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Questions and Answers
What type of beam is supported only at its ends and is free to deflect in the middle under load?
What type of beam is supported only at its ends and is free to deflect in the middle under load?
- Cantilever beam
- Simply supported beam (correct)
- Overhanging beam
- Fixed beam
In the context of beam analysis, what does the bending moment represent?
In the context of beam analysis, what does the bending moment represent?
- The internal force causing shear
- The axial compression in the beam
- The rotational effect of forces acting on the beam (correct)
- The torque applied at a specific point
Which condition correctly describes the relationship between shear force, bending moment, and loading intensity?
Which condition correctly describes the relationship between shear force, bending moment, and loading intensity?
- Bending moment decreases linearly with increasing loading intensity
- Bending moment is the integral of the shear force over a length (correct)
- Loading intensity is the derivative of the bending moment with respect to distance
- Shear force is the product of bending moment and loading intensity
Which type of loading condition typically results in a cantilever beam exhibiting a maximum negative bending moment at the fixed support?
Which type of loading condition typically results in a cantilever beam exhibiting a maximum negative bending moment at the fixed support?
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What is the primary purpose of constructing shear force and bending moment diagrams for beams?
What is the primary purpose of constructing shear force and bending moment diagrams for beams?
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Study Notes
Axial Force, Shear Force, & Bending Moment Diagrams
- Axial Force: A force that acts along the axis of a structural member, causing tension or compression.
- Shear Force: A force that acts perpendicular to the axis of a structural member, causing shearing or sliding.
- Bending Moment: A moment that tends to bend a structural member, causing curvature.
- Beams: Structural elements designed to resist bending moments and shear forces.
Loading and Support Conditions
- Simply Supported Beams: Beams supported at two points, allowing rotation at the supports.
- Cantilever Beams: Beams fixed at one end and free at the other, allowing no rotation at the fixed end.
- Overhang Beams: Beams that extend beyond their supports, creating unbalanced moment loads.
Types of Loadings
- Concentrated Loads: Loads that are applied at a specific point on the structure, represented as a single force.
- Uniformly Distributed Loads: Loads spread evenly across a length of the structure, represented as a force per unit length.
- Varying Loads: Loads that change in intensity along the length of the structure.
Relation between Shear Force, Bending Moment & Loading Intensity
- Shear Force Diagram: The graphical representation of the shear force along the length of a beam.
- Bending Moment Diagram: The graphical representation of the bending moment along the length of a beam.
- Shear Force and Bending Moment Relationships:
- The slope of the shear force diagram equals the loading intensity.
- The area under the shear force diagram equals the change in bending moment.
- The maximum bending moment occurs where the shear force is zero.
Key Concepts
- Equilibrium: The summation of forces and moments acting on a beam must be zero.
- Sign Convention: To ensure consistency, a standard sign convention is used for shear forces and bending moments.
- Applications: Understanding these diagrams is crucial for designing safe and structurally sound beams.
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