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Questions and Answers
What is the value of the shear force at point A for beam ABCD?
What is the value of the shear force at point A for beam ABCD?
Which of the following represents the shear force between points B and C for beam ABCD?
Which of the following represents the shear force between points B and C for beam ABCD?
What is the bending moment at point B for the beam ABCD?
What is the bending moment at point B for the beam ABCD?
Calculate the resultant bending moment at point C for beam ABCD.
Calculate the resultant bending moment at point C for beam ABCD.
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What are the values of the reactions at supports B and C respectively in Example 2?
What are the values of the reactions at supports B and C respectively in Example 2?
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Study Notes
Example 1: Theory of Structures IA
- Beam ABCD: Simply supported at B and C, with a point load (60 kN) at A, a distributed load (60 kN/m) between B and C, and a moment (80 kNm) at D.
- Calculations: Reactions at supports (RB, RC) were calculated using equilibrium equations (ΣM = 0, ΣFy = 0).
- Shear Force Diagram (SFD): Shows variation of shear force along the beam. Calculated values at key points (A, B, C, D) are included. Key feature is the change in shear force due to the point load and distributed load.
- Bending Moment Diagram (BMD): Shows variation of bending moment along the beam. Calculated values at key points (A, B, C, D) are included. Bending moment changes due to the point load and distributed load, as well as the applied moment. Important to note points where the bending moment changes from positive to negative (or vice versa) and the calculation of the maximum/minimum moment.
Example 2: Shear and Bending Moment Diagrams
- Beam Description: A beam with multiple point loads and a uniformly distributed load. Supports at points B and C. Dimensions and forces are given.
- Calculations: Equilibrium equations (ΣM =0, ΣFy=0) used to find reaction forces at supports (Rb, Rc).
- Diagram Creation: Method used to plot SFD and BMD: values at key locations (supports, points with significant changes in load) are calculated, and the shape of the diagrams is depicted (straight lines, parabolic segments,etc.). Note, changes in load cause changes in the shape of the diagram.
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Description
Explore the fundamentals of shear and bending moment diagrams in structural analysis with this quiz. You'll calculate reactions at supports and analyze the variation of shear force and bending moment along a simply supported beam under various loads. Test your understanding of key concepts and calculations essential for structural engineering.
