Answered: SITUATION: An inclined steel beam is…

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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Solve for max deflection of the beam

$### Inclined Steel Beam Deflection Analysis #### Situation: An inclined steel beam is provided below with load $ W = 1.5 \sin\left(\frac{1}{2} x - \pi\right) + 3 $ kN/m. Determine the maximum deflection of the beam. #### Beam Configuration: - The beam is inclined and supported at both ends. - A point load ($ W $) is applied to the beam. - The left support is a simple support reacting only to vertical loads. - The right support is a roller support, allowing vertical displacement but not horizontal movement. #### Beam Dimensions: - The beam spans a total length of 8 meters. - Distance from left support to the applied load is 6 meters. - Distance from right support to the applied load is 2 meters. - Vertical distance from the highest point of the beam to the support at the right end is 2.1 meters. - Vertical distance from the lowest point of the beam to the support at the left end is 0.7 meters. #### Load Distribution: - $ W = 1.5 \sin\left(\frac{1}{2} x - \pi\right) + 3 $ kN/m #### Detail of the Cross-Section of the Beam: The cross-section of the beam is provided around the coordinate points given by: - $ y = \ln(x-2) + 3 $ - $ y = e^{(x-3)} $ All units are in decimeters on the cross-section graph. #### Graph Explanation: 1. **Beam Schematic**: - Displays an inclined beam with specified dimensions. - Shows the loading condition and support types. - Notable dimensions marked include the lengths (6 m and 2 m spans), and heights (0.7 m and 2.1 m). 2. **Cross-Section Detail**: - Description of the beam's cross-section profile with coordinates: - $ y = \ln(x - 2) + 3 $ - $ y = e^{(x - 3)} $ - Emphasizes that all measurements are provided in decimeters. #### Analysis Objective: Determine the maximum deflection of the inclined beam under the given load. This involves understanding the load distribution, beam properties, and the support conditions. Applying principles such as superposition, beam deflection formulas, and$

Transcribed Image Text:### Inclined Steel Beam Deflection Analysis #### Situation: An inclined steel beam is provided below with load $ W = 1.5 \sin\left(\frac{1}{2} x - \pi\right) + 3 $ kN/m. Determine the maximum deflection of the beam. #### Beam Configuration: - The beam is inclined and supported at both ends. - A point load ($ W $) is applied to the beam. - The left support is a simple support reacting only to vertical loads. - The right support is a roller support, allowing vertical displacement but not horizontal movement. #### Beam Dimensions: - The beam spans a total length of 8 meters. - Distance from left support to the applied load is 6 meters. - Distance from right support to the applied load is 2 meters. - Vertical distance from the highest point of the beam to the support at the right end is 2.1 meters. - Vertical distance from the lowest point of the beam to the support at the left end is 0.7 meters. #### Load Distribution: - $ W = 1.5 \sin\left(\frac{1}{2} x - \pi\right) + 3 $ kN/m #### Detail of the Cross-Section of the Beam: The cross-section of the beam is provided around the coordinate points given by: - $ y = \ln(x-2) + 3 $ - $ y = e^{(x-3)} $ All units are in decimeters on the cross-section graph. #### Graph Explanation: 1. **Beam Schematic**: - Displays an inclined beam with specified dimensions. - Shows the loading condition and support types. - Notable dimensions marked include the lengths (6 m and 2 m spans), and heights (0.7 m and 2.1 m). 2. **Cross-Section Detail**: - Description of the beam's cross-section profile with coordinates: - $ y = \ln(x - 2) + 3 $ - $ y = e^{(x - 3)} $ - Emphasizes that all measurements are provided in decimeters. #### Analysis Objective: Determine the maximum deflection of the inclined beam under the given load. This involves understanding the load distribution, beam properties, and the support conditions. Applying principles such as superposition, beam deflection formulas, and

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