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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?
- -60KN (correct)
- 0KN
- 170KN
- 60KN
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?
- 170KN (correct)
- 60KN
- -170KN
- 0KN
What is the bending moment at point B for the beam ABCD?
What is the bending moment at point B for the beam ABCD?
- 60KNm
- -120KNm (correct)
- 0KNm
- -60KNm
Calculate the resultant bending moment at point C for beam ABCD.
Calculate the resultant bending moment at point C for beam ABCD.
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?
Flashcards
What is the Shear Force Diagram (SFD)?
What is the Shear Force Diagram (SFD)?
The Shear Force Diagram (SFD) represents the internal shear force acting at various points along the beam. It's a graphical representation of how the shear force changes along the beam's length. It can be positive or negative depending on the direction of the shear force.
What is the Bending Moment Diagram (BMD)?
What is the Bending Moment Diagram (BMD)?
The Bending Moment Diagram (BMD) represents the internal bending moment acting at various points along the beam. It's a graphical representation of how the bending moment changes along the beam's length. The BMD is crucial for assessing the strength of the beam, as it indicates where the bending stresses are highest.
How do we calculate the reactions at supports?
How do we calculate the reactions at supports?
To calculate the reactions at supports, we need to apply the principles of statics, mainly the equations of equilibrium. These equations ensure the summation of forces and moments in both horizontal and vertical directions equals zero. This ensures the beam remains in a state of static equilibrium.
How is the SFD plotted?
How is the SFD plotted?
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How is the BMD plotted?
How is the BMD plotted?
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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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