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
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Textbook Question
Chapter 3, Problem 3.4.17P
.17 A mountain-bike rider going uphill applies torque T = Fd(F = l5lb, d = 4 in.) to the end of the handlebars ABCD by pulling on the handlebar extenders DE. Consider the right half of the handlebar assembly only (assume the bars are fixed at the fork at A). Segments AB and CD are prismatic with lengths L, = 2 in.andL3 = 8.5 in, and with outer diameters and thicknesses d01 = 1.25 in. 101 = 0.125 in. and d03 = O.87in.,i03 = 0.ll5in, respectively as shown. Segment BC’ of length L, = 1.2 in. however. is tapered, and outer diameter and thickness vary linearly between dimensions at B and C.
Consider torsion effects only. Assume G = 4000 ksi is constant.
Derive an integral expression for the angle of twist of half of the handlebar tube when it is subjected to torque T = Fd acting at the end. Evaluate ‘b1-, for the given numerical1ues.
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Exercises
Find the solution of the following Differential Equations
1) y" + y = 3x²
3)
"+2y+3y=27x
5) y"+y=6sin(x)
7) y"+4y+4y = 18 cosh(x)
9) (4)-5y"+4y = 10 cos(x)
11) y"+y=x²+x
13) y"-2y+y=e*
15) y+2y"-y'-2y=1-4x³
2) y"+2y' + y = x²
4) "+y=-30 sin(4x)
6) y"+4y+3y=sin(x)+2 cos(x)
8) y"-2y+2y= 2e* cos(x)
10) y+y-2y=3e*
12) y"-y=e*
14) y"+y+y=x+4x³ +12x²
16) y"-2y+2y=2e* cos(x)
The state of stress at a point is σ = -4.00 kpsi, σy = 16.00 kpsi, σ = -14.00 kpsi, Try = 11.00 kpsi,
Tyz = 8.000 kpsi, and T = -14.00 kpsi.
Determine the principal stresses.
The principal normal stress σ₁ is determined to be [
The principal normal stress σ2 is determined to be [
The principal normal stress σ3 is determined to be
kpsi.
kpsi.
The principal shear stress 71/2 is determined to be [
The principal shear stress 7½ is determined to be [
The principal shear stress T₁/, is determined to be [
kpsi.
kpsi.
kpsi.
kpsi.
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...
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