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5-2.2-2: Find the deflection at midspan using a W14X22 1 k/ft 4' 3' 2 k/ft 6'

5-2.2-2: Find the deflection at midspan using a W14X22 1 k/ft 4' 3' 2 k/ft 6'

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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Find the deflection at midspan using a W14X22

### Problem 5-2.2-2: Structural Deflection Calculation **Objective**: Find the deflection at midspan using a W14X22 structural steel beam. **Beam Configuration**: - The beam is simply supported at points A and B. - A uniformly distributed load of 1 k/ft is applied over the span from A for a distance of 4 feet. - A uniformly distributed load of 2 k/ft is applied over the span immediate to the right of the 1 k/ft load, extending for 3 feet. - The total span of the beam is 13 feet with distances broken down into: - 4 feet from A to the end of the first load - 3 feet from the end of the first load to the end of the second load - 6 feet from the end of the second load to support B **Diagram**: - The beam is shown horizontal with supports at both ends. - A uniformly distributed load (UDL) of 1 k/ft is shown between points A and the end of a 4-foot section. - Another UDL of 2 k/ft is applied just after the former load for a length of 3 feet. - Support A is a fixed support, and support B is a roller support. ### Steps to Solve: 1. **Determine Reactions at Supports**: Calculate the reactions at supports A and B due to the applied loads. 2. **Construct Shear Force and Bending Moment Diagrams**: Use the reactions to develop shear force and bending moment diagrams for the beam. 3. **Locate Midspan**: Identify the midspan of the beam. 4. **Calculate Deflection**: Use appropriate beam deflection formulas or methods such as moment-area method, conjugate beam method, or integration method to find the deflection at midspan. ### Assumptions: - Beam material assume to be elastic and isotropic. - Deflection calculations based on linear elastic theory. ### Solution Techniques: 1. **Equilibrium Equations**: Sum of vertical forces and moments about one support equals zero. 2. **Integration Method**: Integrate the moment equation derived from the loading conditions to get the slope and deflection equations. 3. **Superposition Principle** (if applicable): If multiple loads, the deflections due to each load can be added to find the overall deflection. **Note**: Numerical solution will
Transcribed Image Text:### Problem 5-2.2-2: Structural Deflection Calculation **Objective**: Find the deflection at midspan using a W14X22 structural steel beam. **Beam Configuration**: - The beam is simply supported at points A and B. - A uniformly distributed load of 1 k/ft is applied over the span from A for a distance of 4 feet. - A uniformly distributed load of 2 k/ft is applied over the span immediate to the right of the 1 k/ft load, extending for 3 feet. - The total span of the beam is 13 feet with distances broken down into: - 4 feet from A to the end of the first load - 3 feet from the end of the first load to the end of the second load - 6 feet from the end of the second load to support B **Diagram**: - The beam is shown horizontal with supports at both ends. - A uniformly distributed load (UDL) of 1 k/ft is shown between points A and the end of a 4-foot section. - Another UDL of 2 k/ft is applied just after the former load for a length of 3 feet. - Support A is a fixed support, and support B is a roller support. ### Steps to Solve: 1. **Determine Reactions at Supports**: Calculate the reactions at supports A and B due to the applied loads. 2. **Construct Shear Force and Bending Moment Diagrams**: Use the reactions to develop shear force and bending moment diagrams for the beam. 3. **Locate Midspan**: Identify the midspan of the beam. 4. **Calculate Deflection**: Use appropriate beam deflection formulas or methods such as moment-area method, conjugate beam method, or integration method to find the deflection at midspan. ### Assumptions: - Beam material assume to be elastic and isotropic. - Deflection calculations based on linear elastic theory. ### Solution Techniques: 1. **Equilibrium Equations**: Sum of vertical forces and moments about one support equals zero. 2. **Integration Method**: Integrate the moment equation derived from the loading conditions to get the slope and deflection equations. 3. **Superposition Principle** (if applicable): If multiple loads, the deflections due to each load can be added to find the overall deflection. **Note**: Numerical solution will
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