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Determine the reactions at Supports A & D. There is an internal hinge at B. 550 lb/ft 250 lb/ft 5,500 lboft D |B 5.625 lb 9 ft 9 ft 6 ft 4 ft

Determine the reactions at Supports A & D. There is an internal hinge at B. 550 lb/ft 250 lb/ft 5,500 lboft D |B 5.625 lb 9 ft 9 ft 6 ft 4 ft

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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### Analysis of Beam Reactions with Hinge and Distributed Loads This diagram illustrates a beam subjected to various forces and supports, including an internal hinge at point B. Here is a detailed explanation of the diagram: #### Beam and Supports - **Support A**: On the left side of the beam, there is a pin support at point A, which can resist both vertical and horizontal forces. - **Support D**: On the right side, there is a roller support at point D, which resists vertical forces only. #### Loading Conditions 1. **Triangular Distributed Load**: - Applied from point A to point B. - Maximum intensity of 550 lb/ft at point A. - Decreases linearly to 250 lb/ft at point B. - The span for this load is 9 feet. 2. **Point Load**: - At point C, which is 6 feet from point B. - The point load is 5,500 lb·ft (this could be a typo, generally represented in lb). 3. **Concentrated Load**: - A downward load of 5.625 lb applied 4 feet from point C towards point D. 4. **Rectangular Distributed Load**: - Covers the last 3 feet of the beam before support D. - Intensified at 4 from 3 with incrementing load pattern (this seems like a mixed incremental and uniform load, requiring specific breakdown). #### Internal Hinge - **Location B**: - The internal hinge divides the beam into two segments, allowing them to rotate independently. This hinge affects how the loads will distribute between the two sections of the beam. #### Overall Span - The entire beam spans 28 feet from support A to support D, with sections divided as: - 9 feet from A to B - 9 feet from B to C - 6 feet from C to near end section - 4 feet from the near end section to D ### Objective The objective is to determine the reactions at supports A and D due to the forces and the moment applied on the beam. The internal hinge at B will influence the moment distribution and reactions. This setup requires the application of static equilibrium equations to solve for reactions: - Sum of vertical forces - Sum of moments - Effects due to internal hinge. Understanding these components and principles is crucial in structural analysis and
Transcribed Image Text:### Analysis of Beam Reactions with Hinge and Distributed Loads This diagram illustrates a beam subjected to various forces and supports, including an internal hinge at point B. Here is a detailed explanation of the diagram: #### Beam and Supports - **Support A**: On the left side of the beam, there is a pin support at point A, which can resist both vertical and horizontal forces. - **Support D**: On the right side, there is a roller support at point D, which resists vertical forces only. #### Loading Conditions 1. **Triangular Distributed Load**: - Applied from point A to point B. - Maximum intensity of 550 lb/ft at point A. - Decreases linearly to 250 lb/ft at point B. - The span for this load is 9 feet. 2. **Point Load**: - At point C, which is 6 feet from point B. - The point load is 5,500 lb·ft (this could be a typo, generally represented in lb). 3. **Concentrated Load**: - A downward load of 5.625 lb applied 4 feet from point C towards point D. 4. **Rectangular Distributed Load**: - Covers the last 3 feet of the beam before support D. - Intensified at 4 from 3 with incrementing load pattern (this seems like a mixed incremental and uniform load, requiring specific breakdown). #### Internal Hinge - **Location B**: - The internal hinge divides the beam into two segments, allowing them to rotate independently. This hinge affects how the loads will distribute between the two sections of the beam. #### Overall Span - The entire beam spans 28 feet from support A to support D, with sections divided as: - 9 feet from A to B - 9 feet from B to C - 6 feet from C to near end section - 4 feet from the near end section to D ### Objective The objective is to determine the reactions at supports A and D due to the forces and the moment applied on the beam. The internal hinge at B will influence the moment distribution and reactions. This setup requires the application of static equilibrium equations to solve for reactions: - Sum of vertical forces - Sum of moments - Effects due to internal hinge. Understanding these components and principles is crucial in structural analysis and
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