Mechanics of Materials, 7th Edition
7th Edition
ISBN: 9780073398235
Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek
Publisher: McGraw-Hill Education
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Chapter 6.6, Problem 84P
(a)
To determine
The torque T that would cause the channel to twist in the same way.
(b)
To determine
The maximum shearing stress in the channel caused by the load P.
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3.46 The electric motor exerts a torque of 800 N · m on the steel shaft
ABCD when it is rotating at a constant speed. Design specifications
require that the diameter of the shaft be uniform from A to D and
that the angle of twist between A and D not exceed 1.5°. Knowing
that Tmas s 60 MPa and G = 77 GPa, determine the minimum
diameter shaft that can be used.
300 N- m
500 N- m
04 m
0.6 m
0.3 m
Fig. P3.46
3.38 The aluminum rod AB (G = 27 GPa) is bonded to the brass rod
BD (G = 39 GPa). Knowing that portion CD of the brass rod is
hollow and has an inner diameter of 40 mm, determine the angle
of twist at A.
60 mm
T = 1600 N m
36 mm
TA = S00 N - mn
250 mm
B
375 mm
A
400 mm
Fig. P3.38
5.86 The cast iron inverted T-section supports two concentrated loads of magnitude P. The working stresses are 48 MPa in tension, 140 MPa in compression, and 30 MPa in shear. (a) Show that the neutral axis of the cross section is located at d ¼ 48:75 mm and that the moment of inertia of the cross-sectional area about this axis is I ¼ 11:918 106 mm4. (b) Find the maximum allowable value of P.
Chapter 6 Solutions
Mechanics of Materials, 7th Edition
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Ch. 6.2 - 6.9 through 6.12 For beam and loading shown,...Ch. 6.2 - 6.9 through 6.12 For beam and loading shown,...Ch. 6.2 - 6.13 and 6.14 For a beam having the cross section...Ch. 6.2 - 6.13 and 6.14 For a beam having the cross section...Ch. 6.2 - For a timber beam having the cross section shown,...Ch. 6.2 - Two steel plates of 12 220-mm rectangular cross...Ch. 6.2 - Two W8 31 rolled sections may be welded at A and...Ch. 6.2 - For the beam and. loading shown, determine the...Ch. 6.2 - Fig. P6.19 6.19 A timber beam AB of length L and...Ch. 6.2 - A timber beam AB of Length L and rectangular cross...Ch. 6.2 - 6.21 and 6.22 For the beam and loading shown,...Ch. 6.2 - 6.21 and 6.22 For the beam and loading shown,...Ch. 6.2 - 6.23 and 6.24 For the beam and loading shown,...Ch. 6.2 - 6.23 and 6.24 For the beam and loading shown,...Ch. 6.2 - 6.25 through 6.28 A beam having the cross section...Ch. 6.2 - 6.25 through 6.28 A beam having the cross section...Ch. 6.2 - Prob. 27PCh. 6.2 - 6.25 through 6.28 A beam having the cross section...Ch. 6.5 - The built-up timber beam shown is subjected to a...Ch. 6.5 - The built-up beam shown is made by gluing together...Ch. 6.5 - The built-up beam was made by gluing together...Ch. 6.5 - Several wooden planks are glued together to form...Ch. 6.5 - The built-up wooden beam shown is subjected to a...Ch. 6.5 - Knowing that a W360 122 rolled-steel beam is...Ch. 6.5 - 6.35 and 6.36 An extruded aluminum beam has the...Ch. 6.5 - 6.35 and 6.36 An extruded aluminum beam has the...Ch. 6.5 - Knowing that a given vertical shear V causes a...Ch. 6.5 - The vertical shear is 1200 lb in a beam having the...Ch. 6.5 - The vertical shear is 1200 lb in a beam having the...Ch. 6.5 - 6.40 and 6.47 The extruded aluminum beam has a...Ch. 6.5 - Prob. 41PCh. 6.5 - Prob. 42PCh. 6.5 - Three planks are connected as shown by bolts of...Ch. 6.5 - A beam consists of three planks connected as shown...Ch. 6.5 - A beam consists of five planks of 1.5 6-in. cross...Ch. 6.5 - Four L102 102 9.5 steel angle shapes and a 12 ...Ch. 6.5 - A plate of 14-in. thickness is corrugated as shown...Ch. 6.5 - Prob. 48PCh. 6.5 - An extruded beam has the cross section shown and a...Ch. 6.5 - Prob. 50PCh. 6.5 - The design of a beam calls for connecting two...Ch. 6.5 - The cross section of an extruded beam is a hollow...Ch. 6.5 - Prob. 53PCh. 6.5 - Prob. 54PCh. 6.5 - Prob. 55PCh. 6.5 - 6.56 and 6.57 A composite beam is made by...Ch. 6.5 - 6.56 and 6.57 A composite beam is made by...Ch. 6.5 - Prob. 58PCh. 6.5 - Prob. 59PCh. 6.5 - Prob. 60PCh. 6.6 - 6.61 through 6.64 Determine the location of the...Ch. 6.6 - 6.61 through 6.64 Determine the location of the...Ch. 6.6 - 6.61 through 6.64 Determine the location of the...Ch. 6.6 - Prob. 64PCh. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.69 through 6.74 Determine the location of the...Ch. 6.6 - Prob. 70PCh. 6.6 - Prob. 71PCh. 6.6 - Prob. 72PCh. 6.6 - Prob. 73PCh. 6.6 - Prob. 74PCh. 6.6 - Prob. 75PCh. 6.6 - 6.75 and 6.76 A thin-walled beam has the cross...Ch. 6.6 - 6.77 and 6.78 A thin-walled beam of uniform...Ch. 6.6 - Prob. 78PCh. 6.6 - Prob. 79PCh. 6.6 - Prob. 80PCh. 6.6 - Prob. 81PCh. 6.6 - Prob. 82PCh. 6.6 - Prob. 83PCh. 6.6 - Prob. 84PCh. 6.6 - Prob. 85PCh. 6.6 - Solve Prob. 6.85, assuming that the thickness of...Ch. 6.6 - Prob. 87PCh. 6.6 - Prob. 88PCh. 6 - Three boards are nailed together to form the beam...Ch. 6 - For the beam and loading shown, consider section...Ch. 6 - For the wide-flange beam with the loading shown,...Ch. 6 - For the beam and loading shown, consider section...Ch. 6 - The built-up timber beam is subjected to a 1500-lb...Ch. 6 - Knowing that a given vertical shear V causes a...Ch. 6 - Three planks are connected as shown by bolts of...Ch. 6 - Three 1 18-in. steel plates are bolted to four L6...Ch. 6 - The composite beam shown is made by welding C200 ...Ch. 6 - Prob. 98RPCh. 6 - A thin-walled beam of uniform thickness has the...Ch. 6 - Determine the location of the shear center O of a...
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- 3.36 The torques shown are exerted on pulleys B, C, and D. Knowing that the entire shaft is made of aluminum (G = 27 GPa), deter- mine the angle of twist between (a) C and B, (b) D and B. 30 mm 30 mm 400 N- m GG 36 mm 900 N- m 36 mm 500 N. m B "0.6 m E. 0.5 m D m 0.5 Fig. P3.36arrow_forwardExercises: 1. The box wrench in Fig. 99 is used to tighten the bolt at A. If the wrench does not turn when the load is applied to the handle, determine the torque or moment applied to the bolt and the force of the wrench on the bolt. 300 mm 400 mm 60° 12 52'N 30 N Fig. 99 2. Determine the horizontal and vertical 750 lb components of reaction on the member at the pin A, and the normal reaction at the roller B in Fig. 100. 3 ft 3 ft 2 ft 30 Fig. 100 3. The uniform smooth rod shown in Fig. 101 is subjected to a force and couple moment. If the rod is supported at A by a smooth wall and at B and C either at the top or bottom by rollers, determine the reactions at these supports. Neglect the weight of the rod. 2 m 4 m 4000 N m 2m B 300 N 2 m 30° Fig. 101 4. Determine the support reactions on the member in Fig. 102. The collar at A is fixed to the member and can slide vertically along the vertical shaft. 900 N 1.5 m- 1.5 m 1 m 45° 500 N marrow_forwardThe electric motor exerts a 220 N• m-torque on the aluminum shaft ABCD when it is rotating at a constant speed. Knowing that G = 27 GPa and that the torques exerted on pulleys B and C are as shown, determine the angle of twist between (a) B and C, (b) B and D. 100 N. m D 120 N. m 50 mm 1 m 40 mm A 1 m 1 marrow_forward
- 1. The aluminium rod AB is bonded to the brass rod BD. Knowing that portion CD of the brass rod is hollow and has an inner diameter of 40 mm, determine the angle of twist at A. Take GAL = 27 GPa and GBr = 39 GPa respectively. 60 mm T = 1600 N - m 36 mm T = S00 N. m 250 mm 375 mm 400 mm Figure Q4.1: Compound shaftarrow_forward5.86 The cast iron inverted T-section supports two concentrated loads of magni- tude P. The working stresses are 48 MPa in tension, 140 MPa in compression, and 30 MPa in shear. (a) Show that the neutral axis of the cross section is located at d = 48.75 mm and that the moment of inertia of the cross-sectional area about this axis is I = 11.918 x 106 mm“. (b) Find the maximum allowable value of P. 1.0 m 1.0 m 15 mm 3 m 150 mm NA- d 15 mm 150 mm FIG. P5.86arrow_forwardSolve using method of forces and then separately by method of displacements, using matrix form: Two cylindrical rods, one of steel and the other of brass, are joined at C and restrained by rigid supports at A and E. Knowing the loading shown and using Es = 200 GPa, E, = 105 GPa determine the reactions and A and E and the displacements of B, C, D. 100 100 Steel B. Bras 60 kN 40 kN 40-mm dlam. 30-mm diam.arrow_forward
- 1. The aluminium rod AB is bonded to the brass rod BD. Knowing that portion CD of the brass rod is hollow and has an inner diameter of 40 mm, determine the angle of twist at A. Take GAL = 27 GPa and Gay = 39 GPa respectively. 60 mm T- 1600 N- m 36 mm T- S00 N. m 250 mm 375 mm 400 mm Figure Q4.1: Compound shaftarrow_forward3.6 Two forces, each of magnitude P, are applied to the wrench. The diameter of the steel shaft AB is 20 mm. Determine the largest allowable value of P if the shear stress in the shaft is not to exceed 120 MPa and its angle of twist is limited to 7°. Use G= 80 GPa for steel. 300 mm B 500 mm FIG. P3.6arrow_forwardProblem 2.5: A hoisting drum 0.5 m in diameter is keyed to a shaft which is supported in two bearings and driven through a 12:1 reduction ratio by an electric motor. Determine the power of driving motor, if the max. load of 8 kN is hoisted at a speed of 50 m/min. and the efficiency of the drive is 80%; Also determine the torque on the drum shaft and the speed of the motor in r.p.m. Determine also the diameter of the shaft. The drive gear whose dia. is 450 mm is mounted at the end of the shaft such that it overhangs the nearest bearing by 150 mm Motor Pinion Drum Gear 150arrow_forward
- 2.4 An 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 P is applied. Know- ing that E = 200 GPa, determine (a) the magnitude of the force P, (b) the corresponding normal stress in the wire.arrow_forwardAn annular washer distributes the load P applied to a steel rod to a timber support. The rod's diameter is 22 mm, and the washer's inner diameter is 25 mm, which is larger than the hole's permissible outer diameter. Knowing that the axial normal stress in the steel rod is 35 MPa and the average bearing stress between the washer and the timber must not exceed 5 MPa, examine the smallest allowed outer diameter, d, of the washer. %3D %3D +22 mm P Figure 4arrow_forward300 N.m 500 N.m B 0.4 m 0,6 m Fig. P3.48 0.3 m PROBLEM 3.48 The electric motor exerts a torque of 800 Nm on the steel shaft ABCD when it is rotating at constant speed. Design specifications require that the diameter of the shaft be uniform from A to D and that the angle of twist between A and D should not exceed 1.5°. Knowing that tmax S 60 MPa and G = 77 GPa, determine the minimum diameter shaft that may be used. [Ans. 42.1 mm] PROBLEM 3.52 14/04/2022 BANG 6 OLUESEN delete home end pg up pg dn num 9 + backspace * lockarrow_forward
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