Exam (elaborations)
MECH 344 PROBLEM SET 2-CHAPTER 4_STATIC BODY STRESSES CONCORDIA UNIVERSITY
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MECH 344 PROBLEM SET 2-CHAPTER 4_STATIC BODY STRESSES CONCORDIA UNIVERSITY
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MECH 344 PROBLEM SET 2-CHAPTER 4_STATIC BODYSTRESSES CONCORDIA UNIVERSITY
SOLUTION (4.18)
Known: A steel propeller shaft with a given diameter transmits a known power at a
specified angular velocity.
Find:
(a) Determine the nominal shear stress at the surface.
(b) Determine the outside diameter required to give the same outer surface
stress if a hollow shaft of inside diameter 0.85 times the outside diameter is
used.
(c) Compare the weights of the solid and hollow shafts.
Schematic and Given Data:
Rotation
3200 hp, n = 2000 rpm
2.5 in.
do di d
Assumptions:
1. Bending and axial loads are negligible.
2. The bar is straight and round.
3. The material is homogeneous, and perfectly elastic within the stress
4-24
, range involved.
4. The effect of stress raisers is negligible.
Analysis:
1. From Eq. (1.3), T = 5252
n
W
5252(3200)
T= = 8403 lb ft = 100, 838 lb in.
2000
2. From Eq. (4.4), = 16 T
d3
16 (100, 838)
= = 32, 868 psi = 33 ksi
(2. 5)3 ■
4-25
,3. For a hollow shaft,
do3 - (0.85)4 do3 = 2.53
0.478 do3 = 15.625
do = 3.20 in. ■
3. 202 - (0. 85 3. 20)2
4. Wt. hollow = Area hollow = = 0. 46 ■
Wt. solid Area solid 2. 52
Comment: It is more economical to use a hollow shaft when pure shear stress is
involved.
SOLUTION (4.19)
Known: The maximum shear stress is given for a hollow shaft of known geometry
subjected to pure torsion.
Find: Determine the torque that produces the given maximum shear stress.
Schematic and Given Data:
Assumptions:
1. The shaft is straight.
2. The material is homogeneous and perfectly elastic.
3. There are no stress raisers.
Analysis:
1. From Eq. (4.3), = Tr = 16Tdo
J d - d4
4
o i
4 4
2. (570) 25 - 20 6 16(25)
T= = 10.325 10
4-26
, N•mm = 10,325 N•m ■
4-27
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