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Using Double Integration method: Solve for the deflection and slope at the free end of the beam if El is constant.

Using Double Integration method: Solve for the deflection and slope at the free end of the beam if El is constant.

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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Using Double Integration method: Solve for the deflection and slope at the free end of the beam if El is constant.
**Transcription for Educational Website:** ### Triangular Load Distribution on a Cantilever Beam This diagram illustrates a cantilever beam with a triangular load distribution. Below is a detailed description and explanation of the components and elements in the diagram: 1. **Cantilever Beam**: - The left end of the beam is fixed to a wall or other supporting structure. This is depicted by the series of diagonal lines representing the fixed end. 2. **Beam Dimensions**: - The beam extends horizontally from the fixed end, marked with two segments, each measuring 5 meters, summing up to a total span of 10 meters. 3. **Triangular Load Distribution**: - The beam is subjected to a triangular distributed load with the maximum intensity of 30 kN/m occurring at the midpoint of the beam (5 meters from the fixed end). 4. **Load Distribution Annotation**: - The triangular load distribution starts at the fixed end and rises linearly to the maximum load of 30 kN/m at the midpoint before tapering off symmetrically down to zero at the far end of the beam. The graph of this load distribution is depicted by two straight sloping lines that form a triangle on the beam, with the load value marked as 30 kN/m at the peak. ### Explanation of Triangular Load Distribution A triangular load distribution on a beam means that the load intensity varies linearly along the length of the beam. In this specific case, the load starts at zero at the fixed end, increases linearly to the maximum value of 30 kN/m at the center, and then decreases linearly back to zero at the free end. The effects of this load distribution need to be analyzed to determine the shear forces, bending moments, and deflections along the beam. This setup is commonly used in educational contexts to explain the concepts of varying distributed loads on beams and their impact on structural analysis. Understanding how these forces interact helps in designing beams and other structural elements to ensure safety and stability in various engineering applications.
Transcribed Image Text:**Transcription for Educational Website:** ### Triangular Load Distribution on a Cantilever Beam This diagram illustrates a cantilever beam with a triangular load distribution. Below is a detailed description and explanation of the components and elements in the diagram: 1. **Cantilever Beam**: - The left end of the beam is fixed to a wall or other supporting structure. This is depicted by the series of diagonal lines representing the fixed end. 2. **Beam Dimensions**: - The beam extends horizontally from the fixed end, marked with two segments, each measuring 5 meters, summing up to a total span of 10 meters. 3. **Triangular Load Distribution**: - The beam is subjected to a triangular distributed load with the maximum intensity of 30 kN/m occurring at the midpoint of the beam (5 meters from the fixed end). 4. **Load Distribution Annotation**: - The triangular load distribution starts at the fixed end and rises linearly to the maximum load of 30 kN/m at the midpoint before tapering off symmetrically down to zero at the far end of the beam. The graph of this load distribution is depicted by two straight sloping lines that form a triangle on the beam, with the load value marked as 30 kN/m at the peak. ### Explanation of Triangular Load Distribution A triangular load distribution on a beam means that the load intensity varies linearly along the length of the beam. In this specific case, the load starts at zero at the fixed end, increases linearly to the maximum value of 30 kN/m at the center, and then decreases linearly back to zero at the free end. The effects of this load distribution need to be analyzed to determine the shear forces, bending moments, and deflections along the beam. This setup is commonly used in educational contexts to explain the concepts of varying distributed loads on beams and their impact on structural analysis. Understanding how these forces interact helps in designing beams and other structural elements to ensure safety and stability in various engineering applications.
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