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Questions and Answers
Match each support type with its corresponding description:
Match each support type with its corresponding description:
Simply Supported = A beam resting on supports at both ends, allowing rotation but resisting vertical movement. Cantilever = A beam fixed at one end and free at the other, resisting both rotation and vertical movement at the fixed end. Overhanging = A beam that extends beyond its supports, creating both a simply supported section and a cantilevered section.
Which of the following statements accurately describes the behavior of a simply supported beam?
Which of the following statements accurately describes the behavior of a simply supported beam?
- It is fixed at one end and free at the other.
- It is rigidly fixed at both ends, preventing rotation and vertical movement.
- It extends beyond its supports, creating a cantilevered section.
- It is supported at both ends, allowing rotation but resisting vertical movement. (correct)
A cantilever beam is characterized by being supported at both ends, similar to a bridge.
A cantilever beam is characterized by being supported at both ends, similar to a bridge.
False (B)
Describe the primary difference between a statically determinate and statically indeterminate structure.
Describe the primary difference between a statically determinate and statically indeterminate structure.
For a structure to be statically __________, the number of unknown reactions must be less than or equal to the number of equilibrium equations.
For a structure to be statically __________, the number of unknown reactions must be less than or equal to the number of equilibrium equations.
What condition defines an unstable structure in terms of reactions (R) and number of equilibrium equations (N)?
What condition defines an unstable structure in terms of reactions (R) and number of equilibrium equations (N)?
Improperly constrained structures always maintain stability regardless of load application.
Improperly constrained structures always maintain stability regardless of load application.
Explain why a structure is considered 'improperly constrained' when force reactions converge at a single point.
Explain why a structure is considered 'improperly constrained' when force reactions converge at a single point.
A ________ support resists both vertical and horizontal forces but allows rotation, whereas a fixed support resists vertical and horizontal forces and also prevents ________.
A ________ support resists both vertical and horizontal forces but allows rotation, whereas a fixed support resists vertical and horizontal forces and also prevents ________.
For a 2D problem, how many independent equilibrium equations can be applied to solve for unknown forces and moments?
For a 2D problem, how many independent equilibrium equations can be applied to solve for unknown forces and moments?
In a rigid frame, joints are assumed to allow free rotation without transferring any moment.
In a rigid frame, joints are assumed to allow free rotation without transferring any moment.
Define the term 'hinge' within the context of structural analysis and explain its effect on moment transfer.
Define the term 'hinge' within the context of structural analysis and explain its effect on moment transfer.
The determinacy of a structure is evaluated by comparing the number of unknowns (reactions) with the number of available __________ __________.
The determinacy of a structure is evaluated by comparing the number of unknowns (reactions) with the number of available __________ __________.
Which type of support is most suitable for allowing thermal expansion of a long beam without inducing significant stress?
Which type of support is most suitable for allowing thermal expansion of a long beam without inducing significant stress?
A statically indeterminate structure will always experience lower stresses compared to a statically determinate structure under the same loading conditions.
A statically indeterminate structure will always experience lower stresses compared to a statically determinate structure under the same loading conditions.
Flashcards
Roller Support
Roller Support
A support that resists vertical forces but allows rotation. It has one unknown reaction force.
Pinned Support
Pinned Support
A support that resists both vertical and horizontal forces, but allows rotation. It has two unknown reaction forces.
Fixed Support
Fixed Support
A support that resists vertical and horizontal forces and prevents rotation. It has three unknown reaction forces.
Simply Supported Beam
Simply Supported Beam
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Cantilever Beam
Cantilever Beam
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Overhanging Beam
Overhanging Beam
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Statically Determinate
Statically Determinate
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Statically Unstable
Statically Unstable
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Statically Indeterminate
Statically Indeterminate
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Improperly Constrained
Improperly Constrained
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Study Notes
- There are three types of supports for beams: simply supported, cantilever, and overhanging.
Homework 5 & 6
- Problem 2.29, which is similar to problem 2.28 and considers joint C, involves calculating forces by setting the sum of forces in the x and y directions to zero.
- Trigonometric functions are used to resolve forces into x and y components to solve for unknown forces Sca and Scb.
- Problem 2.30 discusses a eyebolt in equilibrium, and it's analyzed as a point in space.
- Two unknowns, P and α, can thus be solved with two equilibrium equations ΣFx=0 and ΣFy=0.
- Problem considers joint A, resolving forces and then solving for an angle.
Reading assignment
- Book 1 includes pages 84-94.
- Book 2 includes chapter 13.
Determinacy and Stability
- There are three equations of equilibrium in a 2D problem: ΣFx=0, ΣFy=0, and ΣM=0.
- The total number of unknowns equals R = R' + 2 x the number of hinges, and the number of equilibrium equations is 3 x N.
- Reactions with equations of equilibrium are determinate when 3N = R (statically determined).
- A structure is statistically determinate if this is the case.
- Rigid body moves and will not stand if 3N > R (unstable).
- Equations of equilibrium alone aren't enough if 3N < R (statically indeterminate).
- Compatibility equations are used in this case.
- Instability can result from improper constraints, which is also when force reactions converge at one point.
Homework 7
- Refers to the provided link
- Using the video to define a roller, pinned and fixed supports
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Description
Exploration of beam supports (simply supported, cantilever, overhanging) and equilibrium equations (ΣFx=0, ΣFy=0, ΣM=0) in 2D problems. Includes homework problem-solving with trigonometric functions and joint analysis. Reading assignment spans pages 84-94 of Book 1 and chapter 13 of Book 2.
