2 120 mm x x′ A2 For the circular cutout about x0y0 J0 O2DIx02CIy0 2D1 4R4C1 4R4 J0 O2D1.257 ð105C1.257 ð105mm4 (h) 80 mm […]

Problem 8.1 Use the method described in Active Example 8.1 to determine IYand kyfor the rectangular x 0.6 m 30.4m 0.2mD0.0416 m4 The radius of gyration about the yaxis is kyDIy AD0.0416 m4 (0.4 m) (0.6 m) D0.416 m 0.4 […]

Problem 7.103 The mass of the bar per unit length is 2 kg/m. Choose the dimension bso that part BC of the suspended bar is horizontal. What is the dimension b, and what are the resulting reactions on the bar […]

Problem 7.66 In Example 7.9, determine the ycoor- dinate of the centroid of the line. x y y ⫽ x2 (1, 1) L (1, 1) dy x y dL Solution: The expression derived in Example 7.9 for the element dL […]

Problem 7.38 If the cross-sectional area of the beam shown in Problem 7.37 is 8400 mm2and the ycoordi- nate of the centroid of the area is yD90 mm, what are the dimensions band h? Solution: From the solution to Problem […]

Problem 7.1 In Active Example 7.1, Suppose that the triangular area is oriented as shown. Use integration to determine the xand ycoordinates of its centroid. (Notice b ydA Solution: The height of the vertical strip is h⊲h/b⊳ x so the […]

Problem 7.124 Determine the reactions on member ABCD at Aand D. AF B C DE 2 kN/m 1 m 1 m 1 m 1 m 1 m 2 kN/m Solution: First, replace the distributed forces with equivalent concentrated forces, then […]

Problem 6.124 The truss supports a 400-N load at G. Determine the axial forces in members AC,CD, and CF.400 N 300 mm B D F H G ECA 300 mm300 mm300 mm 600 mm from which AyD400 N. The method […]

6.69 (Continued) Carry out the indicated operations on the moments to obtain the vectors defining the moments:    0.4391 0.1901 0.8781  ijk    DjTADj⊲0.7605i0.4391jC0.4753⊳ DjTADj⊲iuADx CjuADy CjuADz ⊳ rAðTAF DjTAFj     ij […]

Problem 6.111 The four-bar linkage operates the forks of a fork lift truck. The force supported by the forks is WD8 kN. Determine the reactions on member CDE. 0.7 m 0.15 m 0.2 m 0.15 m 0.2 m 0.2 m […]

Problem 6.89 The woman using the exercise machine is holding the 80-lb weight stationary in the position shown. What are the reactions at the built-in support E and the pin support F?(Aand Care pinned connections.) EF 80 lb A B […]

Problem 6.47 The Howe truss helps support a roof. Model the supports at Aand Gas roller supports. (a) Use the method of joints to determine the axial force in member BI. (b) Use the method of sections to determine the […]

Problem 6.22 The Warren truss supporting the walkway is designed to support vertical 50-kN loads at B,D,F, and H. If the truss is subjected to these loads, what are the resulting axial forces in members BC,CD, and CE? 6 m6 […]

Problem 6.1 In Active Example 6.1, suppose that in addition to the 2-kN downward force acting at point D, a 2-kN downward force acts at point C. Draw a sketch of the truss showing the new loading. Determine the axial […]

Problem 5.61 The dimensions aD2 m and bD1m. The couple MD2400 N-m. The spring constant is kD 6000 N/m, and the spring would be unstretched if hD0. The system is in equilibrium when hD2 m and the beam is horizontal. […]

Problem 5.32 In a measure to decrease costs, the manufacturer of the fan described in Problem 5.31 proposes to support the fan with three equally spaced legs instead of four. An engineer is assigned to analyze the safety implications of […]

Problem 5.87 The force Facting on the boom ABC at Cpoints in the direction of the unit vector 0.512i 0.384jC0.768kand its magnitude is 8 kN. The boom is supported by a ball and socket at Aand the cables BD and […]

Problem 5.1 In Active Example 5.1, suppose that the beam is subjected to a 6kN-m counterclockwise couple at the right end in addition to the 4-kN downward force. Draw a sketch of the beam showing its new loading. Draw the […]

Problem 5.129 The hydraulic piston exerts a hori- zontal force at Bto support the weight WD1500 lb of the bucket of the excavator. Determine the magnitude of the force the hydraulic piston must exert. (The vector sum of the forces […]

Problem 5.109 The rocket launcher is supported by the hydraulic jack DE and the bearings Aand B. The bearings lie on the xaxis and support shafts parallel to the xaxis. The hydraulic cylinder DE exerts a force on the launcher […]

Problem 4.146 The system is in equilibrium. If you represent the forces FAB and FAC by a force Facting at Aand a couple M, what are Fand M? A A BC 60°40° y FAB FAC x Solution: The sum of […]

Problem 4.174 A plumber exerts the two forces shown to loosen a pipe. (a) What total moment does he exert about the axis of the pipe? (b) If you represent the two forces by a force Facting at Oand a […]

Problem 4.75 The 200-kg slider at Ais held in place on the smooth vertical bar by the cable AB. Determine the moment about the bottom of the bar (point Cwith coordinates xD2m,yDzD0) due to the force exerted on the slider […]

Problem 4.107* The yaxis points upward. The weight of the 4-kg rectangular plate acts at the midpoint Gof the plate. The sum of the moments about the straight line through the supports Aand Bdue to the weight of the plate […]

Problem 4.37 The cable AB exerts a 290-kN force on the building crane’s boom at B. The cable AC exerts a 148-kN force on the boom at C. Determine the sum of the moments about Pdue to the forces the […]

Problem 4.1 In Active Example 4.1, the 40-kN force points 30°above the horizontal. Suppose that the force points 30°below the horizontal instead. Draw a sketch of the beam with the new orientation of the force. What is the moment of […]

Problem 3.80 The cable AB keeps the 8-kg collar Ain place on the smooth bar CD. The yaxis points upward. What is the tension in the cable? 0.4 m 0.15 m y BC Solution: We develop the following position vectors […]

Problem 3.59 Problem 3.58 shows pulley systems containing one, two, and three pulleys. The number of pulleys in the type of system shown could obviously be Solution: By extrapolation of the previous problem (a) TDW Problem 3.60 A 14,000-kg airplane […]

cables. Cable AC is equipped with a turnbuckle so that its tension can be adjusted and a strain gauge that allows its tension to be measured. If the tension in cable AC is 40 N, what are the tensions in […]

Problem 3.1 In Active Example 3.1, suppose that the angle between the ramp supporting the car is increased from 20°to 30°. Draw the free-body diagram of the car showing the new geometry. Suppose that the cable from Ato Bmust exert […]

Problem 2.125 Two vectors UD3iC2jand VD2i C4j. Solution: Use Eq. (2.34) and expand into 2 by 2 determinants.   ijk   Ck⊲⊲3⊳⊲4⊳⊲2⊳⊲2⊳⊳ D8k VðUD      ijk 240 320      Di⊲⊲4⊳⊲0⊳⊲2⊳⊲0⊳⊳ […]

Problem 2.85 Determine the direction cosines of the vectors FAand FB. y z 40⬚ 50⬚ 30⬚ FAD⊲82.2iC90.0jC68.9k⊳lb FBD100 lb⊲[cos 60°sin 30°]iC[sin 60°]jC[cos 60°cos 30°]k⊳ FBD⊲25.0iC86.6jC43.3k⊳lb The direction cosines for FAare cos xD82.2 lb 140 lb D0.587,cos yD90.0 lb 140 lb […]

Problem 2.44 The rope ABC exerts forces FBA and FBC on the block at B. Their magnitudes are equal: jFBAjDjFBC j. The magnitude of the total force exerted on the block at Bby the rope is jFBA CFBC jD920 N. […]

Problem 2.1 In Active Example 2.1, suppose that the vectors Uand Vare reoriented as shown. The vector Vis vertical. The magnitudes are jUjD8 and jVjD3. Graphically determine the magnitude of the vector UC2V. V U 45⬚ Problem 2.2 Suppose that […]

Problem 1.1 The value of is 3.14159265… If Cis Solution: CD2r )r CD1 2D0.159154943. To four significant digits we have r CD0.1592 Problem 1.2 The base of natural logarithms is eD 2.718281828 … (a) Express eto five significant digits. (b) […]