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Engineering
Civil Engineering
3 kN/m 3 m B 3 m 6 kN/m

3 kN/m 3 m B 3 m 6 kN/m

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.
### Analyzing Beam Loading This diagram represents a beam (ABC) subjected to various loads and is a common example used in structural engineering. #### Beam Description: 1. **Beam Structure:** - The beam is supported at two points, designated as A (left end) and C (right end). - Point A is supported by a pinned support, allowing rotation but not translation. - Point C is supported by a roller support, allowing horizontal movement but not vertical. 2. **Loading Conditions:** - **Distributed Load:** A uniformly distributed load of 3 kN/m is applied over the segment AB of the beam, extending from point A to point B. - **Varying Load:** A linearly varying distributed load starts from point B with a value of 3 kN/m and increases linearly to 6 kN/m at point C. This load acts on segment BC of the beam. #### Dimensions and Notations: - **Span AB:** 3 meters - **Span BC:** 3 meters #### Analysis: 1. **Uniformly Distributed Load (AB):** - The load is evenly distributed along the length of 3 meters (from A to B) with an intensity of 3 kN/m. 2. **Linearly Varying Load (BC):** - This load starts at 3 kN/m at B and increases uniformly to 6 kN/m at C across the 3-meter length of BC. Understanding such diagrams is crucial for determining reactions at the supports and internal moments and shear forces within the beam. The areas of evenly and variably distributed loads influence how the load transfers through the beam and affects bending and deflection.
Transcribed Image Text:### Analyzing Beam Loading This diagram represents a beam (ABC) subjected to various loads and is a common example used in structural engineering. #### Beam Description: 1. **Beam Structure:** - The beam is supported at two points, designated as A (left end) and C (right end). - Point A is supported by a pinned support, allowing rotation but not translation. - Point C is supported by a roller support, allowing horizontal movement but not vertical. 2. **Loading Conditions:** - **Distributed Load:** A uniformly distributed load of 3 kN/m is applied over the segment AB of the beam, extending from point A to point B. - **Varying Load:** A linearly varying distributed load starts from point B with a value of 3 kN/m and increases linearly to 6 kN/m at point C. This load acts on segment BC of the beam. #### Dimensions and Notations: - **Span AB:** 3 meters - **Span BC:** 3 meters #### Analysis: 1. **Uniformly Distributed Load (AB):** - The load is evenly distributed along the length of 3 meters (from A to B) with an intensity of 3 kN/m. 2. **Linearly Varying Load (BC):** - This load starts at 3 kN/m at B and increases uniformly to 6 kN/m at C across the 3-meter length of BC. Understanding such diagrams is crucial for determining reactions at the supports and internal moments and shear forces within the beam. The areas of evenly and variably distributed loads influence how the load transfers through the beam and affects bending and deflection.
This image displays a Cartesian coordinate system, frequently used in mathematics to graph and analyze algebraic equations. Here's a detailed description of the graph: ### Detailed Description 1. **Axes**: - **X-axis (Horizontal axis)**: Labeled as 'X', extending from -6 to 6. - **Y-axis (Vertical axis)**: Labeled as 'Y', extending from -12 to 12. 2. **Grid Lines**: - **Horizontal and Vertical Lines**: These lines form a grid with intervals of 1 unit, both horizontally and vertically. The lines make it easier to pinpoint exact coordinates on the graph. - The primary grid lines intersect at integer values for both axes. 3. **Origin**: - **(0,0)**: This point lies where the X-axis and Y-axis intersect. It's the center of the coordinate plane. ### Usage in Educational Context - **Teaching Graphing**: This coordinate system can be used to teach students how to plot points, lines, and curves. - **Analyzing Functions**: Students can use this graph to analyze various mathematical functions, identify their properties, and understand their behaviors. - **Solving Equations**: It serves as a tool to visualize solutions to algebraic equations. Understanding and using the Cartesian coordinate system is crucial for various mathematical and scientific analyses. It forms the foundation for more advanced topics like geometry, calculus, and physics.
Transcribed Image Text:This image displays a Cartesian coordinate system, frequently used in mathematics to graph and analyze algebraic equations. Here's a detailed description of the graph: ### Detailed Description 1. **Axes**: - **X-axis (Horizontal axis)**: Labeled as 'X', extending from -6 to 6. - **Y-axis (Vertical axis)**: Labeled as 'Y', extending from -12 to 12. 2. **Grid Lines**: - **Horizontal and Vertical Lines**: These lines form a grid with intervals of 1 unit, both horizontally and vertically. The lines make it easier to pinpoint exact coordinates on the graph. - The primary grid lines intersect at integer values for both axes. 3. **Origin**: - **(0,0)**: This point lies where the X-axis and Y-axis intersect. It's the center of the coordinate plane. ### Usage in Educational Context - **Teaching Graphing**: This coordinate system can be used to teach students how to plot points, lines, and curves. - **Analyzing Functions**: Students can use this graph to analyze various mathematical functions, identify their properties, and understand their behaviors. - **Solving Equations**: It serves as a tool to visualize solutions to algebraic equations. Understanding and using the Cartesian coordinate system is crucial for various mathematical and scientific analyses. It forms the foundation for more advanced topics like geometry, calculus, and physics.
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