Bundle: Mechanics Of Materials, Loose-leaf Version, 9th + Mindtap Engineering, 1 Term (6 Months) Printed Access Card
9th Edition
ISBN: 9781337594318
Author: Barry J. Goodno; James M. Gere
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 3, Problem 3.8.2P
A solid circular bar A BCD with fixed supports at ends A and D is acted upon by two equal and oppositely directed torques T0, as shown in the figure. The torques arc applied at points B and C each of which is located at distance x from one end of the bar. (The distance x may vary from zero to L/2.)
- For what distance x will the angle of twist at points B and C be a maximum?
- What is the corresponding angle of twist 0max?
Expert Solution & Answer
Trending nowThis is a popular solution!
Chapter 3 Solutions
Bundle: Mechanics Of Materials, Loose-leaf Version, 9th + Mindtap Engineering, 1 Term (6 Months) Printed Access Card
Ch. 3 - A circular tube is subjected to torque Tat its...Ch. 3 - -2. A plastic bar of diameter d = 56 mm is to be...Ch. 3 - A copper rod of length L = 18.0 in. is to be...Ch. 3 - A circular steel tube of length L = 1.0 m is...Ch. 3 - Solve the preceding problem if the length L = 56...Ch. 3 - A circular aluminum tube subjected to pure torsion...Ch. 3 - A solid steel bar of circular cross section has...Ch. 3 - A solid copper bar of circular cross section has...Ch. 3 - Repeat Problem 3.3-1, but now use a circular tube...Ch. 3 - A copper tube with circular cross section has...
Ch. 3 - A prospector uses a hand-powered winch (see...Ch. 3 - When drilling a hole in a table leg, a furniture...Ch. 3 - While removing a wheel to change a tire, a driver...Ch. 3 - -8 An aluminum bar of solid circular cross section...Ch. 3 - A high-strength steel drill rod used for boring a...Ch. 3 - The steel shaft of a socket wrench has a diameter...Ch. 3 - A circular tube of aluminum is subjected to...Ch. 3 - A propeller shaft for a small yacht is made of a...Ch. 3 - Three identical circular disks A, B, and Care...Ch. 3 - The steel axle of a large winch on an ocean liner...Ch. 3 - A hollow steel shaft used in a construction auger...Ch. 3 - Solve the preceding problem if the shaft has an...Ch. 3 - A vertical pole of solid, circular cross section...Ch. 3 - A vertical pole of solid, circular cross section...Ch. 3 - A solid brass bar of diameter d = 1.25 in. is...Ch. 3 - A hollow aluminum tube used in a roof structure...Ch. 3 - A circular tube of inner radius r1and outer radius...Ch. 3 - .1 A stepped shaft ABC consisting of two solid...Ch. 3 - A circular tube of outer diameter d3= 70 mm and...Ch. 3 - A stepped shaft ABCD consisting of solid circular...Ch. 3 - A solid, circular bar ABC consists of two...Ch. 3 - A hollow tube ABCDE constructed of monel metal is...Ch. 3 - A shaft with a solid, circular cross section...Ch. 3 - Prob. 3.4.7PCh. 3 - Two sections of steel drill pipe, joined by bolted...Ch. 3 - Prob. 3.4.9PCh. 3 - -10. A tapered bar AB with a solid circular cross...Ch. 3 - A tapered bar AB with a solid circular cross...Ch. 3 - The bar shown in the figure is tapered linearly...Ch. 3 - The non prismatic, cantilever circular bar shown...Ch. 3 - A uniformly tapered tube AB with a hollow circular...Ch. 3 - A uniformly tapered aluminum-alloy tube AB with a...Ch. 3 - For the thin nonprismatic steel pipe of constant...Ch. 3 - .17 A mountain-bike rider going uphill applies...Ch. 3 - A prismatic bar AB of length L and solid circular...Ch. 3 - A prismatic bar AB with a solid circular cross...Ch. 3 - A magnesium-alloy wire of diameter d = 4mm and...Ch. 3 - A nonprismatic bar ABC with a solid circular cross...Ch. 3 - -22 Two tubes (AB, BC) of the same material arc...Ch. 3 - A circular copper bar with diameter d = 3 in. is...Ch. 3 - A circular steel tube with an outer diameter of 75...Ch. 3 - A hollow aluminum shaft (see figure) has an...Ch. 3 - A hollow steel bar (G = 80 GPa ) is twisted by...Ch. 3 - A tubular bar with outside diameterd2= 4.0 in, is...Ch. 3 - A solid circular bar of diameter d = 50 mm (see...Ch. 3 - -7 A steel tube (G = 11.5 x 106 psi) has an outer...Ch. 3 - A solid circular bar of steel (G = 78 GPa)...Ch. 3 - The normal strain in the 45n direction on the...Ch. 3 - An aluminum tube has inside diameter dx= 50 mm,...Ch. 3 - -11 A solid steel bar (G = 11.8 X 106 psi ) of...Ch. 3 - A solid aluminum bar (G = 27 GPa ) of diameter d =...Ch. 3 - Two circular aluminum pipes of equal length L = 24...Ch. 3 - A generator shaft in a small hydroelectric plant...Ch. 3 - A motor drives a shaft at 12 Hz and delivers 20 kW...Ch. 3 - A motor driving a solid circular steel shaft with...Ch. 3 - Prob. 3.7.4PCh. 3 - The propeller shaft of a large ship has an outside...Ch. 3 - The drive shaft for a truck (outer diameter 60 mm...Ch. 3 - A hollow circular shaft for use in a pumping...Ch. 3 - A tubular shaft being designed for use on a...Ch. 3 - A propeller shaft of solid circular cross section...Ch. 3 - What is the maximum power that can be delivered by...Ch. 3 - A motor delivers 275 hp at 1000 rpm to the end of...Ch. 3 - Prob. 3.7.12PCh. 3 - A solid circular bar ABCD with fixed supports is...Ch. 3 - A solid circular bar A BCD with fixed supports at...Ch. 3 - A solid circular shaft AB of diameter d is fixed...Ch. 3 - A ho 1 low st e el shaft ACB of outside diameter...Ch. 3 - A stepped shaft ACB having solid circular cross...Ch. 3 - A stepped shaft ACB having solid circular cross...Ch. 3 - A stepped shaft ACE is held against rotation at...Ch. 3 - A solid circulai' aluminum bar AB is fixed at both...Ch. 3 - Two sections of steel drill pipe, joined by bolted...Ch. 3 - A circular bar AB of length L is fixed against...Ch. 3 - A circular bar AB with ends fixed against rotation...Ch. 3 - A solid steel bar of diameter d1= 25.0 mm is...Ch. 3 - A solid steel bar of diameter d1= 1.50 in. is...Ch. 3 - The composite shaft shown in the figure is...Ch. 3 - The composite shaft shown in the figure is...Ch. 3 - A steel shaft (Gs= 80 GPa) of total length L = 3.0...Ch. 3 - A uniformly tapered aluminum-ally tube AB of...Ch. 3 - Two pipes {L, = 2.5 m and L, = 1.5 m) are joined...Ch. 3 - A solid circular bar of steel (G = 1L4 × 106 psi)...Ch. 3 - A solid circular bar of copper (G = 45 GPa) with...Ch. 3 - A stepped shaft of solid circular cross sections...Ch. 3 - A stepped shaft of solid circular cross sections...Ch. 3 - A circular tube AB is fixed at one end and free at...Ch. 3 - A cantilever bar of circular cross section and...Ch. 3 - Obtain a formula for the strain energy U of the...Ch. 3 - A statically indeterminate stepped shaft ACE is...Ch. 3 - Derive a formula for the strain energy U of the...Ch. 3 - A thin-walled hollow tube AB of conical shape has...Ch. 3 - A hollow circular tube A fits over the end of a...Ch. 3 - A heavy flywheel rotating at n revolutions per...Ch. 3 - A hollow circular tube having an inside diameter...Ch. 3 - A solid circular bar having diameter d is to be...Ch. 3 - A thin-walled aluminum tube of rectangular cross...Ch. 3 - A thin-walled steel tube of rectangular cross...Ch. 3 - A square tube section has side dimension of 20 in....Ch. 3 - A thin-walled circular tube and a solid circular...Ch. 3 - A thin-walled steel tube having an elliptical...Ch. 3 - Calculate the shear stress and the angle of twist...Ch. 3 - A torque T is applied to a thin-walled tube having...Ch. 3 - Compare the angle of twist 1 for a thin-walled...Ch. 3 - A tubular aluminum bar (G = 4 × 106 psi) of square...Ch. 3 - A thin tubular shaft with a circular cross section...Ch. 3 - A thin-walled rectangular tube has uniform...Ch. 3 - A long, thin-walled tapered tube AB with a...Ch. 3 - A stepped shaft consisting of solid circular...Ch. 3 - A stepped shaft with diameters D1= 40 mm and D2=...Ch. 3 - A full quarter-circular fillet is used at the...Ch. 3 - The stepped shaft shown in the figure is required...Ch. 3 - A stepped shaft (see figure) has diameter D2= 1.5...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- A hollow tube ABCDE constructed of monel metal is subjected to five torques acting in the directions shown in the figure. The magnitudes of the torques are T1= 1000 lb-in., T2= T4= 500 lb-in., and T3= T5= 800 lb-in. The tube has an outside diameter of d2= 1.0 in. The allowable shear stress is 12,000 psi and the allowable rate of twist is 2.0°/ft. Determine the maximum permissible inside diameter d1, of the tube.arrow_forwardA solid brass bar of diameter d = 1.25 in. is subjected to torques T1as shown in part a of the figure. The allowable shear stress in the brass is 12 ksi. What is the maximum permissible value of the torques T1? If a hole of diameter 0.625 in. is drilled longitudinally through the bar, as shown in part b of the figure, what is the maximum permissible value of the torques T2? What is the percent decrease in torque and the percent decrease in weight due to the hole?arrow_forwardA tubular bar with outside diameterd2= 4.0 in, is twisted by torques T = 70,0 kip-in. (see figure). Under the action of these torques, the maximum tensile stress in the bar is found to be 6400 psi. Determine the inside diameter rtf of the bar. If the bar has length L = 48.0 in. and is made of aluminum with shear modulus G = 4,0 × 106 psi, what is the angle of twist d (in degrees) between the ends of the bar? (c) Determine the maximum shear strain y (in radians)?arrow_forward
- A long, thin-walled tapered tube AB with a circular cross section (see figure) is subjected to a torque T. The tube has length L and constant wall thickness t. The diameter to the median lines of the cross sections at the ends A and B are dAand dB, respectively. Derive the following formula for the angle of twist of the tube: Hint: If the angle of taper is small, you may obtain approximate results by applying the formulas for a thin-walled prismatic tube to a differential element of the tapered tube and then integrating along the axis of the tube.arrow_forwardA stepped shaft ABC consisting of two solid, circular segments is subjected to torques T}and T2acting in opposite directions, as shown in the figure. The larger segment of the shaft has a diameter of dv- 2.25 in. and a length Lt= 30 in.; the smaller segment has a diameter d2— 1.75 in. and a length L, = 20 in. The torques are T, = 21,000 lb-in. and fz=10.000 lb-in. (a) Find reaction torque TAat support A. (b) Find the internal torque T(x) at two locations: x = L1/2 and x = L1+ L2/2. Show these internal torques on properly drawn free-body diagrams (FBDs).arrow_forwardA uniformly tapered aluminum-alloy tube AB with a circular cross section and length L is shown in the figure. The outside diameters at the ends arc dAand dB= 2dA. A hollow section of length LB and constant thickness t = dA/10 is cast into the tube and extends from B halfway toward A. (a) Find the angle of twist é of the tube when it is subjected to torques T acting at the ends. Use numerical values: dA= 2.5 in., L = 48 in., G = 3.9 × 106 psi, and T =40,000 in.-lb. (b) Repeat part (a) if the hollow section has con stant diameter rfj (see figure part b)arrow_forward
- A solid circular bar ABCD with fixed supports is acted upon by torques T0and 2T0at the locations shown in the figure. (a) Obtain a formula for the maximum angle of twist 0maxof the bar. (b) What is 0max if the applied torque T0at B is reversed in direction?arrow_forward-10. A tapered bar AB with a solid circular cross section is twisted by torques T(see figure). The diameter of the bar varies linearly from dAat the left-hand end to dBat the right-hand end. (a) Confirm that the angle of twist of the tapered bar is (b) For what ratio dBld4will the angle of twist of the tapered bar be one-half the angle of twist of a prismatic bar of diameter d41 (The prismatic bar is made of the same material- has the same length, and is subjected to the same torque as the tapered bar.)arrow_forwardA circular steel tube of length L = 1.0 m is loaded in torsion by torques T (see figure). (a) If the inner radius of the tube is r1= 45 mm and the measured angle of twist between the ends is 0.5°, what is the shear strain y1(in radians) at the inner surface? (b) If the maximum allowable shear strain is 0.0004 rad and the angle of twist is to be kept at 0.45° by adjusting the torque T, what is the maxi mum permissible outer radius (r2)max?arrow_forward
- When drilling a hole in a table leg, a furniture maker uses a hand-operated drill (see figure) with a bit of diameter d = 4.0 mm. If the resisting torque supplied by the table leg is equal to 0.3 N · m, what is the maximum shear stress in the drill bit? If the allowable shear stress in the drill bit is 32 MPa, what is the maximum resisting torque before the drill binds up? If the shear modulus of elasticity of the steel is G = 75 GPa, what is the rate of twist of the drill bit (degrees per meter)?arrow_forward-8 An aluminum bar of solid circular cross section is twisted by torques T acting at the ends (see figure). The dimensions and shear modulus of elasticity arc L = 1.4 m, d = 32 mm, and G = 28 GPa. Determine the torsional stiffness of the bar. If the angle of twist of the bar is 5º, what is the maximum shear stress? What is the maximum shear strain (in radians)? If a hole of diameter d/2 is drilled longitudinally through the bar, what is the ratio of the torsional stiffnesses of the hollow and solid bars? What is the ratio of their maximum shear stresses if both arc acted on by the same torque? If the hole diameter remains at d/2, what new outside diameter d2will result in equal stiffnesses of the hollow and solid bars?arrow_forwardA circular tube of aluminum is subjected to torsion by torques T applied at the ends (see figure). The bar is 24 in. long, and the inside and outside diameters are 1.25 in. and 1.75 in., respectively. It is determined by measurement that the angle of twist is 4° when the torque is 6200 lb-in. Calculate the maximum shear stress in the tube, the shear modulus of elasticity G, and the maximum shear strain (in radians). If the maximum shear strain in the tube is limited to 2.5 × 10-3 and the inside diameter is increased to 1.375 in., what is the maximum permissible torque?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Understanding Torsion; Author: The Efficient Engineer;https://www.youtube.com/watch?v=1YTKedLQOa0;License: Standard YouTube License, CC-BY