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The A-frame shown is pin-connected at A, B, C, and D. The surface at E is level and frictionless. Calculate the reaction at E and the reaction components at the pins.

The A-frame shown is pin-connected at A, B, C, and D. The surface at E is level and frictionless. Calculate the reaction at E and the reaction components at the pins.

Elements Of Electromagnetics
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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The A-frame shown is pin-connected at A, B, C, and D. The surface at E is level and frictionless. Calculate the reaction at E and the reaction components at the pins.

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The image depicts a structural framework consisting of several members joined together, forming a truss-like assembly. **Components of the Structure:** 1. **Members:** - The structure consists of five members: AB, BC, CD, DE, and AE. These are represented by straight lines connecting various joints in the diagram. 2. **Joints:** - **A:** The leftmost joint, secured with a pin connection to the ground. - **C:** The top joint, where the two inclined members (BC and CD) meet. - **B:** A joint below C on the left side, connecting member AB to BC. - **D:** A joint vertically aligned with B on the right side, connecting member CD to DE. - **E:** The rightmost joint, resting on a roller support. 3. **Supports:** - **Pin Support at A:** This allows rotation but no translation in any direction. - **Roller Support at E:** This allows horizontal movement but restrains vertical movement. **Forces Applied:** 1. **External Forces:** - A horizontal force of 2 kN is applied at joint B, directed to the right. - A vertical force of 3 kN is applied at joint D, directed downward. **Dimensions:** - The vertical distance from A to B is 5 meters. - The vertical distance from B to C is 5 meters, totaling 10 meters from A to C. - The horizontal distance from A to E is 10 meters, composed of 5 meters from A to B, 2 meters from B to D, and 3 meters from D to E. This framework illustrates a typical problem in structural analysis, where one must calculate the internal forces within each member and the reactions at the supports under given load conditions.
Transcribed Image Text:The image depicts a structural framework consisting of several members joined together, forming a truss-like assembly. **Components of the Structure:** 1. **Members:** - The structure consists of five members: AB, BC, CD, DE, and AE. These are represented by straight lines connecting various joints in the diagram. 2. **Joints:** - **A:** The leftmost joint, secured with a pin connection to the ground. - **C:** The top joint, where the two inclined members (BC and CD) meet. - **B:** A joint below C on the left side, connecting member AB to BC. - **D:** A joint vertically aligned with B on the right side, connecting member CD to DE. - **E:** The rightmost joint, resting on a roller support. 3. **Supports:** - **Pin Support at A:** This allows rotation but no translation in any direction. - **Roller Support at E:** This allows horizontal movement but restrains vertical movement. **Forces Applied:** 1. **External Forces:** - A horizontal force of 2 kN is applied at joint B, directed to the right. - A vertical force of 3 kN is applied at joint D, directed downward. **Dimensions:** - The vertical distance from A to B is 5 meters. - The vertical distance from B to C is 5 meters, totaling 10 meters from A to C. - The horizontal distance from A to E is 10 meters, composed of 5 meters from A to B, 2 meters from B to D, and 3 meters from D to E. This framework illustrates a typical problem in structural analysis, where one must calculate the internal forces within each member and the reactions at the supports under given load conditions.
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