ME219 Problem Set 6-2 Solutions PDF

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Problem Set 6-2 Solutions...

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Department of Mechanical and Mechatronics Engineering Statically Indeterminate Torsion

ME219 – Mechanics of Deformable Solids 1

Problem Set 6-2

1. The steel shaft is made from two segments: AC has a diameter of 0.5 in, and CB has a diameter of 1 in. If the shaft is fixed at its ends A and B and subjected to a torque of 500 lb-ft, determine the maximum shear stress in the shaft. Gst = 10.8×103 ksi.

Ans: τmax = 29.3 ksi

2. The Am1004-T61 magnesium tube is bonded to the A-36 steel rod. If the allowable shear stresses for the magnesium and steel are (τallow)mg = 45 MPa and (τallow)st = 75 MPa, respectively, determine the maximum allowable torque that can be applied at A. Also, find the corresponding angle of twist of end A.

Some problems and solutions from: “Mechanics of Materials”, Hibbeler, 2017

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ME219 F20

Statically Indeterminate Torsion

Problem Set 6-2

Ans: T = 4.3 kN-m, φA = 2.6°

Some problems and solutions from: “Mechanics of Materials”, Hibbeler, 2017

Page 2 of 9

ME219 F20

Statically Indeterminate Torsion

Problem Set 6-2

3. The assembly shown below consists of a tubular aluminum shell fixed at each end, A and C. The tube has a mean diameter of 100 mm, and a wall thickness of 1 mm. It has a rigid bulkhead at B to which the 25 mm diameter solid aluminum shaft is attached with a bolted flange coupling. The coupling uses 4 10 mm diameter, equally spaced bolts on a circle with diameter d. The bolts have a maximum allowable shear stress of 80 MPa. Determine the minimum acceptable bolt circle diameter, d, for an applied torque of 1 kN∙m, as shown. Through what angle will end D turn relative to the fixed end C. Use a modulus of rigidity, G, of 26 GPa.

A

B

C

25

d

75

D

150 mm

1 kN∙m

75

Ans: d = 80 mm; φ = 13°

Some problems and solutions from: “Mechanics of Materials”, Hibbeler, 2017

Page 3 of 9

ME219 F20

Statically Indeterminate Torsion

Some problems and solutions from: “Mechanics of Materials”, Hibbeler, 2017

Problem Set 6-2

Page 4 of 9

ME219 F20

Statically Indeterminate Torsion

Problem Set 6-2

4. A composite shaft consists of a steel rod of 25 mm diameter, encased in a gunmetal tube 25.01 mm internal diameter and 38 mm external diameter. The rod and the tube are rigidly attached to each other at their ends. The shaft is subjected to a torque of 625 Nm. Calculate the maximum shear stress in the two materials and the angle of twist per unit length. Use Gsteel = 80 GPa, and Ggunmetal = 37 GPa. Ans: τsteel = 68 MPa; τgunmetal = 48 MPa; φ = 4 °/m.

Some problems and solutions from: “Mechanics of Materials”, Hibbeler, 2017

Page 5 of 9

ME219 F20

Statically Indeterminate Torsion

Some problems and solutions from: “Mechanics of Materials”, Hibbeler, 2017

Problem Set 6-2

Page 6 of 9

ME219 F20

Statically Indeterminate Torsion

Some problems and solutions from: “Mechanics of Materials”, Hibbeler, 2017

Problem Set 6-2

Page 7 of 9

ME219 F20

Statically Indeterminate Torsion

Problem Set 6-2

5. A hollow circular tube A fits over the end of a solid circular bar B, as shown in the figure. The far ends of both the tube and the bar are fixed. The inner and outer radii of tube A are 18 mm and 20 mm, respectively. The radius of bar B is 18 mm. The shear modulus of both components is G = 77 GPa. A hole through bar B makes an angle of β = 2° with a line through two holes in tube A. Bar B is twisted until the holes are aligned and then a pin is placed through the holes and the system is released. When the system returns to static equilibrium, what is the maximum shear stress in tube A?

Ans: τ = 44 MPa

Some problems and solutions from: “Mechanics of Materials”, Hibbeler, 2017

Page 8 of 9

ME219 F20

Statically Indeterminate Torsion

Some problems and solutions from: “Mechanics of Materials”, Hibbeler, 2017

Problem Set 6-2

Page 9 of 9...