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 3.8.7P
A stepped shaft ACE is held against rotation at ends A and B and subjected to a torque T0acting at section C(see figure). The two segments of the shaft (AC and CB) have diameters dAand dg, respectively, and polar moments of inertia IpAand IpBrespectively. The shaft has length L and segment AC has length a.
- For what ratio a/L will the maximum shear stresses be the same in both segments of the shaft?
- For what ratio a/L will the internal torques be the same in both segments of the shaft?
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
Problem 6. The circular plate shown rotates about its vertical diameter. At the instant shown, the
angular velocity ₁ of the plate is 10 rad/s and is decreasing at the rate of 25 rad/s². The disk lies
in the XY plane and Point D of strap CD moves upward. The relative speed u of Point D of strap
CD is 1.5 m/s and is decreasing at the rate of 3 m/s².
Determine (a) the velocity of D, (b) the acceleration of D.
Answers: =0.75 +1.299]-1.732k m/s a=-28.6 +3.03-10.67k m/s²
200 mm
x
Z
Problem 1. The flywheel A has an angular velocity o 5 rad/s. Link AB is connected via ball
and socket joints to the flywheel at A and a slider at B. Find the angular velocity of link AB and
the velocity of slider B at this instant. (Partial Answer: @ABN = -2î + 2.25; red
Z
-1.2 ft
C
-7 Y
-1.5 ft-
B
2.0 ft
Need help please
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
- PROBLEM 15.225 The bent rod shown rotates at the constant rate @₁ = 5 rad/s and collar C moves toward point B at a constant relative speed u = 39 in./s. Knowing that collar C is halfway between points B and D at the instant shown, determine its velocity and acceleration. Answers: v=-45 +36.6)-31.2 k in./s āc = -2911-270} in./s² 6 in 20.8 in. 14.4 in.arrow_forwardNeed help, please show all work, steps, units and please box out and round answers to 3 significant figures. Thank you!..arrow_forwardNeed help, please show all work, steps, units and please box out and round answers to 3 significant figures. Thank you!...arrow_forward
- FL y b C Z Determine the moment about O due to the force F shown, the magnitude of the force F = 76.0 lbs. Note: Pay attention to the axis. Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value a 1.90 ft b 2.80 ft с 2.60 ft d 2.30 ft Mo 144 ft-lb = -212 × 1 + xk) ☑+212arrow_forward20 in. PROBLEM 15.206 Rod AB is connected by ball-and-socket joints to collar A and to the 16-in.-diameter disk C. Knowing that disk C rotates counterclockwise at the constant rate ₁ =3 rad/s in the zx plane, determine the velocity of collar A for the position shown. 25 in. B 8 in. Answer: -30 in/s =arrow_forwardB Z 001 2.5 ft PROBLEM 15.236 The arm AB of length 16 ft is used to provide an elevated platform for construction workers. In the position shown, arm AB is being raised at the constant rate de/dt = 0.25 rad/s; simultaneously, the unit is being rotated about the Y axis at the constant rate ₁ =0.15 rad/s. Knowing that 20°, determine the velocity and acceleration of Point B. Answers: 1.371 +3.76)+1.88k ft/s a=1.22 -0.342)-0.410k ft/s² Xarrow_forward
- F1 3 5 4 P F2 F2 Ꮎ Ꮎ b P 3 4 5 F1 The electric pole is subject to the forces shown. Force F1 245 N and force F2 = 310 N with an angle = 20.2°. Determine the moment about point P of all forces. Take counterclockwise moments to be positive. = Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value a 2.50 m b 11.3 m C 13.0 m The moment about point P is 3,414 m. × N- If the moment about point P sums up to be zero. Determine the distance c while all other values remained the same. 1.26 m.arrow_forwardZ 0.2 m B PROBLEM 15.224 Rod AB is welded to the 0.3-m-radius plate, which rotates at the constant rate ₁ = 6 rad/s. Knowing that collar D moves toward end B of the rod at a constant speed u = 1.3 m, determine, for the position shown, (a) the velocity of D, (b) the acceleration of D. Answers: 1.2 +0.5-1.2k m/s a=-7.21-14.4k m/s² A 0.25 m 0.3 marrow_forwardI am trying to code in MATLAB the equations of motion for malankovich orbitlal elements. But, I am having a problem with the B matrix. Since f matrix is 7x1 and a_d matrix has to be 3x1, the B matrix has to be 7x3. I don't know how that is possible. Can you break down the B matrix for me and let me know what size it is?arrow_forward
- I am trying to code the solution to the problem in the image in MATLAB. I wanted to know what is the milankovich constraint equation that is talked about in part b.arrow_forwardmylabmastering.pearson.com Chapter 12 - Lecture Notes.pptx: (MAE 272-01) (SP25) DY... P Pearson MyLab and Mastering Scoresarrow_forwardAir modeled as an ideal gas enters an insulated compressor at a temperature of 300 K and 100 kPa, and leaves at 600 kPa. The mass flowrate of air entering the compressor is 50 kg/hr, and the power consumed by the compressor is 3 kW. (Rair = 0.287 kJ/kg-K, k = 1.4, cp = 1.0045 kJ/kg-K, cv = 0.718 kJ/kg-K) Determine the isentropic exit temperature (Te,s) of the air in [K]. Determine the actual exit temperature (Te) of the air in [K]. Determine the isentropic efficiency of the compressor. (Answer: ηc,s = 93.3%) Determine the rate of entropy generated through the compressor in [kW/K]. (Answer: Ṡgen = 0.000397 kW/K)arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_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
Everything About COMBINED LOADING in 10 Minutes! Mechanics of Materials; Author: Less Boring Lectures;https://www.youtube.com/watch?v=N-PlI900hSg;License: Standard youtube license