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Questions and Answers
Which type of beam is supported at both ends and is free to rotate?
Which type of beam is supported at both ends and is free to rotate?
- Overhanging Beam
- Cantilever Beam
- Simply Supported Beam (correct)
- Fixed Beam
A beam is subjected to a uniformly distributed load (UDL). How does the shear force vary along the length of the beam?
A beam is subjected to a uniformly distributed load (UDL). How does the shear force vary along the length of the beam?
- Parabolically
- Cubically
- Constant
- Linearly (correct)
What is the sign convention for shear force if the resultant of the forces to the left of the section is upward?
What is the sign convention for shear force if the resultant of the forces to the left of the section is upward?
- Zero
- Negative
- Unpredictable
- Positive (correct)
In pure bending, what is the value of shear force?
In pure bending, what is the value of shear force?
For a cantilever beam with a point load at the free end, how does the bending moment vary along its length?
For a cantilever beam with a point load at the free end, how does the bending moment vary along its length?
A simply supported beam has a concentrated load at its center. What are the reactions at the supports?
A simply supported beam has a concentrated load at its center. What are the reactions at the supports?
What type of loading is represented by 'UVL'?
What type of loading is represented by 'UVL'?
If a beam deflects such that the top fibers are in compression and the bottom fibers are in tension, what type of bending moment is it experiencing?
If a beam deflects such that the top fibers are in compression and the bottom fibers are in tension, what type of bending moment is it experiencing?
Under what condition is a beam said to be in a state of pure bending?
Under what condition is a beam said to be in a state of pure bending?
A cantilever beam of length L carries a point load W at the free end. What is the bending moment at the fixed end?
A cantilever beam of length L carries a point load W at the free end. What is the bending moment at the fixed end?
What is the bending moment at the free end of a cantilever beam?
What is the bending moment at the free end of a cantilever beam?
For a simply supported beam with a uniformly distributed load (UDL) of 'w' per unit length over the entire span 'L', what is the maximum bending moment?
For a simply supported beam with a uniformly distributed load (UDL) of 'w' per unit length over the entire span 'L', what is the maximum bending moment?
What is the characteristic of a 'fixed' beam?
What is the characteristic of a 'fixed' beam?
Which of the following is true for an overhanging beam?
Which of the following is true for an overhanging beam?
How is the bending moment calculated?
How is the bending moment calculated?
What does a bending moment diagram (BMD) represent?
What does a bending moment diagram (BMD) represent?
Which type of beam has more than two supports along its length?
Which type of beam has more than two supports along its length?
For a uniformly varying load (UVL) on a beam, how does the intensity of the load change?
For a uniformly varying load (UVL) on a beam, how does the intensity of the load change?
What does a positive bending moment typically indicate?
What does a positive bending moment typically indicate?
How is shear force related to the load applied on a beam?
How is shear force related to the load applied on a beam?
If the bending moment is constant over a certain length of a beam, what does that signify about the shear force in that region?
If the bending moment is constant over a certain length of a beam, what does that signify about the shear force in that region?
Which of the following diagrams helps in visualizing the internal forces in a beam?
Which of the following diagrams helps in visualizing the internal forces in a beam?
What is the correct expression for the relationship between bending moment (M), shear force (V), and distributed load (w)?
What is the correct expression for the relationship between bending moment (M), shear force (V), and distributed load (w)?
What causes hogging in a beam?
What causes hogging in a beam?
How does the bending moment at a section affect the stress distribution across the cross-section?
How does the bending moment at a section affect the stress distribution across the cross-section?
A beam of length 'L' is fixed at both ends and carries a uniformly distributed load 'w' per unit length. What is the bending moment at the supports?
A beam of length 'L' is fixed at both ends and carries a uniformly distributed load 'w' per unit length. What is the bending moment at the supports?
Which of the following loads causes only shear force in a beam but no bending moment?
Which of the following loads causes only shear force in a beam but no bending moment?
For a pure bending condition in a beam, what is consistent along the length of the beam?
For a pure bending condition in a beam, what is consistent along the length of the beam?
Which support type provides both horizontal and vertical reaction forces as well as a moment reaction?
Which support type provides both horizontal and vertical reaction forces as well as a moment reaction?
Flashcards
Shear force and bending moment diagrams
Shear force and bending moment diagrams
Diagrams showing the variation of shear force and bending moment along the length of a beam.
Simply supported beam
Simply supported beam
A beam supported at both ends.
Cantilever beam
Cantilever beam
A beam fixed at one end and free at the other.
Overhanging beam
Overhanging beam
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Continuous beam
Continuous beam
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Point load
Point load
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Uniformly Distributed Load (UDL)
Uniformly Distributed Load (UDL)
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Uniformly Varying Load (UVL)
Uniformly Varying Load (UVL)
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Positive Shear Force
Positive Shear Force
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Sagging Bending Moment
Sagging Bending Moment
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Hogging Bending Moment
Hogging Bending Moment
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Pure Bending
Pure Bending
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Study Notes
- MEC201 Solid Mechanics, Unit 4 focuses on shear force and bending moment.
- Diagrams are used to represent the variation of shear force (SF) and bending moment (BM) along a beam's length.
Types Of Beams
- Cantilever beams have one end fixed and the other end free.
- Simply supported beams are supported at both ends.
- Overhanging beams extend beyond one or both supports.
- Fixed beams are supported/fixed at both ends.
- Continuous beams have more than two supports.
Types Of Loads
- Point loads (i.e W(N)) are concentrated at a single point.
- Uniformly Distributed Loads (UDL) are evenly spread across a section of the beam, measured in N/m.
- Uniformly Varying Loads (UVL) increase (or decrease) linearly across the section.
Sign Conventions
- Shear force is considered positive if the resultant of forces to the left of a section act upwards.
- Bending moment is positive if it causes sagging (i.e. "happy" curvature).
- Bending moment is negative if it causes hogging (i.e. "sad" curvature).
Hogging
- A negative bending moment results in hogging.
Sagging
- A positive bending moment results in sagging.
Pure Bending
- A beam is in a state of pure bending when shear forces are zero across any cross-section perpendicular to its longitudinal axis.
- This implies F = 0, and dM/dX = F = 0
- Thus, M is constant.
Shear Force & Bending Moment Diagrams for Cantilever Beams with Point Loads
- Key aspects to note are the specific calculations and shapes of the diagrams for cantilever beams under point loads, UDLs, and UVLs to accurately represent internal forces and moments.
Uniformly Distributed Load (UDL)
- Focus on how to calculate SFD and BMD.
Uniformly Varying Load (UVL)
- Focus on how to calculate SFD and BMD.
Simply Supported Beam
- First find the reaction forces and mark them on the diagram.
- Bending moment at points A & B is zero.
Overhanging Beam Notes
- Bending moment at points C and E is zero.
Simply Supported Beam with Moment Couple Notes
- Focus on how to calculate SFD and BMD.
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