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W 1 -L/2 -L/2 W Figure 20.4 Fixed-end moment expressions wL²/12+ Pab²/L² wL²/20 zobac 23wL²/960 5wL²/96 bsonsledn (wb³/12L)(4-3b/L) 6EIA/L2 wL²/12 + Pa²b/L² Mhesudiyil. wL²/30 7wL²/960 5wL²/96 (wb2/12)(6-8b/L+ 3b²/L²) 6EIA/L²

W 1 -L/2 -L/2 W Figure 20.4 Fixed-end moment expressions wL²/12+ Pab²/L² wL²/20 zobac 23wL²/960 5wL²/96 bsonsledn (wb³/12L)(4-3b/L) 6EIA/L2 wL²/12 + Pa²b/L² Mhesudiyil. wL²/30 7wL²/960 5wL²/96 (wb2/12)(6-8b/L+ 3b²/L²) 6EIA/L²

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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**Transcription for Educational Use:** --- **Part Three: Statically Indeterminate Structures** --- **Figure 20.4: Fixed-End Moment Expressions** The diagram consists of a series of beam loading scenarios and their corresponding fixed-end moment expressions. Each row in the table illustrates a particular loading case on a beam, accompanied by a graphical representation of the moment distribution along the beam. 1. **Uniform Load on Entire Span:** - **Beam Loading:** A beam of length \( L \) with a uniform distributed load \( w \). - **Fixed-End Moments:** \( wL^2/12 \) and \( wL^2/12 \). 2. **Concentrated Load at Any Point:** - **Beam Loading:** A concentrated load \( P \) located at distance \( a \) from one end and \( b \) from the other. - **Fixed-End Moments:** \( Pab^2/L^2 \) and \( Pa^2b/L^2 \). 3. **Combination of Uniform Load and Concentrated Load:** - **Beam Loading:** Includes both a uniform load \( w \) and a concentrated load \( P \). - **Fixed-End Moments:** \( wL^2/12 + Pab^2/L^2 \) and \( wL^2/12 + Pa^2b/L^2 \). 4. **Triangular Load (Left Maximized):** - **Beam Loading:** A triangular distributed load along the beam. - **Fixed-End Moments:** \( 23wL^2/960 \) and \( 7wL^2/960 \). 5. **Triangular Load (Right Maximized):** - **Beam Loading:** Similar to the left maximized triangular load but mirrored. - **Fixed-End Moments:** \( 5wL^2/96 \) and \( wL^2/96 \). 6. **Parabolic Load:** - **Beam Loading:** A parabolic distributed load along the beam. - **Fixed-End Moments:** \( (wb^3/12L)(4 - 3b/L) \) and \( (wb^2/12)(6 - 8b/L + 3b^2/L^2) \). 7. **Point Load at Mid-Span:** - **Beam Loading:** A concentrated point load in the middle of
Transcribed Image Text:**Transcription for Educational Use:** --- **Part Three: Statically Indeterminate Structures** --- **Figure 20.4: Fixed-End Moment Expressions** The diagram consists of a series of beam loading scenarios and their corresponding fixed-end moment expressions. Each row in the table illustrates a particular loading case on a beam, accompanied by a graphical representation of the moment distribution along the beam. 1. **Uniform Load on Entire Span:** - **Beam Loading:** A beam of length \( L \) with a uniform distributed load \( w \). - **Fixed-End Moments:** \( wL^2/12 \) and \( wL^2/12 \). 2. **Concentrated Load at Any Point:** - **Beam Loading:** A concentrated load \( P \) located at distance \( a \) from one end and \( b \) from the other. - **Fixed-End Moments:** \( Pab^2/L^2 \) and \( Pa^2b/L^2 \). 3. **Combination of Uniform Load and Concentrated Load:** - **Beam Loading:** Includes both a uniform load \( w \) and a concentrated load \( P \). - **Fixed-End Moments:** \( wL^2/12 + Pab^2/L^2 \) and \( wL^2/12 + Pa^2b/L^2 \). 4. **Triangular Load (Left Maximized):** - **Beam Loading:** A triangular distributed load along the beam. - **Fixed-End Moments:** \( 23wL^2/960 \) and \( 7wL^2/960 \). 5. **Triangular Load (Right Maximized):** - **Beam Loading:** Similar to the left maximized triangular load but mirrored. - **Fixed-End Moments:** \( 5wL^2/96 \) and \( wL^2/96 \). 6. **Parabolic Load:** - **Beam Loading:** A parabolic distributed load along the beam. - **Fixed-End Moments:** \( (wb^3/12L)(4 - 3b/L) \) and \( (wb^2/12)(6 - 8b/L + 3b^2/L^2) \). 7. **Point Load at Mid-Span:** - **Beam Loading:** A concentrated point load in the middle of
**Educational Content: Slope Deflection Equations for Beam Analysis** **Topic: Structural Engineering - Beam Analysis** **Objective:** Understanding the application of regular slope deflection equations for analyzing beams not modified for simple end supports. **Problem Statement:** Use the regular slope deflection equations on a structural beam system with the given parameters. **Diagram Explanation:** The diagram illustrates a beam with fixed and pinned supports, subject to various loads and spans: - **Beam Dimensions:** - Fixed at one end and pinned support at the other. - The length of the section between the fixed support and the pinned support is 30 ft. - Another span of 40 ft is attached to the pinned support, extending in the perpendicular direction, supported at the end. - **Loads:** - A distributed load of 3.6 kips per linear foot (klf) is applied across the topmost horizontal section. - A concentrated load of 60 kips (k) is applied at the intersection of the two beam spans. - **Member Span Lengths:** - Horizontal section: 40 ft. - Vertical section (up to the fixed support): 30 ft twice, summing to 60 ft overall. **Calculation Output:** - **Moment at B-A:** \( M_{BA} = -328.1 \text{ ft-k} \) - **Moment at C-B:** \( M_{CB} = -173.9 \text{ ft-k} \) **Instructions:** Use the slope deflection equations without any modifications for simple end supports. This involves using raw equations to find moments and deflections at the various points of interest on the beam system. --- This educational content provides an example of applying theoretical structural analysis methods in practical engineering scenarios. Students should familiarize themselves with interpreting both graphical and textual data to solve the problem effectively.
Transcribed Image Text:**Educational Content: Slope Deflection Equations for Beam Analysis** **Topic: Structural Engineering - Beam Analysis** **Objective:** Understanding the application of regular slope deflection equations for analyzing beams not modified for simple end supports. **Problem Statement:** Use the regular slope deflection equations on a structural beam system with the given parameters. **Diagram Explanation:** The diagram illustrates a beam with fixed and pinned supports, subject to various loads and spans: - **Beam Dimensions:** - Fixed at one end and pinned support at the other. - The length of the section between the fixed support and the pinned support is 30 ft. - Another span of 40 ft is attached to the pinned support, extending in the perpendicular direction, supported at the end. - **Loads:** - A distributed load of 3.6 kips per linear foot (klf) is applied across the topmost horizontal section. - A concentrated load of 60 kips (k) is applied at the intersection of the two beam spans. - **Member Span Lengths:** - Horizontal section: 40 ft. - Vertical section (up to the fixed support): 30 ft twice, summing to 60 ft overall. **Calculation Output:** - **Moment at B-A:** \( M_{BA} = -328.1 \text{ ft-k} \) - **Moment at C-B:** \( M_{CB} = -173.9 \text{ ft-k} \) **Instructions:** Use the slope deflection equations without any modifications for simple end supports. This involves using raw equations to find moments and deflections at the various points of interest on the beam system. --- This educational content provides an example of applying theoretical structural analysis methods in practical engineering scenarios. Students should familiarize themselves with interpreting both graphical and textual data to solve the problem effectively.
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