l-and-socket connection in the horizonta ate the magnitudes of the forces P ar e ball end B of the shaft by the vertical

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
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**Problem 3/64**

One of the vertical walls supporting end \(B\) of the 200-kg uniform shaft of Sample Problem 3/5 is turned through a \(30^\circ\) angle as shown here. End \(A\) is still supported by the ball-and-socket connection in the horizontal \(x\)-\(y\) plane. Calculate the magnitudes of the forces \(P\) and \(R\) exerted on the ball end \(B\) of the shaft by the vertical walls \(C\) and \(D\), respectively.

---

**Explanation of the Diagram:**

The diagram represents a 3-dimensional view of the problem setup:

- There is an \(x\)-\(y\)-\(z\) coordinate system shown to provide a spatial reference.
- Two vertical walls, labeled \(C\) and \(D\), form a corner and support end \(B\) of the shaft.
- The shaft is uniform, has a total mass of 200 kg, and is shown by a brown rod.
- End \(A\) of the shaft is connected to the horizontal \(x\)-\(y\) plane at a ball-and-socket joint.
- The shaft makes a \(30^\circ\) angle with the \(y\)-axis on the \(x\)-\(y\) plane.
- Key dimensions:
  - The length of the shaft: \(7\) meters.
  - The distance from point \(A\) to the \(y\)-axis: \(2\) meters.
  - The distance from point \(A\) along the \(x\)-axis to wall \(C\): \(6\) meters.

The problem requires determining the forces \(P\) and \(R\) exerted on the ball end \(B\) of the shaft by the vertical walls \(C\) and \(D\), respectively.
Transcribed Image Text:**Problem 3/64** One of the vertical walls supporting end \(B\) of the 200-kg uniform shaft of Sample Problem 3/5 is turned through a \(30^\circ\) angle as shown here. End \(A\) is still supported by the ball-and-socket connection in the horizontal \(x\)-\(y\) plane. Calculate the magnitudes of the forces \(P\) and \(R\) exerted on the ball end \(B\) of the shaft by the vertical walls \(C\) and \(D\), respectively. --- **Explanation of the Diagram:** The diagram represents a 3-dimensional view of the problem setup: - There is an \(x\)-\(y\)-\(z\) coordinate system shown to provide a spatial reference. - Two vertical walls, labeled \(C\) and \(D\), form a corner and support end \(B\) of the shaft. - The shaft is uniform, has a total mass of 200 kg, and is shown by a brown rod. - End \(A\) of the shaft is connected to the horizontal \(x\)-\(y\) plane at a ball-and-socket joint. - The shaft makes a \(30^\circ\) angle with the \(y\)-axis on the \(x\)-\(y\) plane. - Key dimensions: - The length of the shaft: \(7\) meters. - The distance from point \(A\) to the \(y\)-axis: \(2\) meters. - The distance from point \(A\) along the \(x\)-axis to wall \(C\): \(6\) meters. The problem requires determining the forces \(P\) and \(R\) exerted on the ball end \(B\) of the shaft by the vertical walls \(C\) and \(D\), respectively.
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