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Questions and Answers
What must be true for a rigid body to be in equilibrium?
What must be true for a rigid body to be in equilibrium?
- Both the net force and net moment about any arbitrary point must be zero. (correct)
- Only the net moment about one specific point is zero.
- The body must have at least one force acting in the opposite direction.
- The net force must be zero, but the net moment can be non-zero.
Which type of support prevents both translation in one direction and rotation?
Which type of support prevents both translation in one direction and rotation?
- Fixed Support (correct)
- Slider Support
- Roller Support
- Pin Support
What characterizes a statistically determinate structure?
What characterizes a statistically determinate structure?
- It cannot be solved using equilibrium equations.
- It has more unknowns than equations of equilibrium.
- It has more equations of equilibrium than unknowns.
- It has exactly the same number of equations of equilibrium as unknowns. (correct)
Which constraint allows for rotation and has forces as reactions?
Which constraint allows for rotation and has forces as reactions?
What type of constraint means that the rigid body could not possibly move?
What type of constraint means that the rigid body could not possibly move?
Flashcards
What is a Rigid Body?
What is a Rigid Body?
A rigid body is an idealized object that doesn't deform under the influence of forces. All particles within the body maintain fixed distances from each other.
Concurrent vs. Non-concurrent Forces
Concurrent vs. Non-concurrent Forces
Concurrent forces act on a single point, while non-concurrent forces act on different points.
Support Reactions
Support Reactions
A support prevents movement, creating a force or moment on the body. Cables, contacting surfaces, roller supports, pin supports, sliders, and fixed supports have different numbers of unknowns (forces or moments they can exert).
Pin Connections
Pin Connections
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Constraint and Determinacy
Constraint and Determinacy
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Study Notes
Rigid Body Statics
- Statics calculates external forces acting on rigid bodies in equilibrium.
- A rigid body is a collection of particles with fixed positions relative to each other.
Conditions of Rigid-Body Equilibrium
- Concurrent forces act on a single point.
- Forces can be non-concurrent.
- Equilibrium requires zero net force and zero net moment about any point.
Support Reactions
- Supports resisting translation create reaction forces in the direction of prevention.
- Supports preventing rotation create a couple moment.
Types of Supports and Unknown Variables
- Cables - 1 unknown
- Contacting surfaces - 1 unknown
- Rollers - 1 unknown
- Pins - 2 unknowns
- Sliding pins - 1 unknown
- Fixed supports - 3 unknowns
Reactions and Moments
- Pin connections allow rotation.
- Pin reactions are forces, not moments.
Constraints and Determinacy
- Completely constrained: Rigid body cannot move.
- Partially constrained: Insufficient constraints for movement prevention.
- Statically determinate: Enough equilibrium equations to solve unknown forces.
- Statically indeterminate: More unknowns than equilibrium equations.
- Structures aim for complete constraint and static determinacy.
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