1 Tension, Compression, And Shear 2 Axially Loaded Members 3 Torsion 4 Shear Forces And Bending Moments 5 Stresses In Beams (basic Topics) 6 Stresses In Beams (advanced Topics) 7 Analysis Of Stress And Strain 8 Applications Of Plane Stress (pressure Vessels, Beams, And Combined Loadings) 9 Deflections Of Beams 10 Statically Indeterminate Beams 11 Columns Chapter3: Torsion
Chapter Questions Section: Chapter Questions
Problem 3.2.1P: A circular tube is subjected to torque Tat its ends. The resulting maximum shear strain in the tube... Problem 3.2.2P: -2. A plastic bar of diameter d = 56 mm is to be twisted by torques T (see figure) until the angle... Problem 3.2.3P: A copper rod of length L = 18.0 in. is to be twisted by torques T (see figure) until the angle of... Problem 3.2.4P: A circular steel tube of length L = 1.0 m is loaded in torsion by torques T (see figure). (a) If the... Problem 3.2.5P: Solve the preceding problem if the length L = 56 in., the inner radius r1— 1.25 in., the angle of... Problem 3.2.6P: A circular aluminum tube subjected to pure torsion by torques T(sec figure) has an outer radius... Problem 3.3.1P: A solid steel bar of circular cross section has diameter d = 2.5 in., L = 60 in., and shear modulus... Problem 3.3.2P: A solid copper bar of circular cross section has length L = 1.25 m and shear modulus of elasticity G... Problem 3.3.3P: Repeat Problem 3.3-1, but now use a circular tube with outer diameter d0= 2.5 in. and inner diameter... Problem 3.3.4P: A copper tube with circular cross section has length L = 1.25 m, thickness t = 2 mm, and shear... Problem 3.3.5P: A prospector uses a hand-powered winch (see figure) to raise a bucket of ore in his mine shaft. The... Problem 3.3.6P: When drilling a hole in a table leg, a furniture maker uses a hand-operated drill (see figure) with... Problem 3.3.7P: While removing a wheel to change a tire, a driver applies forces P = 25 lb at the ends of two of the... Problem 3.3.8P: -8 An aluminum bar of solid circular cross section is twisted by torques T acting at the ends (see... Problem 3.3.9P: A high-strength steel drill rod used for boring a hole in the earth has a diameter of 0.5 in. (see... Problem 3.3.10P: The steel shaft of a socket wrench has a diameter of 8.0 mm and a length of 200 mm (see figure). If... Problem 3.3.11P: A circular tube of aluminum is subjected to torsion by torques T applied at the ends (see figure).... Problem 3.3.12P: A propeller shaft for a small yacht is made of a solid steel bar 104 mm in diameter. The allowable... Problem 3.3.13P: Three identical circular disks A, B, and Care welded to the ends of three identical solid circular... Problem 3.3.14P: The steel axle of a large winch on an ocean liner is subjected to a torque of 1.65 kN · m (see... Problem 3.3.15P: A hollow steel shaft used in a construction auger has an outer diameter d2= 6.0 in. and inner... Problem 3.3.16P: Solve the preceding problem if the shaft has an outer diameter d2=150 mm and inner diameter d1= 100... Problem 3.3.17P: A vertical pole of solid, circular cross section is twisted by horizontal forces P = 1100 lb acting... Problem 3.3.18P: A vertical pole of solid, circular cross section is twisted by horizontal forces P = 5kN acting at... Problem 3.3.19P: A solid brass bar of diameter d = 1.25 in. is subjected to torques T1as shown in part a of the... Problem 3.3.20P: A hollow aluminum tube used in a roof structure has an outside diameter d2= 104mm and an inside d1=... Problem 3.3.21P: A circular tube of inner radius r1and outer radius r2is subjected to a torque produced by forces P =... Problem 3.4.1P: .1 A stepped shaft ABC consisting of two solid circular segments is subjected to torques ‘1 and T,... Problem 3.4.2P: A circular tube of outer diameter d3= 70 mm and inner diameter d2= 60 mm is welded at the right-hand... Problem 3.4.3P: A stepped shaft ABCD consisting of solid circular segments is subjected to three torques, as shown... Problem 3.4.4P: A solid, circular bar ABC consists of two segments, as shown in the figure. One segment has a... Problem 3.4.5P: A hollow tube ABCDE constructed of monel metal is subjected to five torques acting in the directions... Problem 3.4.6P: A shaft with a solid, circular cross section consisting of two segments is shown in part a of the... Problem 3.4.7P Problem 3.4.8P: Two sections of steel drill pipe, joined by bolted flange plates at Ä are being tested to assess the... Problem 3.4.9P Problem 3.4.10P: -10. A tapered bar AB with a solid circular cross section is twisted by torques T(see figure). The... Problem 3.4.11P: A tapered bar AB with a solid circular cross section is twisted by torques T = 36,000 lb-in. (sec... Problem 3.4.12P: The bar shown in the figure is tapered linearly from end A to end B and has a solid circular cross... Problem 3.4.13P: The non prismatic, cantilever circular bar shown has an internal cylindrical hole from 0 to y, so... Problem 3.4.14P: A uniformly tapered tube AB with a hollow circular cross section is shown in the figure. The tube... Problem 3.4.15P: A uniformly tapered aluminum-alloy tube AB with a circular cross section and length L is shown in... Problem 3.4.16P: For the thin nonprismatic steel pipe of constant thickness t and variable diameter d shown with... 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... Problem 3.4.18P: A prismatic bar AB of length L and solid circular cross section (diameter d) is loaded by a... Problem 3.4.19P: A prismatic bar AB with a solid circular cross section (diameter d) is loaded by a distributed... Problem 3.4.20P: A magnesium-alloy wire of diameter d = 4mm and length L rotates inside a flexible tube in order to... Problem 3.4.21P: A nonprismatic bar ABC with a solid circular cross section is loaded by distributed torques (sec... Problem 3.4.22P: -22 Two tubes (AB, BC) of the same material arc connected by three pins (pin diameter = d ) just... Problem 3.5.1P: A circular copper bar with diameter d = 3 in. is subjected to torques T = 30 kip-in. at its ends.... Problem 3.5.2P: A circular steel tube with an outer diameter of 75 mm and inner diameter of 65 mm is subjected to... Problem 3.5.3P: A hollow aluminum shaft (see figure) has an outside diameter d2= 4.0 in. and inside diameter d1= 2.0... Problem 3.5.4P: A hollow steel bar (G = 80 GPa ) is twisted by torques T (see figure). The twisting of the bar... Problem 3.5.5P: A tubular bar with outside diameterd2= 4.0 in, is twisted by torques T = 70,0 kip-in. (see figure).... Problem 3.5.6P: A solid circular bar of diameter d = 50 mm (see figure) is twisted in a testing maching until the... Problem 3.5.7P: -7 A steel tube (G = 11.5 x 106 psi) has an outer diameter d2= 2.0 in. and an inner diameter dt=1,5... Problem 3.5.8P: A solid circular bar of steel (G = 78 GPa) transmits a torque T = 360 N - m. The allowable stresses... Problem 3.5.9P: The normal strain in the 45n direction on the surface of a circular tube (sec figure) is 880 × 10... Problem 3.5.10P: An aluminum tube has inside diameter dx= 50 mm, shear modulus of elasticity G = 27 GPa, v = 0.33,... Problem 3.5.11P: -11 A solid steel bar (G = 11.8 X 106 psi ) of diameter d = 2,0 in. is subjected to torques T = 8.0... Problem 3.5.12P: A solid aluminum bar (G = 27 GPa ) of diameter d = 40 mm is subjected to torques T = 300 N - m... Problem 3.5.13P: Two circular aluminum pipes of equal length L = 24 in. arc loaded by torsional moments T (sec... Problem 3.7.1P: A generator shaft in a small hydroelectric plant turns at 120 rpm and delivers 50 hp (see figure).... Problem 3.7.2P: A motor drives a shaft at 12 Hz and delivers 20 kW of power (sec figure), If the shaft has a... Problem 3.7.3P: A motor driving a solid circular steel shaft with diameter d = 1.5 in, transmits 50 hp to a gear at... Problem 3.7.4P Problem 3.7.5P: The propeller shaft of a large ship has an outside diameter 18 in. and inside diameter 12 in,, as... Problem 3.7.6P: The drive shaft for a truck (outer diameter 60 mm and inner diameter 40 mm) is running at 2500 rpm... Problem 3.7.7P: A hollow circular shaft for use in a pumping station is being designed with an inside diameter equal... Problem 3.7.8P: A tubular shaft being designed for use on a construction site must transmit 120 kW at 1,75 Hz, The... Problem 3.7.9P: A propeller shaft of solid circular cross section and diameter d is spliced by a collar of the same... Problem 3.7.10P: What is the maximum power that can be delivered by a hollow propeller shaft (outside diameter 50 mm,... Problem 3.7.11P: A motor delivers 275 hp at 1000 rpm to the end of a shaft (see figure). The gears at B and Ctake out... Problem 3.7.12P Problem 3.8.1P: A solid circular bar ABCD with fixed supports is acted upon by torques T0and 2T0at the locations... 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... Problem 3.8.3P: A solid circular shaft AB of diameter d is fixed against rotation at both ends (sec figure), A... Problem 3.8.4P: A ho 1 low st e el shaft ACB of outside diameter 50 mm and inside diameter 40 mm is held against... Problem 3.8.5P: A stepped shaft ACB having solid circular cross sections with two different diameters is held... Problem 3.8.6P: A stepped shaft ACB having solid circular cross sections with two different diameters is held... Problem 3.8.7P: A stepped shaft ACE is held against rotation at ends A and B and subjected to a torque T0acting at... Problem 3.8.8P: A solid circulai' aluminum bar AB is fixed at both ends and loaded by a uniformly distributed torque... Problem 3.8.9P: Two sections of steel drill pipe, joined by bolted flange plates at B, arc subjected to a... Problem 3.8.10P: A circular bar AB of length L is fixed against rotation at the ends and loaded by a distributed... Problem 3.8.11P: A circular bar AB with ends fixed against rotation has a hole extending for half of its length (sec... Problem 3.8.12P: A solid steel bar of diameter d1= 25.0 mm is enclosed by a steel tube of outer diameter d3= 37.5 mm... Problem 3.8.13P: A solid steel bar of diameter d1= 1.50 in. is enclosed by a steel tube of outer diameter d3= 2.25... Problem 3.8.14P: The composite shaft shown in the figure is manufactured by shrink-Fitting a steel sleeve over a... Problem 3.8.15P: The composite shaft shown in the figure is manufactured by shrink-fitting a steel sleeve over a... Problem 3.8.16P: A steel shaft (Gs= 80 GPa) of total length L = 3.0 m is encased for one-third of its length by a... Problem 3.8.17P: A uniformly tapered aluminum-ally tube AB of circular cross section and length L is fixed against... Problem 3.8.18P: Two pipes {L, = 2.5 m and L, = 1.5 m) are joined al B by flange plales (thickness (, = 14 mm) with... Problem 3.9.1P: A solid circular bar of steel (G = 1L4 × 106 psi) with length L = 30 in, and diameter d = 1.75 in,... Problem 3.9.2P: A solid circular bar of copper (G = 45 GPa) with length L = 315n m and diameter d = 40 mm is... Problem 3.9.3P: A stepped shaft of solid circular cross sections (see figure) has length L = 45 in., diameter d2=1.2... Problem 3.9.4P: A stepped shaft of solid circular cross sections (see figure) has length L = 0.80 m, diameter d2= 40... Problem 3.9.5P: A circular tube AB is fixed at one end and free at the other. The tube is subjected to concentrated... Problem 3.9.6P: A cantilever bar of circular cross section and length L is fixed at one end and free at the other... Problem 3.9.7P: Obtain a formula for the strain energy U of the statically indeterminate circular bar shown in the... Problem 3.9.8P: A statically indeterminate stepped shaft ACE is fixed at ends A and B and loaded by a torque TQat... Problem 3.9.9P: Derive a formula for the strain energy U of the cantilever bar shown in the figure. The bar has... Problem 3.9.10P: A thin-walled hollow tube AB of conical shape has constant thickness I and average diameters dAand... Problem 3.9.11P: A hollow circular tube A fits over the end of a solid circular bar B, as shown in the figure. The... Problem 3.9.12P: A heavy flywheel rotating at n revolutions per minute is rigidly attached to the end of a shaft of... Problem 3.11.1P: A hollow circular tube having an inside diameter of 10.0 in, and a wall thickness of 1.0 in. (see... Problem 3.11.2P: A solid circular bar having diameter d is to be replaced by a rectangular tube having... Problem 3.11.3P: A thin-walled aluminum tube of rectangular cross section (sec fig me) has a centerline dimensions b... Problem 3.11.4P: A thin-walled steel tube of rectangular cross section (see figure) has centerline dimensions b = 150... Problem 3.11.5P: A square tube section has side dimension of 20 in. arid thickness of 0.5 in. If the section is used... Problem 3.11.6P: A thin-walled circular tube and a solid circular bar of the same material (see figure) are subjected... Problem 3.11.7P: A thin-walled steel tube having an elliptical cross section with constant thickness t (see figure)... Problem 3.11.8P: Calculate the shear stress and the angle of twist in degrees) for a steel tube (G = 76 GPa) having... Problem 3.11.9P: A torque T is applied to a thin-walled tube having a cross section in the shape of a regular hexagon... Problem 3.11.10P: Compare the angle of twist 1 for a thin-walled circular tube (see figure) calculated from the... Problem 3.11.11P: A tubular aluminum bar (G = 4 × 106 psi) of square cross section (see figure) with outer dimensions... Problem 3.11.12P: A thin tubular shaft with a circular cross section (see figure) and with inside diameter 100 mm is... Problem 3.11.13P: A thin-walled rectangular tube has uniform thickness t and dimensions a x b to the median line of... Problem 3.11.14P: A long, thin-walled tapered tube AB with a circular cross section (see figure) is subjected to a... Problem 3.12.1P: A stepped shaft consisting of solid circular segments having diameters D1= 2.0 in, and D2= 2.4 in.... Problem 3.12.2P: A stepped shaft with diameters D1= 40 mm and D2= 60 mm is loaded by torques T = 1100 N · m (see... Problem 3.12.3P: A full quarter-circular fillet is used at the shoulder of a stepped shaft having diameter D2= 1.0... Problem 3.12.4P: The stepped shaft shown in the figure is required to transmit 600 kW of power at 400 rpm. The shaft... Problem 3.12.5P: A stepped shaft (see figure) has diameter D2= 1.5 in, and a full quarter-circular fillet. The... Problem 3.4.20P: A magnesium-alloy wire of diameter d = 4mm and length L rotates inside a flexible tube in order to...
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Solid mechanics solve part d
Transcribed Image Text: Problem 3. The following composite shaft is loaded as shown in the figure. The AC segment of the shaft is solid; it is
connected to the hollow shaft CD with the help of a rigid flange at C. A torque of 100 Nm is applied at B, as shown. A
uniformly distributed torque of 200 Nm/m is applied over the entire length of CD (2m), also shown in the figure.
Please ignore the thickness of the rigid flange at C.
Given: GAC = 140 GPa, diameter of AC = 20 mm.
Gco = 200 GPa, inner diameter of AC = 40 mm, outer diameter of AC = 50 mm.
a. Determine the absolute maximum shear stress on the shaft. Specify where it occurs along the length of the
shaft and on the circumference of the shaft. Draw the state of stress on a volume element corresponding to
the maximum absolute shear stress location. Show proper perspective when drawing the state of stress.
b. Determine the absolute maximum shear strain on the shaft. Specify where it occurs along the length of the
shaft and on the circumference of the shaft. Be careful here - this location may not be the same as the
maximum shear stress location because the composite shaft has different material properties.
c. Determine the angle of twist of the cross-section at A relative to the fixed cross-section at D, and the flange
at C. What do the signs of these relative angles of twist (values in your answers) mean?
200 Nmhm, wnifo, over emtire
loo N
Fixed
emd
d. For part d, we introduce a wall at cross-section A. Determine the absolute maximum shear stress on the
shaft. Specify where it occurs along the length of the shaft and on the circumference of the shaft.
2 me
200 Nm hn, uni , over emtwe
loo N
Fixed
emd
Fixed
end
1m
Branch of science that deals with the stationary and moving bodies under the influence of forces.
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