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F4-7. Determine the internal shear and moment in the beam as a function of .x. A 6 kN -3 m 18 kN/m B

F4-7. Determine the internal shear and moment in the beam as a function of .x. A 6 kN -3 m 18 kN/m B

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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**Problem 5** **F4–7.** Determine the internal shear and moment in the beam as a function of \( x \). **Diagram Explanation:** The diagram shows a beam, denoted as AB, which is 3 meters long. There are two forces acting on the beam: 1. A concentrated load of 6 kN acting downward at point A. 2. A linear distributed load that starts at 0 kN/m at point A and increases linearly to 18 kN/m at point B. The span of the beam is labeled as AB, and the distance from point A to any point along the beam is denoted as \( x \). The task is to determine how both the internal shear force and bending moment vary along the length of the beam, represented as a function of \( x \). **Instructions for Solving:** To solve this problem, follow these steps: 1. **Calculate Reactions:** First, use equilibrium equations to determine the reactions at the supports. 2. **Shear Force Calculation:** Analyze the beam segmentally to express the shear as a function of \( x \). 3. **Bending Moment Calculation:** Integrate the shear force function from step 2 or use moment equilibrium to find the bending moment as a function of \( x \). 4. **Plot Shear and Moment Diagrams:** Use the functions derived to sketch the shear and moment diagrams for the beam. This problem requires knowledge of static equilibrium, internal forces, and integration to solve for shear and moment along the beam.
Transcribed Image Text:**Problem 5** **F4–7.** Determine the internal shear and moment in the beam as a function of \( x \). **Diagram Explanation:** The diagram shows a beam, denoted as AB, which is 3 meters long. There are two forces acting on the beam: 1. A concentrated load of 6 kN acting downward at point A. 2. A linear distributed load that starts at 0 kN/m at point A and increases linearly to 18 kN/m at point B. The span of the beam is labeled as AB, and the distance from point A to any point along the beam is denoted as \( x \). The task is to determine how both the internal shear force and bending moment vary along the length of the beam, represented as a function of \( x \). **Instructions for Solving:** To solve this problem, follow these steps: 1. **Calculate Reactions:** First, use equilibrium equations to determine the reactions at the supports. 2. **Shear Force Calculation:** Analyze the beam segmentally to express the shear as a function of \( x \). 3. **Bending Moment Calculation:** Integrate the shear force function from step 2 or use moment equilibrium to find the bending moment as a function of \( x \). 4. **Plot Shear and Moment Diagrams:** Use the functions derived to sketch the shear and moment diagrams for the beam. This problem requires knowledge of static equilibrium, internal forces, and integration to solve for shear and moment along the beam.
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