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 3.11.14P
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.
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
Q6] (20 Marks) Select the most suitable choice for the following statements: modo digi
-1A 10 af5
1 -The copper-based alloy which is responded to age hardening is
a) copper-nickel
b) aluminum bronze c) copper - beryllium d) brass besincaluy
2- Highly elastic polymers may experience elongations to greater than....
b) 500%
bromsia-P
c) 1000%. d) 1200% 15m or -2
a)100%
3- The cooling rate of quenching the steel in saltwater will be ......the cooling rate of quenching ir
c) faster than sold) none of them
a) slower than
4- Adding of
a) Cr
b) the same as
...... Will lead to stabilize the
b) Mo
10
austenite in steel.
c) Nimble avolls 1d) Sized loloin nl
5- The adjacent linear chains of crosslinked polymers are joined one to another at various positic
DIR...
by.........bonds
c) covalent noisqo gd) ionic lg 120M
6- For the ceramic with coordination number 6 the cation to anion radius ratio will be
a) Van der Waals
a) 0.155-0.225
a) linear
b) hydrogen
(b) 0.225-0.414
c) 0.414 0.732
..polymers.…
Examine
Notes: Attempt Six Questions Only.
rever necessa ,
Q1] (20 Marks) Answer with true (T) or false (F), corrects the wrong phrases, and gives sho
reasons for correct and corrected statements:
1- High chromium irons are basically grey cast irons alloyed with 12 to 30 % Cr.
yous board-19qgo orT-1
2- The drawbacks of Al- Li alloys are their high young modulus and high density.&M 0) (0
3- Vulcanized rubbers are classified under thermoplastic polymers.
4- Diamond is a stable carbon polymorph at room temperature and atmospheric pressure. (
5- The metallic ions of ceramic are called anions, and they are positively charged.
yldgiH-S
69001(6
H.W 5.4
Calculate the load that will make point A move to the left by 6mm, E-228GPa. The diameters
of the rods are as shown in fig. below.
2P-
PA
50mm
B
200mm
2P
0.9m
1.3m
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
- d₁ = = Two solid cylindrical road AB and BC are welded together at B and loaded as shown. Knowing that 30mm (for AB) and d₂ 50mm (for BC), find the average normal stress in each road and the total deformation of road AB and BC. E=220GPa H.W 5.3 60kN A For the previous example calculate the value of force P so that the point A will not move, and what is the total length of road AB at that force? P◄ A 125kN 125kN 0.9m 125kN 125kN 0.9m B B 1.3m 1.3marrow_forwardClass: B Calculate the load that will make point A move to the left by 6mm, E-228GPa The cross sections of the rods are as shown in fig. below. 183 P- Solution 1.418mm 200mm 80mm 3P- 18.3 A 080mm B 200mm 3P- 0.9m إعدادات العرض 1.3m 4.061mmarrow_forwardH.W6 Determine the largest weight W that can be supported by two wires shown in Fig. P109. The stress in either wire is not to exceed 30 ksi. The cross- sectional areas of wires AB and AC are 0.4 in2 and 0.5 in2, respectively. 50° 30° Warrow_forward
- Find equation of motion and natural frequency for the system shown in fig. by energy method. H.W2// For the system Fig below find 1-F.B.D 2-Eq.of motion 8wn 4-0 (5) m. Jo marrow_forward2. Read the following Vernier caliper measurements. (The scales have been enlarged for easier reading.) The Vernier caliper is calibrated in metric units. (a) 0 1 2 3 4 5 سلسلسله (b) 1 2 3 4 5 6 سلسل (c) 1 23456 (d) 1 2 3 4 5 6 سلسلسarrow_forwardExplain why on the interval 0<x<1000 mm and 1000<x<2000mm, Mt is equal to positive 160 Nm, but at x= 0mm and x=1000mm Mt is equal to -160 Nm (negative value!). What is the reason for the sign change of Mt?arrow_forward
- 20 3. 2-233 2520 Тр Gears 1079 A pair of helical gears consist of a 20 teeth pinion meshing with a 100 teeth gear. The pinion rotates at Ta 720 r.p.m. The normal pressure angle is 20° while the helix angle is 25°. The face width is 40 mm and the normal module is 4 mm. The pinion as well as gear are made of steel having ultimate strength of 600 MPa and heat treated to a surface hardness of 300 B.H.N. The service factor and factor of safety are 1.5 and 2 respectively. Assume that the velocity factor accounts for the dynamic load and calculate the power transmitting capacity of the gears. [Ans. 8.6 kWarrow_forward4. A single stage helical gear reducer is to receive power from a 1440 r.p.m., 25 kW induction motor. The gear tooth profile is involute full depth with 20° normal pressure angle. The helix angle is 23°, number of teeth on pinion is 20 and the gear ratio is 3. Both the gears are made of steel with allowable beam stress of 90 MPa and hardness 250 B.H.N. (a) Design the gears for 20% overload carrying capacity from standpoint of bending strength and wear, (b) If the incremental dynamic load of 8 kN is estimated in tangential plane, what will be the safe power transmitted by the pair at the same speed?arrow_forwardDetermine the stress in each section of the bar shown in Fig. when subjected to an axial tensile load shown in Fig. The central section is 30 mm hollow square cross- section; the other portions are of circular section, their diameters being indicated What will be the total deformation of the bar? For the bar material E = 210GPa. 20mi О 30mm 30mmm 2.6 15mm 30kN 1 2 10kN - 20kN 3 -329 91mm 100mm 371mmarrow_forward
- Calculate the load that will make point A move to the left by 6mm, E=228GPa. The diameters of the rods are as shown in fig. below. 2P- PA 80mm B 200mm 2P 0.9m 1.3m.arrow_forwardIf the rods are made from a square section with the dimension as shown. Calculate the load that will make point A move to the left by 6mm, E=228GPa. 2P- P A 80mm B 200mm 2P 0.9m 1.3marrow_forward3. 9. 10. The centrifugal tension in belts (a) increases power transmitted (b) decreases power transmitted (c) have no effect on the power transmitted (d) increases power transmitted upto a certain speed and then decreases When the belt is stationary, it is subjected to some tension, known as initial tension. The value of this tension is equal to the (a) tension in the tight side of the belt (b) tension in the slack side of the belt (c) sum of the tensions in the tight side and slack side of the belt (d) average tension of the tight side and slack side of the belt The relation between the pitch of the chain (p) and pitch circle diameter of the sprocket (d) is given by 60° (a) p=d sin (c) p=d sin (120° T where T Number of teeth on the sprocket. 90° (b) p=d sin T 180° (d) p=d sin Tarrow_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
EVERYTHING on Axial Loading Normal Stress in 10 MINUTES - Mechanics of Materials; Author: Less Boring Lectures;https://www.youtube.com/watch?v=jQ-fNqZWrNg;License: Standard YouTube License, CC-BY