Determine the magnitudes of all pin reactions for the frame loaded as shown.

College Physics
11th Edition
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Diagram Explanation: Free-Body Diagram of Bar ABC**

This diagram represents the free-body diagram for bar ABC. The objective is to solve for the force BD, considering that bar BD is a two-force member.

**Components of the Diagram:**

- **Bar ABC:** This is the main structure depicted, with points A, B, and C.
- **Forces at Point A:** Two forces are acting at point A - \( A_x \) (horizontal force) and \( A_y \) (vertical force). They are represented by blue arrows originating from point A.
- **Force BD:** Acts at point B at a specified angle of \( 57^\circ \). This force is shown with a blue arrow.
- **Load at Point C:** There is a downward force of 640 N at point C, indicated by a red arrow.

**Objective:**

Using the information given in the diagram, calculate the force BD. The fact that bar BD is a two-force member means it is subjected to forces at only two points, and these forces are equal in magnitude and opposite in direction along the line joining the two points.
Transcribed Image Text:**Diagram Explanation: Free-Body Diagram of Bar ABC** This diagram represents the free-body diagram for bar ABC. The objective is to solve for the force BD, considering that bar BD is a two-force member. **Components of the Diagram:** - **Bar ABC:** This is the main structure depicted, with points A, B, and C. - **Forces at Point A:** Two forces are acting at point A - \( A_x \) (horizontal force) and \( A_y \) (vertical force). They are represented by blue arrows originating from point A. - **Force BD:** Acts at point B at a specified angle of \( 57^\circ \). This force is shown with a blue arrow. - **Load at Point C:** There is a downward force of 640 N at point C, indicated by a red arrow. **Objective:** Using the information given in the diagram, calculate the force BD. The fact that bar BD is a two-force member means it is subjected to forces at only two points, and these forces are equal in magnitude and opposite in direction along the line joining the two points.
The problem statement asks to determine the magnitudes of all pin reactions for the frame loaded as shown in the diagram.

### Diagram Description:

The diagram illustrates a frame with four points labeled A, B, C, and D:

- **Point A** is on the left and appears to be a pin support connected to the ground.
- From point A, a member extends diagonally upwards to the right to point B, at a length of 810 mm and an angle of 33° from the horizontal.
- **Point B** is a joint connecting the member from A to another member heading from B to point C.
- The member from B to C extends to the right, at a length of 335 mm.
- **Point C** is at the end of the member from B, where a vertical load of 640 N acts downward.
- Another member extends from point C downwards to point D, creating a 57° angle from the horizontal.
- **Point D** is a pin support at the ground.

### Key Details:

- The vertical load of 640 N downward at point C.
- The length and angle measurements of the members between A and C, with specified angles and dimensions for precision in calculations.

The task is to calculate the reaction forces at the pin supports (points A and D) due to the applied load.
Transcribed Image Text:The problem statement asks to determine the magnitudes of all pin reactions for the frame loaded as shown in the diagram. ### Diagram Description: The diagram illustrates a frame with four points labeled A, B, C, and D: - **Point A** is on the left and appears to be a pin support connected to the ground. - From point A, a member extends diagonally upwards to the right to point B, at a length of 810 mm and an angle of 33° from the horizontal. - **Point B** is a joint connecting the member from A to another member heading from B to point C. - The member from B to C extends to the right, at a length of 335 mm. - **Point C** is at the end of the member from B, where a vertical load of 640 N acts downward. - Another member extends from point C downwards to point D, creating a 57° angle from the horizontal. - **Point D** is a pin support at the ground. ### Key Details: - The vertical load of 640 N downward at point C. - The length and angle measurements of the members between A and C, with specified angles and dimensions for precision in calculations. The task is to calculate the reaction forces at the pin supports (points A and D) due to the applied load.
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