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The bent rod ACDB is supported by a sleeve at A and a ball-and-socket joint at B. Determine the components of the reactions and the tension in the cable. Neglect the mass of the rod and any moment reactions at A. E 0.7 ml 0.5 m 0.4 m 1.0 m 0.5 m 0.4 m 147 kg

The bent rod ACDB is supported by a sleeve at A and a ball-and-socket joint at B. Determine the components of the reactions and the tension in the cable. Neglect the mass of the rod and any moment reactions at A. E 0.7 ml 0.5 m 0.4 m 1.0 m 0.5 m 0.4 m 147 kg

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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The bent rod ACDB is supported by a sleeve at A and a ball-and-socket joint at B. Determine the components of the reactions and the tension in the cable. Neglect the mass of the rod and any moment reactions at A.

1) Find all A reactions:

Ay=?

Ax=?

2) Find all B reactions:

Bx=?

By=?

Bz=?

3) Find the tension force:

T=?

**Problem Statement:** The bent rod ACDB is supported by a sleeve at A and a ball-and-socket joint at B. Determine the components of the reactions and the tension in the cable. Neglect the mass of the rod and any moment reactions at A. **Diagram Explanation:** - The diagram shows a 3D setup of a bent rod labeled ACDB. - The rod is supported horizontally from point A on the left to point B on the right. - A weight of 147 kg hangs vertically from point C. - A cable is connected from point D of the rod to a wall at point E. **Dimensions and Points:** - Distance from A to C along the x-axis is 1.0 m. - Distance from C to D along the x-axis is 0.5 m. - Distance from D to B along the y-axis is 0.4 m. - Vertical distance from point E to the wall in line with the rod is 0.7 m from the xz-plane origin (O). - The horizontal distance parallel to the z-axis is 0.4 m. **Supporting Elements:** - **Sleeve at A:** Provides support but allows the rod to rotate, hence doesn't prevent rotation. - **Ball-and-Socket Joint at B:** Prevents translation in all directions but allows rotation, providing support and stability. - **Cable DE:** Keeps the rod in position, countering any rotational moments due to the hanging weight. The task involves accounting for the reaction forces at supports A and B and calculating the tension in the cable DE to maintain equilibrium under the load.
Transcribed Image Text:**Problem Statement:** The bent rod ACDB is supported by a sleeve at A and a ball-and-socket joint at B. Determine the components of the reactions and the tension in the cable. Neglect the mass of the rod and any moment reactions at A. **Diagram Explanation:** - The diagram shows a 3D setup of a bent rod labeled ACDB. - The rod is supported horizontally from point A on the left to point B on the right. - A weight of 147 kg hangs vertically from point C. - A cable is connected from point D of the rod to a wall at point E. **Dimensions and Points:** - Distance from A to C along the x-axis is 1.0 m. - Distance from C to D along the x-axis is 0.5 m. - Distance from D to B along the y-axis is 0.4 m. - Vertical distance from point E to the wall in line with the rod is 0.7 m from the xz-plane origin (O). - The horizontal distance parallel to the z-axis is 0.4 m. **Supporting Elements:** - **Sleeve at A:** Provides support but allows the rod to rotate, hence doesn't prevent rotation. - **Ball-and-Socket Joint at B:** Prevents translation in all directions but allows rotation, providing support and stability. - **Cable DE:** Keeps the rod in position, countering any rotational moments due to the hanging weight. The task involves accounting for the reaction forces at supports A and B and calculating the tension in the cable DE to maintain equilibrium under the load.
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