8-33 to 8-36 The figure illustrates the non-permanent connection of a steel cylinder head to a grade 30 cast- iron pressure vessel using N bolts. A confined gasket seal has an effective sealing diameter D. The cylinder stores gas at a maximum pressure pg. For the specifications given in the table for the specific problem assigned, select a suitable bolt length from the preferred sizes in Table A-17, then determine the yielding factor of safety np, the load factor nL, and the joint separation factor n0.
Problem Number | 8-33 | 8-34 | 8-35 | 8-36 |
A | 20 mm |
|
20 mm |
|
B | 20 mm |
|
25 mm |
|
C | 100 mm | 3.5 in | 0.8 m | 3.25 in |
D | 150 mm | 4.25 in | 0.9 m | 3.5 in |
E | 200 mm | 6 in | 1.0 m | 5.5 in |
F | 300 mm | 8 in | 1.1 m | 7 in |
N | 10 | 10 | 36 | 8 |
pg | 6 MPa | 1500 psi | 550 kPa | 1200 psi |
Bolt grade | ISO 9.8 | SAE 5 | ISO 10.9 | SAE 8 |
Bolt spec. | M12 × 1.75 |
|
M10 × 1.5 |
|
The yield factor of safety
The load factor of safety.
The joint separation factor.
Answer to Problem 35P
The yield factor of safety is
The load factor of safety is
The joint separation factor is
Explanation of Solution
Write the expression of the length of the material squeeze between the bolt face and washer face.
Here the length of the material squeeze between the bolt face and washer face is
Write the expression for the length of the bolt.
Here the length of bolt is
Write the expression of the threaded length for hexagonal bolt.
Here the threaded length is
Write the expression of the length of the unthreaded portion in grip.
Here, the length of the unthreaded portion in the grip is
Write the expression of the length of the threaded portion in grip.
Here, the length of threaded portion in the grip is
Write the expression of the major area diameter.
Here the nominal diameter of the bolt is
Write the expression of the stiffness for the bolt.
Here the bolt stiffness is
Write the expression of stiffness for the steel cylinder.
Here the stiffness of the steel cylinder is
Write the expression for the midpoint of the complete joint.
Here, the midpoint of the joint is
Write the expression of the thickness of the upper frustum.
Here, the thickness of upper frustum of the gasket is
Write the expression for the effective sealing diameter of the gasket sealing in upper frustum.
Here, the effective sealing diameter of upper frustum of the gasket sealing is
Write the expression for the stiffness of the upper frustum of cast iron vessel.
Here, the stiffness of the cast-iron pressure vessel in the upper frustum is
Write the expression for the stiffness of the lower frustum of the cast iron vessel.
Here, the stiffness of the cast-iron pressure vessel in the lower frustum is
Write the expression for the stiffness of the member or assembly.
Here, the stiffness of the member is
Write the expression of joint constant.
Here the joint constant is
Write the expression of initial tension in the bolt.
Here the tensile stress area is
Write the expression of the effective area of the cylinder.
Here, the effective area of the cylinder is
Write the expression for the total force acting on the assembly.
Here, the total load acting on the assembly is
Write the expression for the load acting on each bolt.
Here, the number of bolt is
Write the expression for yield factor of safety.
Here the overload factor of safety is
Write the expression of overload factor of safety.
Here the overload factor of safety is
Write the expression of joint separation factor of safety.
Here the factor of safety based on joint separation is
Conclusion:
Substitute
Refer to Table
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Substitute
Substitute
Refer to Table
Substitute
Substitute
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Substitute
Substitute
Refer to Table
Substitute
Substitute
Substitute
Substitute
Refer to Table
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the yield factor of safety is
Substitute
Thus, the load factor of safety is
Substitute
Thus, the joint separation factor is
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Chapter 8 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
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