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Civil Engineering
19kN/m B 6、

19kN/m B 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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Draw the shear diagram and moment diagram for the beam.
### Analysis of Linearly Distributed Load and Moment on a Beam #### Description The diagram illustrates a beam subjected to a linearly varying distributed load and an applied moment. The beam extends from point A to point B, covering a horizontal length of 3 meters. Key features of the beam and the applied loads are highlighted below: - **Distributed Load:** - The load varies linearly along the beam length, starting from point A with a magnitude of 9 kN/m and reducing to 0 kN/m at point B. - Load Representation: Arrows pointing downward indicate the direction and variance of the load. The density of arrows suggests the intensity of the load. - **Moment at Point B:** - A moment of 6 kN·m is applied clockwise at point B. #### Key Points: - **Points and Length:** - Point \( A \) marks the left edge of the beam. - Point \( B \) is located at 3 meters from point \( A \). - **Load Distribution:** - The load begins at 9 kN/m at point \( A \) and decreases uniformly to 0 kN/m at point \( B \). - This indicates a linearly decreasing distributed load. - **Applied Moment:** - A moment of 6 kN·m is applied at the end point \( B \) in a clockwise direction. ### Diagram Explanation 1. **Beam Representation:** - The beam is represented as a horizontal line, supported at point \( A \) and extending to point \( B \). 2. **Distributed Load:** - The distributed load is depicted by a series of vertical arrows. - Arrows at point \( A \) are fully spaced and intense (high density), representing the start of the distributed load at 9 kN/m. - Moving towards point \( B \), the density and size of the arrows decrease, showing the linear reduction of the load intensity to 0 kN/m. 3. **Applied Moment:** - At point \( B \), a clockwise curved arrow with a magnitude labeled 6 kN·m indicates the applied moment. ### Conclusion Understanding this diagram is crucial for analyzing the effects of a linearly varying distributed load and applied moment on beam structures. This includes calculating reactions at the supports, the shear force along the beam length, and the resulting bending moment distribution.
Transcribed Image Text:### Analysis of Linearly Distributed Load and Moment on a Beam #### Description The diagram illustrates a beam subjected to a linearly varying distributed load and an applied moment. The beam extends from point A to point B, covering a horizontal length of 3 meters. Key features of the beam and the applied loads are highlighted below: - **Distributed Load:** - The load varies linearly along the beam length, starting from point A with a magnitude of 9 kN/m and reducing to 0 kN/m at point B. - Load Representation: Arrows pointing downward indicate the direction and variance of the load. The density of arrows suggests the intensity of the load. - **Moment at Point B:** - A moment of 6 kN·m is applied clockwise at point B. #### Key Points: - **Points and Length:** - Point \( A \) marks the left edge of the beam. - Point \( B \) is located at 3 meters from point \( A \). - **Load Distribution:** - The load begins at 9 kN/m at point \( A \) and decreases uniformly to 0 kN/m at point \( B \). - This indicates a linearly decreasing distributed load. - **Applied Moment:** - A moment of 6 kN·m is applied at the end point \( B \) in a clockwise direction. ### Diagram Explanation 1. **Beam Representation:** - The beam is represented as a horizontal line, supported at point \( A \) and extending to point \( B \). 2. **Distributed Load:** - The distributed load is depicted by a series of vertical arrows. - Arrows at point \( A \) are fully spaced and intense (high density), representing the start of the distributed load at 9 kN/m. - Moving towards point \( B \), the density and size of the arrows decrease, showing the linear reduction of the load intensity to 0 kN/m. 3. **Applied Moment:** - At point \( B \), a clockwise curved arrow with a magnitude labeled 6 kN·m indicates the applied moment. ### Conclusion Understanding this diagram is crucial for analyzing the effects of a linearly varying distributed load and applied moment on beam structures. This includes calculating reactions at the supports, the shear force along the beam length, and the resulting bending moment distribution.
### Graph Description - Shear Force Diagram This graph is a Shear Force Diagram that illustrates the variation of shear force (V) along the length of a beam. The horizontal axis (x) represents the position along the beam in meters (m), while the vertical axis (V) represents the shear force in kilonewtons (kN). #### Axis Details: 1. **Horizontal Axis (x):** - The positions are marked from 0 to 3 meters. - Each division on the horizontal axis represents 0.5 meters. 2. **Vertical Axis (V):** - The shear force is marked from -15 kN to 15 kN. - Each division on the vertical axis represents an increment of 2.5 kN. #### Key Points: - The graph plots shear force values along the beam. - The positive shear force is plotted above the horizontal axis, and negative shear force is plotted below the horizontal axis. - The intersection of the x-axis and y-axis represents a shear force of 0 kN at the 0 m point. #### Description of the Graph: - The grid lines aid in determining the exact value of the shear force at specific positions along the beam. - The horizontal axis passing through the middle indicates the reference for zero shear force.
Transcribed Image Text:### Graph Description - Shear Force Diagram This graph is a Shear Force Diagram that illustrates the variation of shear force (V) along the length of a beam. The horizontal axis (x) represents the position along the beam in meters (m), while the vertical axis (V) represents the shear force in kilonewtons (kN). #### Axis Details: 1. **Horizontal Axis (x):** - The positions are marked from 0 to 3 meters. - Each division on the horizontal axis represents 0.5 meters. 2. **Vertical Axis (V):** - The shear force is marked from -15 kN to 15 kN. - Each division on the vertical axis represents an increment of 2.5 kN. #### Key Points: - The graph plots shear force values along the beam. - The positive shear force is plotted above the horizontal axis, and negative shear force is plotted below the horizontal axis. - The intersection of the x-axis and y-axis represents a shear force of 0 kN at the 0 m point. #### Description of the Graph: - The grid lines aid in determining the exact value of the shear force at specific positions along the beam. - The horizontal axis passing through the middle indicates the reference for zero shear force.
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