Mechanics of Materials (MindTap Course List)
9th Edition
ISBN: 9781337093347
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 3.9.10P
A thin-walled hollow tube AB of conical shape has constant thickness I and average diameters dAand dBat the ends (see figure).
- Determine the strain energy U oT the tube when it is subjected to pure torsion by torques T,
- Determine the angle of twist of the tube.
Note: Use the approximate formula / ird^tlA for a thin circular ring; see Case 22 of Appendix E.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
: +0
العنوان
use only
Two rods fins) having same dimensions, one made orass (k = 85 Wm
K) and the mer of copper (k = 375 W/m K), having of their ends inserted
into a furna. At a section 10.5 cm a way from furnace, the temperature of
brass rod 120 Find the distance at which the ame temperature would be
reached in the per rod ? both ends are ex osed to the same environment.
ns
2.05
۲/۱
ostrar
For the beam show below, draw A.F.D, S.F.D, B.M.D
6 kN/m
1
M
B.
3
M M
1. Two long rods of the same diameter-one made of brass (k=85w/m.k) and
the other made of copper (k=375 w/m.k) have one of their ends inserted
into a furnace (as shown in the following figure). Both rods are exposed to
the same environment. At a distance of 105 mm from the furnace, the
temperature of the brass rod is 120°C. At what distance from the furnace
will the same temperature be reached in the copper rod?
Furnace
105 mm T₁
Brass rod
⑪
h
Too-
x2-
Ti
Copper rod
Chapter 3 Solutions
Mechanics of Materials (MindTap Course List)
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
- : +0 العنوان use only Two rods fins) having same dimensions, one made orass (k = 85 Wm K) and the mer of copper (k = 375 W/m K), having of their ends inserted into a furna. At a section 10.5 cm a way from furnace, the temperature of brass rod 120 Find the distance at which the ame temperature would be reached in the per rod ? both ends are ex osed to the same environment. ns 2.05 ۲/۱ ostrararrow_forwardمشر on ۲/۱ Two rods (fins) having same dimensions, one made of brass(k=85 m K) and the other of copper (k = 375 W/m K), having one of their ends inserted into a furnace. At a section 10.5 cm a way from the furnace, the temperature brass rod 120°C. Find the distance at which the same temperature would be reached in the copper rod ? both ends are exposed to the same environment. 22.05 ofthearrow_forwardThe composite wall of oven with A= 1m² as in Fig.1 consists of three materials, two of with kA = 20 W/m K and kc = 50 W/m K with thickness, LA=0.3 m, L= 0.15 m and Lc 0.15 m. The inner surface temperature T1=900 K and the outer surface temperature T4 300 K, and an oven air temperature of To=1100 K, h=25 W/m². K. Determine kɛ and the temperatures T2 and T3 also draw the thermal resistance networkarrow_forward
- Two rods (fins) having same dimensions, one made of brass (k = 85 Wm K) and the other of copper (k = 375 W/m K), having one of their ends inserted into a furnace. At a section 10.5 cm a way from the furnace, the temperature of brass rod 120°C. Find the distance at which the same temperature would be reached in the copper rod ? both ends are exposed to the same environment. Ans 22.05arrow_forwardA long wire (k-8 W/m °C.) with ro 5 mm and surface temperature Ts=180°C as shown in Fig.2. Heat is generated in the wire uniformly at a rate of 5 x107 W/m³. If the energy equation is given by: d 11(77) + - =0 k r dr dr Derive an expression for T(r) and determine the temperature at the center of the wire and at r=2 mm. Air Th T KA LA T2 T3 T Fig.1 KB kc 180°C Го Fig.2arrow_forwardB: Find the numerical solution for the 2D equation below and calculate the temperature values for each grid point shown in Fig. 2 (show all steps). (Do only one trail using following initial values and show the final matrix) T₂ 0 T3 0 I need a real solution, not artificial intelligence locarrow_forward
- Can I solve this problem by calculating the initial kinetic energy with respect to G instead of A.arrow_forwardB: Find the numerical solution for the 2D equation below and calculate the temperature values for each grid point shown in Fig. 2 (show all steps). (Do only one trail using following initial values and show the final matrix) T₂ 0 T3 0 locarrow_forwardShow all work. Indicate the origin that is used for each plane. Identify the Miller indices for the following planes. N 23 1 A) X B) yarrow_forward
- the following table gives weight gain time data for the oxidation of some metal at an elevated temperature W(mg/cm2). Time (min) 4.66 20 11.7 50 41.1 175 a) determin whether the oxidation kinetics obey a linear, parabolic, or logarithmic rate expression. b) Now compute W after a time of 1000 minarrow_forwardA cylindrical specimen of aluminum is pulled in tension. Use the stress v. strain plot below for this specimen of Al to answer parts (a) - (f). Hint: Each strain increment is 0.004. Be sure to include your engineering problem solving method per the class rubric. 400 350 300 250 Stress (MPa) 200 150 100 50 Aluminum (Stress v. Strain) 0 0 0.02 0.04 0.06 0.08 Strain 0.1 0.12 0.14 0.16 a. Compute the modulus of elasticity. b. Determine the yield strength at a strain offset of 0.002. c. Determine the tensile strength of this metal. d. Compute the ductility in percent elongation. e. Compute the modulus of resilience. f. Determine the elastic strain recovery for an unloaded stress of 340 MPa.arrow_forwardConsider a single crystal of silver oriented such that a tensile stress is applied along a [112] direction. If slip occurs on a (011) plane and in a [111] direction and is initiated at an applied tensile stress of 15.9 MPa, compute the critical resolved shear stress.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
Strain energy and strain energy density introduced; Author: Engineer4Free;https://www.youtube.com/watch?v=m14sqLGg4BQ;License: Standard youtube license