ME 270 – Fall 2017 Exam 3 NAME (Last, First): - … 270 – Fall 2017 Exam 3 NAME (Last, First): _____ Fall 2017 Exam 3 Page 2 of 4 PROBLEM 1 (20 points) 1A: A steel rod of varying

ME 270 – Fall 2017 Exam 3 NAME (Last, First): ________________________________

Fall 2017 Exam 3 Page 2 of 4

PROBLEM 1 (20 points)

1A: A steel rod of varying cross section is loaded as shown in the diagram. Determine the axial stresses in region A, σA, and region C, σC. Note that Region A and B are solid shafts, and, Region C is a hollow shaft. All dimensions are shown in the diagram.

1B: A solid circular rod of 10 mm diameter is coupled to a metal tube using a bonded rubber cylinder as shown in the diagram. The shear modulus of rubber is 50 MN/m2. An axial force of 10 kN is applied to the rod,

(a) calculate the average shear stresses between the rod and the rubber (τR ),

(b) determine the shear strain of the rubber (γR).

σ! = Tension Compression Zero (circle one) (2.5 pts)

σ# = Tension Compression Zero (circle one) (2.5 pts)

$% = (3 pts)

&% = (2 pts)

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4

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9.4

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248404m

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2

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'

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200 kn

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.

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15

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(tension)

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5 kn (tension)

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r

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OE

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5.

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30

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o MN

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or l

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ME 270 – Fall 2017 Exam 3 NAME (Last, First): ________________________________

Fall 2017 Exam 3 Page 3 of 3

1C: A solid steel shaft is subjected to a pure torsion of 1500 lb-in. If the maximum shear stress is not to exceed 12 ksi, calculate the minimum diameter of the shaft, d. If a hollow shaft (with an outer diameter, do and an inner diameter, di) is used instead, how does d compares with do? No calculation is needed for this part.

1D: Two rods AC and BC are connected by pins to form a mechanism for supporting a vertical load of P = 100 lb at C. The angle between the rods AC and BC is α = 36.87°. The failure stress of the rod BC is 15 ksi. (a) For a factor of safety of 2.5, determine the maximum allowable axial stress in rod

BC, σallow. (b) Find the minimum cross-sectional area (A) of rod BC such that the axial stress does

not exceed σallow.

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{ =

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(d/2)

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ME 270 – Fall 2017 Exam 3 NAME (Last, First): - … 270 – Fall 2017 Exam 3 NAME (Last, First): _____ Fall 2017 Exam 3 Page 2 of 4 PROBLEM 1 (20 points) 1A: A steel rod of varying