Concept explainers
A cylindrical pressure vessel having a radius r = 14 in. and wall thickness t = 0,5 in, is subjected to internal pressure p = 375 psi, In addition, a torque T = 90 kip-ft acts at each end of the cylinder (see figure),
(a) Determine the maximum tensile stress ctniXand the maximum in-plane shear stress Tmjv in the wall of the cylinder.
(b) If the allowable in-plane shear stress is 4.5 ksi, what is the maximum allowable torque T\
(c) If 7 = 150 kip-ft and allowable in-plane shear and allowable normal stresses are 4.5 ksi and 11.5 ksi, respectively, what is the minimum required wall thickness
(a)
The maximum tensile stress
Answer to Problem 8.5.7P
The maximum tensile stress is
Explanation of Solution
Given Information:
Type of vessel = cylindrical
Radius =
Internal pressure =
Wall thickness =
Torque =
Concept used:
Where
Calculation:
Use the following relation to find the longitudinal stress.
Here, wall thickness is
Substitute
Use the following relation to find the hoop stress.
Substitute
Use the following relation to find the shear stress.
Here, torque is
Express the value of
Substitute
From equation
Find the maximum stress
Use the following relation to find the principal stresses.
Substitute
Calculate the principal stress,
As
Use the following relation to find the maximum in plane shear stress
Substitute
Hence, the maximum shear stress is
Conclusion
The values are found by the concept of longitudinal stress and hoop stress.
(b)
Maximum torque.
Answer to Problem 8.5.7P
The maximum torque is
Explanation of Solution
Given Information:
Concept used:
Calculation:
Find the maximum torque
Substitute
Conclusion:
The maximum torque is calculated by equating 1p , Tmax, r, etc.
(C)
What is the minimum required wall thickness.
Answer to Problem 8.5.7P
The minimum required wall thickness is
Explanation of Solution
Given Information:
Concept used:
Calculation:
Here, allowable in plane shear stress is
Substitute
Express the value of
Here, assumed
Variable are
Evaluate the value of
Evaluate the value of
Substitute
Substitute the value of
Use the trial and error method to find the thickness
Trial
Substitute
Trial
Substitute
Trial
Substitute
Substitute
Express the allowable in plane shear stress.
Substitute
Substitute
As
Hence, from the trial and error method the minimum wall thickness
Conclusion:
The minimum thickness is calculated by trial and error method.
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Chapter 8 Solutions
Mechanics of Materials (MindTap Course List)
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- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning