SAMPLE PROBLEM 4.5 Thermal Stresses in a Tube A 10-in. length of steel tubing (with properties of E= 30 × 106 psi and a = 7 x 10° per degree Fahrenheit) having a cross-sectional area of 1 in. is installed with "fixed" ends so that it is stress-free at 80°F. In operation, the tube is heated throughout to a uniform 480°F. Careful measurements indicate that the fixed ends sep- arate by 0.008 in. What loads are exerted on the ends of the tube, and what are the resultant stresses? SOLUTION Known: A given length of steel tubing with a known cross-sectional area expands. 0.008 in. from a stress-free condition at 80°F when the tube is heated to a uniform 480°F (see Figure 4.45). Find: Determine the steel tubing loads and stresses. Schematic and Given Data: Pa Olb ************ 10.000 in. T = 80°F ← Po Olb 10.008 in To 480°F Pu 60,000 P Pa 60,000 lb FIGURE 4.45 Sample Problem 4.5. Thermal expansion of a constrained tube. Assumptions: 1. The tube material is homogeneous and isotropic. 2. The material stresses remain within the clastic range. Analysis: 1. For the unrestrained tube € = αAT = (7 X 10 )(400) = 2.8 x 10-3 AL = Le = 10 in. (2.8 x 103) = 0.028 in. 2. Since the measured expansion was only 0.008 in., the constraints must apply forces sufficient to produce a deflection of 0.020 in. From the relationship PL 8 = AE which is from elementary elastic theory, and reviewed in Chapter 5, P(10) (1)(30 x 106) or P = 60,000 lb 3. Because the area is unity, o = 60 ksi. 0.020 = Comment: Since these answers are based on elastic relationships, they are valid only if the material has a yield strength of at least 60 ksi at 480°F. (1) (Similar to SAMPLE PROBLEM 4.5, Thermal Stresses in a Tube) If all other things being same as in SAMPLE Problem 4.5, when the Steel tube is heated to 560 deg F, and results in measured expansion of 0.010 inches, What Ioads are exerted on the ends of the tube, and what are the resultant stresses?
SAMPLE PROBLEM 4.5 Thermal Stresses in a Tube A 10-in. length of steel tubing (with properties of E= 30 × 106 psi and a = 7 x 10° per degree Fahrenheit) having a cross-sectional area of 1 in. is installed with "fixed" ends so that it is stress-free at 80°F. In operation, the tube is heated throughout to a uniform 480°F. Careful measurements indicate that the fixed ends sep- arate by 0.008 in. What loads are exerted on the ends of the tube, and what are the resultant stresses? SOLUTION Known: A given length of steel tubing with a known cross-sectional area expands. 0.008 in. from a stress-free condition at 80°F when the tube is heated to a uniform 480°F (see Figure 4.45). Find: Determine the steel tubing loads and stresses. Schematic and Given Data: Pa Olb ************ 10.000 in. T = 80°F ← Po Olb 10.008 in To 480°F Pu 60,000 P Pa 60,000 lb FIGURE 4.45 Sample Problem 4.5. Thermal expansion of a constrained tube. Assumptions: 1. The tube material is homogeneous and isotropic. 2. The material stresses remain within the clastic range. Analysis: 1. For the unrestrained tube € = αAT = (7 X 10 )(400) = 2.8 x 10-3 AL = Le = 10 in. (2.8 x 103) = 0.028 in. 2. Since the measured expansion was only 0.008 in., the constraints must apply forces sufficient to produce a deflection of 0.020 in. From the relationship PL 8 = AE which is from elementary elastic theory, and reviewed in Chapter 5, P(10) (1)(30 x 106) or P = 60,000 lb 3. Because the area is unity, o = 60 ksi. 0.020 = Comment: Since these answers are based on elastic relationships, they are valid only if the material has a yield strength of at least 60 ksi at 480°F. (1) (Similar to SAMPLE PROBLEM 4.5, Thermal Stresses in a Tube) If all other things being same as in SAMPLE Problem 4.5, when the Steel tube is heated to 560 deg F, and results in measured expansion of 0.010 inches, What Ioads are exerted on the ends of the tube, and what are the resultant stresses?
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Please solve the bottom problem using the info from the top problem.
Transcribed Image Text:SAMPLE PROBLEM 4.5 Thermal Stresses in a Tube
A 10-in. length of steel tubing (with properties of E= 30 x 106 psi and
a = 7 x 10° per degree Fahrenheit) having a cross-sectional area of in. is
installed with "fixed" ends so that it is stress-free at 80°F. In operation, the tube is heated
throughout to a uniform 480°F. Careful measurements indicate that the fixed ends sep-
arate by 0.008 in. What loads are exerted on the ends of the tube, and what are the
resultant stresses?
SOLUTION
Known: A given length of steel tubing with a known cross-sectional area expands
0.008 in. from a stress-free condition at 80°F when the tube is heated to a uniform
480°F (see Figure 4.45).
Find: Determine the steel tubing loads and stresses.
Schematic and Given Data:
Pa Ob
10.000 in.
T = 80°F
Po Olb
-10.008 in.
T= 480 F
Pa 60,000 fo Pa 60,000 lb
FIGURE 4.45
Sample
Problem 4.5.
Thermal
expansion of a
constrained
tube.
Assumptions:
1. The tube material is homogeneous and isotropic.
2. The material stresses remain within the clastic range.
Analysis:
1. For the unrestrained tube
€ = αAT = (7 x 10 )(400) = 2.8 × 10-³
AL = Le = 10 in. (2.8 × 10³) = 0.028 in.
2. Since the measured expansion was only 0.008 in., the constraints must apply
forces sufficient to produce a deflection of 0.020 in. From the relationship
PL
8 =
AE
which is from elementary clastic theory, and reviewed in Chapter 5,
P(10)
(1)(30 x 106)
or P = 60,000 lb
3. Because the area is unity, o = 60 ksi.
0.020 =
Comment: Since these answers are based on elastic relationships, they are valid
only if the material has a yield strength of at least 60 ksi at 480°F.
(1) (Similar to SAMPLE PROBLEM 4.5, Thermal Stresses in a Tube)
If all other things being same as in SAMPLE Problem 4.5, when the Steel tube is
heated to 560 deg F, and results in measured expansion of 0.010 inches, What
loads are exerted on the ends of the tube, and what are the resultant stresses?
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