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1 ink full download: Solution Manual for Mechanics of Materials 7th Edition by eer Johnston DeWolf and Mazurek -of-materials-7th-edition-by-beer-johnston-dewolf-and-mazurek/ ROEM.1 nylon thread is subjected to a 8.5-N tension force. Knowing that E. Ga and that the length of the thread increases by 1.1%, determine (a) the diameter of the thread, (b) the stress in the thread. (a) Strain: Stress: rea: Diameter: E (. 10 )(0.011). 10 a m (4)( ) d m d 0.54 mm (b) Stress:. Ma RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 9

2 ROEM. 4.8-ft-long steel wire of 1 -in.-diameter is subjected to a 750-lb tensile load. Knowing that E = psi, determine (a) the elongation of the wire, (b) the corresponding normal stress. (a) Deformation: rea: d ; E 4 (0.5 in.) in 4 (750 lb)(4.8 ft 1 in./ft) ( in )(910 psi) (b) Stress: in in. (750lb) rea: ( in ) psi 15.8 ksi RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 94

3 ROEM. n 18-m-long steel wire of 5-mm diameter is to be used in the manufacture of a prestressed concrete beam. It is observed that the wire stretches 45 mm when a tensile force is applied. Knowing that E 00 Ga, determine (a) the magnitude of the force, (b) the corresponding normal stress in the wire. E (a), or E (b) with 1 1 (0.005) d m (0.045 m)( m )(00 10 N/m ) N 18 m N a m 9.8 kn 500 Ma RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 95

4 ROEM.4 Two gage marks are placed exactly 50 mm apart on a 1-mm-diameter aluminum rod with E = 7 Ga and an ultimate strength of 140 Ma. Knowing that the distance between the gage marks is 50.8 mm after a load is applied, determine (a) the stress in the rod, (b) the factor of safety. (a) mm 50 mm 0.8 mm mm 50 mm E 9 4 (7 10 a)( ) a 81.8 Ma (b) F.S. u 140 Ma Ma 1.71 F.S RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 9

5 ROEM.5 n aluminum pipe must not stretch more than 0.05 in. when it is subjected to a tensile load. Knowing that E psi and that the maximum allowable normal stress is 14 ksi, determine (a) the maximum allowable length of the pipe, (b) the required area of the pipe if the tensile load is 17.5 kips. (a) E Thus, E E ( ) (0.05) in. (b) Thus, in RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 97

6 ROEM. control rod made of yellow brass must not stretch more than mm when the tension in the wire is 4 kn. Knowing that E = 105 Ga and that the maximum allowable normal stress is 180 Ma, determine (a) the smallest diameter rod that should be used, (b) the corresponding maximum length of the rod. d (a) ; 4 Substituting, we have 4 d d 4 4(4 10 N) d ( a) d m d 5. mm (b) E; Substituting, we have E E 9 ( a)( 10 m) m ( a) RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 98

7 ROEM.7 steel control rod is 5.5 ft long and must not stretch more than 0.04 in. when a -kip tensile load is applied to it. Knowing that E 9 10 psi, determine (a) the smallest diameter rod that should be used, (b) the corresponding normal stress caused by the load. (000 lb) (5.51 in.) (a) : 0.04 in. E (910 psi) 1 d in 4 d 0.80 in. d 0.81 in. 000 lb (b) psi ksi in RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 99

8 ROEM.8 cast-iron tube is used to support a compressive load. Knowing that E psi and that the maximum allowable change in length is 0.05%, determine (a) the maximum normal stress in the tube, (b) the minimum wall thickness for a load of 100 lb if the outside diameter of the tube is.0 in. (a) E; E (10 10 psi)(0.0005) psi.50 ksi (b) 100 lb ; 0.4 in psi d d 4 4 di d o d o i 4(0.4 in ) i (.0 in.).1851 in in. 1 1 t ( do d i) (.0 in in.) t in. d i t RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 100

9 ROEM.9 4-m-long steel rod must not stretch more than mm and the normal stress must not exceed 150 Ma when the rod is subjected to a 10-kN axial load. Knowing that E 00 Ga, determine the required diameter of the rod. 4m 10 m, a 9 E a, N Stress: Deformation: N.7 10 m.7 mm a E (10 10 )(4).7 10 m.7 mm 9 E (00 10 )( 10 ) The larger value of governs:.7 mm 4 4(.7) d d 4 d 9.1 mm RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 101

10 ROEM.10 nylon thread is to be subjected to a 10-N tension. Knowing that E. Ga, that the maximum allowable normal stress is 40 Ma, and that the length of the thread must not increase by more than 1%, determine the required diameter of the thread. Stress criterion: 40 Ma a 10 N 10 N : 5010 m a d : d m 4 d 0.54 mm Elongation criterion: 1% 0.01 : E E / 10 N/. 10 a m / d m d 0.1 mm The required diameter is the larger value: d 0.1 mm RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 10

11 ROEM.11 block of 10-in. length and in. cross section is to support a centric compressive load. The material to be used is a bronze for which E psi. Determine the largest load that can be applied, knowing that the normal stress must not exceed 18 ksi and that the decrease in length of the block should be at most 0.1% of its original length. onsidering allowable stress, 18 ksi or 1810 psi ross-sectional area: (1.8 in.)(1. in.).880 in (18 10 psi)(.880 in ) lb 4 or kips onsidering allowable deformation, 0.1% or in. E E (.880 in )(14 10 psi)(0.001 in.) lb 4 or kips The smaller value for resulting from the required deformation criteria governs kips RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 10

12 ROEM.1 square yellow-brass bar must not stretch more than.5 mm when it is subjected to a tensile load. Knowing that E 105 Ga and that the allowable tensile strength is 180 Ma, determine (a) the maximum allowable length of the bar, (b) the required dimensions of the cross section if the tensile load is 40 kn a 4010 N 9 E a.5 10 m (a) (b) E E 9 E (10510 )(.510 ) m m. mm m a a. a mm RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 104

13 10 kips ROEM.1 7 in. D Rod D is made of steel ( E 9 10 psi) and is used to brace the axially compressed member. The maximum force that can be developed in member D is 0.0. If the stress must not exceed 18 ksi and the maximum change in length of D must not exceed times the length of, determine the smallest-diameter rod that can be used for member D. 7 in. 54 in. onsidering stress, F 0.0 (0.0)(10). kips. 10 lb D 18 ksi psi FD FD in 18 onsidering deformation, (0.001)(144) in. arger area governs. FD D FDD (. 10 )(54) 0.0 in E E (910 )(0.144) in 4 (4)( ) d d d 0.49 in. 4 RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 105

14 .5 m.5 m ROEM.14 The 4-mm-diameter cable is made of a steel with E 00 Ga. Knowing that the maximum stress in the cable must not exceed 190 Ma and that the elongation of the cable must not exceed mm, find the maximum load that can be applied as shown. 4.0 m Use bar as a free body m 4 M 0:.5 () F F onsidering allowable stress, a d (0.004) m 4 4 F F ( )(1.510 ).8810 N onsidering allowable elongation, 10 m 9 F E ( )(00 10 )( 10 ) F N E Smaller value governs. F N F (0.9509)( ) N kn RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 10

15 1.5-in. diameter 4 ft d ft ROEM.15 single axial load of magnitude = 15 kips is applied at end of the steel rod. Knowing that E = 0 10 psi, determine the diameter d of portion for which the deflection of point will be 0.05 in. Substituting, we have i E E E i i 4 ft 48 in.; ft in. d (1.5 in.) in lb 48 in. in in psi in in d 4 or d 4 d d 4( in ) 0.87 in. d 0.88 in. RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 107

16 ROEM.1 5 mm mm 8 mm 50 mm 50-mm-long aluminum tube ( E 70 Ga) of -mm outer diameter and 8-mm inner diameter can be closed at both ends by means of single-threaded screw-on covers of 1.5-mm pitch. With one cover screwed on tight, a solid brass rod ( E 105 Ga) of 5-mm diameter is placed inside the tube and the second cover is screwed on. Since the rod is slightly longer than the tube, it is observed that the cover must be forced against the rod by rotating it one-quarter of a turn before it can be tightly closed. Determine (a) the average normal stress in the tube and in the rod, (b) the deformations of the tube and of the rod. (a) tube ( d d ) ( 8 ) 40.1 mm m 4 4 rod d (5) mm m 4 4 (0.50) (70 10 )( ) o i tube 9 Etube tube rod Erod rod (0.50) ( )( ) * 1 turn 1.5 mm 0.75 mm m 4 * * tube rod or tube rod N 9 ( )(10 ) a tube tube a rod rod Ma tube 55. Ma rod (b) 9 tube ( )( ) m tube 0.4 mm 9 rod ( )( ) m rod 0.15 mm RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 108

17 5 50 lb 0.4 in. D 5 50 lb 1 in. 1 in. 1. in. in. 1. in. ROEM.17 The specimen shown has been cut from a 1 -in.-thick sheet 4 of vinyl (E = psi) and is subjected to a 50-lb tensile load. Determine (a) the total deformation of the specimen, (b) the deformation of its central portion. (a) Total deformation: (50 lb)(1. in.) in. E ( psi)(1 in.)(0.5 in.) (50 lb)( in.) in. E ( psi)(0.4 in.)(0.5 in.) in. D D in in. (b) Deformation of portion : in. RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 109

18 ROEM.18 D 1 mm The brass tube ( E 105 Ga) has a cross-sectional area of 140 mm and is fitted with a plug at. The tube is attached at to a rigid plate that is itself attached at to the bottom of an aluminum cylinder ( E 7 Ga) with a cross-sectional area of 50 mm. The cylinder is then hung from a support at D. In order to close the cylinder, the plug must move down through 1 mm. Determine the force that must be applied to the cylinder. 75 mm Shortening of brass tube : E mm 0.7 m 140 mm m a (0.7) E ( )( ) engthening of aluminum cylinder D: 9 D D D 0.75 m 50 mm m E 7 10 a D (0.75) 9 D E (7 10 )(5010 ) Total deflection: D where m D D ( ) N 1.5 kn 9 RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 110

19 ROEM m 0-mm diameter oth portions of the rod are made of an aluminum for which E 70 Ga. Knowing that the magnitude of is 4 kn, determine (a) the value of Q so that the deflection at is zero, (b) the corresponding deflection of. 0.5 m Q 0-mm diameter (a) d 4 4 (0.00) m d 4 4 Force in member is tension. Elongation: (0.00) m (410 )(0.4) m 9 E (7010 )( ) Force in member is Q compression. Shortening: ( Q ) ( Q )(0.5) ( Q) 9 E (7010 )( ) For zero deflection at, ( Q) Q N Q N Q.8 kn (b) m mm RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 111

20 ROEM.0 The rod is made of an aluminum for which E 70 Ga. Knowing that kn and Q 4 kn, determine the deflection of (a) point, (b) point. 0.4 m 0-mm diameter 0.5 m Q 0-mm diameter d 4 4 d 4 4 (0.00) m (0.00) m 10 N Q N 0.4 m 0.5 m ( 10 )(0.4) m 9 E ( )(7010 ) ( 10 )(0.5) m 9 E ( )(7010 ) (a) (b) m m mm m mm or mm RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 11

21 8 kn ROEM.1 D.5 m For the steel truss ( E 00 Ga) and loading shown, determine the deformations of the members and D, knowing that their cross-sectional areas are 400 mm and 1800 mm, respectively. 4.0 m 4.0 m Statics: Reactions are 114 kn upward at and. Member D is a zero force member. Use joint as a free body. Member : F E m.5 Fy 0: 114 F F kn 4 Fx 0: FD F F D (4)( 15.10) 18.4 kn ( )(4.717) 9 (0010 )(40010 ) Member D: D m.11 mm FD E D D ( )(4.0) 9 (0010 )( ).0 10 m.0 mm D RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 11

22 0 kips ROEM. 8 ft 8 ft 0 kips 0 kips D E For the steel truss ( E 9 10 psi) and loading shown, determine the deformations of the members D and DE, knowing that their crosssectional areas are in and in, respectively. 8 ft F G 15 ft Free body: ortion of truss M 0 : F (15 ft) (0 kips)(8 ft) (0 kips)(1 ft) 0 F E D D 48.0 kips Free body: ortion E of truss F 0 : 0 kips 0 kips F 0 F x DE 0.0 kips DE D E ( lb)(8 1 in.) ( in )(9 10 psi) D in. DE E ( lb)(151 in.) ( in )(910 psi) DE in. RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 114

23 ft ft D E 5 ft ROEM. Members and are made of steel ( E 9 10 psi) with crosssectional areas of 0.80 in and 0.4 in, respectively. For the loading shown, determine the elongation of (a) member, (b) member. 8 kips 54 kips (a) ft 9.7 in. Use joint as a free body. 5 Fy 0: F F 4.74 kip lb (b) F E Use joint as a free body. ( )(9.7) (9 10 )(0.80) in. Fx 0: F F ()(4.74) F.0 kip.0 10 lb F E (.0 10 )(7) (9 10 )(0.4) in. RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 115

24 m ROEM.4 The steel frame ( E 00 Ga) shown has a diagonal brace D with an area of 190 mm. Determine the largest allowable load if the change in length of member D is not to exceed 1. mm. D 5 m F D D D D Use joint as a free body. F x 0: D 9 ED m, 190 mm m m, a FDD EDD 9 EDD D (00 10 )( )(1. 10 ) D N 5 FD (5)( ) F D N 50.4 kn RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 11

25 D 5 mm 150 mm E ROEM.5 ink D is made of brass ( E 105 Ga) and has a cross-sectional area of 40 mm. ink E is made of aluminum ( E 7 Ga) and has a crosssectional area of 00 mm. Knowing that they support rigid member, determine the maximum force that can be applied vertically at point if the deflection of is not to exceed 0.5 mm. 15 mm 5 mm Free body member : FD D ( )(0.5) 9 D E ( )(40 10 ) D E D FE E ( )(0.150) 9 E E (7 10 )(00 10 ) E M 0: F 0 F D D M 0: F 0 F E E Deformation Diagram: From the deformation diagram, pply displacement limit. Slope: m (0.15)( ) N kn RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 117

26 180 mm 0 mm F E ROEM. Members and DEF are joined with steel links (E 00 Ga). Each of the links is made of a pair of 5 5-mm plates. Determine the change in length of (a) member E, (b) member F. D 18 kn 40 mm 18 kn Free body diagram of Member : M 0: (0. m)(18 kn) (0.18 m) F 0 F.0 kn F F x 0: 18 kn F.0 kn 0 F E E 44.0 kn F rea for link made of two plates: (a) (0.05 m)(0.05 m) m E FE ( N)(0.40 m) 9 E (0010 a)( m ) m (b) F FF (.0 10 N)(0.40 m) 9 E (0010 a)( m ) m 0.00 mm E mm F RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 118

27 18 in. = 1 kip E D ROEM.7 Each of the links and D is made of aluminum ( E psi) and has a cross-sectional area of 0. in. Knowing that they support the rigid member, determine the deflection of point E. 10 in. in. Free body : D F (87.5)(18) in. E ( )(0.) FD D (1.5)(18) in. E ( )(0.) M 0: () F ()(1 10 ) 0 F 87.5 lb F 0: F 0 y F D 1.5 lb D Deformation diagram: Slope rad E E ()( ) in. E in. RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 119

28 D 4 in. 1.5 in. x 50 lb 1 in. E 1 1 in. ROEM.8 The length of the -in.-diameter steel wire D has been adjusted so that with no load applied, a gap of 1 in. exists between the end of the rigid 1 beam and a contact point E. Knowing that E 9 10 psi, determine where a 50-lb block should be placed on the beam in order to cause contact between and E. Rigid beam rotates through angle to close gap. oint moves downward. 1/ rad 0 D D D in. 4 4(.1510 ) in. d d in FDD E D Free body : For contact, F D E DD D (9 10 )( )( ) lb M 0: 4 F (50)(0 x ) 0 D (4)(00.18) 0 x x.985 in. x.99 in. RORIETRY MTERI. opyright 015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. 10

MECHANICS OF MATERIALS

MECHANICS OF MATERIALS Lecture Notes: Dr. Hussam A. Mohammed Al- Mussiab Technical College Ferdinand P. Beer, E. Russell Johnston, Jr., and John T. DeWolf Introduction Concept of Stress The main objective of the study of mechanics