Problem 4: The gap between the support and bar BC is 0.01 inches. If the magnitude of the force applied is 25 kip, and if the entire structure is cooled by a temperature difference of 10 degrees C, determine the support reactions as well as the stress in each portion of the bar. Coefficient of thermal expansion for portion AC is 12 x 10/C and for BC is 17 x 106/C. Other material properties are as shown below. PAc = 0-5 $3c = ; Eac = Eac = E = 26 x10* ksi P - A B Sgap lac = Ift %3D
Problem 4: The gap between the support and bar BC is 0.01 inches. If the magnitude of the force applied is 25 kip, and if the entire structure is cooled by a temperature difference of 10 degrees C, determine the support reactions as well as the stress in each portion of the bar. Coefficient of thermal expansion for portion AC is 12 x 10/C and for BC is 17 x 106/C. Other material properties are as shown below. PAc = 0-5 $3c = ; Eac = Eac = E = 26 x10* ksi P - A B Sgap lac = Ift %3D
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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![**Problem 4:**
The gap between the support and bar BC is 0.01 inches. If the magnitude of the force applied is 25 kip, and if the entire structure is cooled by a temperature difference of 10 degrees Celsius, determine the support reactions as well as the stress in each portion of the bar. The coefficient of thermal expansion for portion AC is \(12 \times 10^{-6}/°C\) and for BC is \(17 \times 10^{-6}/°C\). Other material properties are as shown below.
\[
\Phi_{AC} = 0.5 \Phi_{BC} = 1 \text{ in} \quad ; \quad E_{AC} = E_{BC} = E = 26 \times 10^{3} \text{ ksi}
\]
**Diagram Explanation:**
- The figure shows a linear structure consisting of two segments, AC and BC.
- Segment AC has a length of \(l_{AC} = 15 \text{ ft}\).
- Segment BC has a length of \(l_{BC} = 1.5 \text{ ft}\).
- A force \(P\) is applied horizontally towards the right on the entire structure.
- The right end at point B has a small gap denoted as \(\delta_{\text{gap}} = 0.01 \text{ in}\).
- The cross-sectional area relationship is \(\Phi_{AC} = 0.5 \Phi_{BC}\), where \(\Phi_{AC}\) and \(\Phi_{BC}\) represent the areas of segments AC and BC, respectively.
- The structure is subject to thermal contraction due to a cooling of 10°C, affecting its dimensions and stress.
This problem involves analyzing both mechanical forces and thermal effects on the bar to determine reactions and stresses under specified conditions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf7e798a-2818-4951-b4d8-f75184883c6d%2F14279185-1f8c-4176-b8bb-3e1a218a2138%2F8tterck_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 4:**
The gap between the support and bar BC is 0.01 inches. If the magnitude of the force applied is 25 kip, and if the entire structure is cooled by a temperature difference of 10 degrees Celsius, determine the support reactions as well as the stress in each portion of the bar. The coefficient of thermal expansion for portion AC is \(12 \times 10^{-6}/°C\) and for BC is \(17 \times 10^{-6}/°C\). Other material properties are as shown below.
\[
\Phi_{AC} = 0.5 \Phi_{BC} = 1 \text{ in} \quad ; \quad E_{AC} = E_{BC} = E = 26 \times 10^{3} \text{ ksi}
\]
**Diagram Explanation:**
- The figure shows a linear structure consisting of two segments, AC and BC.
- Segment AC has a length of \(l_{AC} = 15 \text{ ft}\).
- Segment BC has a length of \(l_{BC} = 1.5 \text{ ft}\).
- A force \(P\) is applied horizontally towards the right on the entire structure.
- The right end at point B has a small gap denoted as \(\delta_{\text{gap}} = 0.01 \text{ in}\).
- The cross-sectional area relationship is \(\Phi_{AC} = 0.5 \Phi_{BC}\), where \(\Phi_{AC}\) and \(\Phi_{BC}\) represent the areas of segments AC and BC, respectively.
- The structure is subject to thermal contraction due to a cooling of 10°C, affecting its dimensions and stress.
This problem involves analyzing both mechanical forces and thermal effects on the bar to determine reactions and stresses under specified conditions.
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