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5m 30 kN/m 5m

5m 30 kN/m 5m

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 Conjugate Beam method: Solve for the deflection and slope at the free end of the beam if El is constant.
### Structural Analysis: Cantilever Beam with Triangular Distributed Load In this diagram, we are analyzing a cantilever beam subjected to a triangular distributed load. #### Beam Description: - **Type**: Cantilever Beam - **Fixed Support**: Left end of the beam - **Length**: 10 meters, divided into two 5-meter segments. #### Load Description: - **Type**: Triangular Distributed Load - **Maximum Load Intensity**: 30 kN/m at the free end (rightmost point of the beam). ### Diagram Description: 1. **Beam Representation**: The beam is represented as a horizontal line. 2. **Support**: - The fixed support on the left is illustrated with cross-hatching. - Arrow on the right indicates the direction of the beam extending horizontally. 3. **Load Distribution**: - The triangular load is depicted as a triangle above the beam. - The peak of the triangle (representing the maximum load intensity of 30 kN/m) is positioned at the center of the beam span. - The load intensity reduces linearly to zero at both ends of the beam. 4. **Dimensions**: - The beam length is divided into two segments of 5 meters each, marked below the beam. #### Analysis: - Determine the bending moment and shear force at various points along the beam. - Assess the deflection at the free end. - Evaluate the stresses induced in the beam due to the applied load. This analysis provides essential information for structural engineers to ensure the beam’s design can withstand the applied loads without failure.
Transcribed Image Text:### Structural Analysis: Cantilever Beam with Triangular Distributed Load In this diagram, we are analyzing a cantilever beam subjected to a triangular distributed load. #### Beam Description: - **Type**: Cantilever Beam - **Fixed Support**: Left end of the beam - **Length**: 10 meters, divided into two 5-meter segments. #### Load Description: - **Type**: Triangular Distributed Load - **Maximum Load Intensity**: 30 kN/m at the free end (rightmost point of the beam). ### Diagram Description: 1. **Beam Representation**: The beam is represented as a horizontal line. 2. **Support**: - The fixed support on the left is illustrated with cross-hatching. - Arrow on the right indicates the direction of the beam extending horizontally. 3. **Load Distribution**: - The triangular load is depicted as a triangle above the beam. - The peak of the triangle (representing the maximum load intensity of 30 kN/m) is positioned at the center of the beam span. - The load intensity reduces linearly to zero at both ends of the beam. 4. **Dimensions**: - The beam length is divided into two segments of 5 meters each, marked below the beam. #### Analysis: - Determine the bending moment and shear force at various points along the beam. - Assess the deflection at the free end. - Evaluate the stresses induced in the beam due to the applied load. This analysis provides essential information for structural engineers to ensure the beam’s design can withstand the applied loads without failure.
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