Determine the minimum diameter d required for pin B for each of the following conditions:
Determine the minimum diameter d required for pin B for each of the following conditions:
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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![### Part 1
The bell-crank mechanism shown is in equilibrium for an applied load of \(P = 6 \text{ kN}\) applied at \(A\). Assume \(a = 180 \text{ mm}\), \(b = 135 \text{ mm}\), \(c = 7 \text{ mm}\), \(t = 8 \text{ mm}\) and \(\theta = 65^\circ\). Determine the minimum diameter \(d\) required for pin \(B\) for each of the following conditions:
(a) The shear stress in the pin may not exceed \(40 \text{ MPa}\).
(b) The bearing stress in the bell crank may not exceed \(100 \text{ MPa}\).
(c) The bearing stress in the support bracket may not exceed \(165 \text{ MPa}\).
#### Diagrams
1. **Bell-crank mechanism:**
- The bell crank is depicted as a blue L-shaped lever pivoted around a point. The load \(P\) is applied at point \(A\) at an angle \(\theta\).
- Point \(B\) is where the pin is located, holding the bell crank to a support bracket.
- The force \(F_1\) acts at point \(C\) vertically upwards.
2. **Pin B details:**
- A close-up diagram of pin \(B\) shows it inserted through a section, highlighting its diameter \(d\).
- The distances \(c\) (on either side of the pin) and the thickness \(t\) of the support elements are labeled alongside the diameter \(d\).
Calculate the force \(F_1\) in the rod that is connected at \(C\). Assume the direction to the right or up is positive, otherwise as negative.
**Answer:**
\[ F_1 = \boxed{ \ \ \ \ } \text{ N}\]
**Instruction:**
Click "Submit Answer" after entering the calculated value for \( F_1 \).
**Additional Features:**
- Save your work for later by clicking the "Save for Later" button.
- You have 0 of 5 attempts used to submit your final answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8209b3d5-f39b-4753-8582-d28823046294%2Fbb5b7be0-7560-46f1-9a4e-fb229ac01dd3%2Fo6m1je_processed.png&w=3840&q=75)
Transcribed Image Text:### Part 1
The bell-crank mechanism shown is in equilibrium for an applied load of \(P = 6 \text{ kN}\) applied at \(A\). Assume \(a = 180 \text{ mm}\), \(b = 135 \text{ mm}\), \(c = 7 \text{ mm}\), \(t = 8 \text{ mm}\) and \(\theta = 65^\circ\). Determine the minimum diameter \(d\) required for pin \(B\) for each of the following conditions:
(a) The shear stress in the pin may not exceed \(40 \text{ MPa}\).
(b) The bearing stress in the bell crank may not exceed \(100 \text{ MPa}\).
(c) The bearing stress in the support bracket may not exceed \(165 \text{ MPa}\).
#### Diagrams
1. **Bell-crank mechanism:**
- The bell crank is depicted as a blue L-shaped lever pivoted around a point. The load \(P\) is applied at point \(A\) at an angle \(\theta\).
- Point \(B\) is where the pin is located, holding the bell crank to a support bracket.
- The force \(F_1\) acts at point \(C\) vertically upwards.
2. **Pin B details:**
- A close-up diagram of pin \(B\) shows it inserted through a section, highlighting its diameter \(d\).
- The distances \(c\) (on either side of the pin) and the thickness \(t\) of the support elements are labeled alongside the diameter \(d\).
Calculate the force \(F_1\) in the rod that is connected at \(C\). Assume the direction to the right or up is positive, otherwise as negative.
**Answer:**
\[ F_1 = \boxed{ \ \ \ \ } \text{ N}\]
**Instruction:**
Click "Submit Answer" after entering the calculated value for \( F_1 \).
**Additional Features:**
- Save your work for later by clicking the "Save for Later" button.
- You have 0 of 5 attempts used to submit your final answer.
Expert Solution
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Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step 1: Given Data and Find Out
VIEWStep 2: Free Body Diagram and The Force F1
VIEWStep 3: The resultant force acting at point B
VIEWStep 4: The diameter using the shear stress
VIEWStep 5: The value of diameter using the bending stress in the bell crank
VIEWStep 6: The value of diameter bearing stress in the support bracket
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