Rigid Body Statics Quiz

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Questions and Answers

What must be true for a rigid body to be in equilibrium?

The net force and net moment about any arbitrary point must be zero. (correct)
The net force is equal to the weight of the body.
The body must be under a uniform load.
Only the net moment needs to be considered.

Which type of support can develop three unknown reactions?

Slider or Constrained Pin
Roller Support
Fixed Support (correct)
Pin Support

What characterizes a completely constrained rigid body?

It is held in place by various dynamic forces.
It can move but not rotate.
It can rotate freely about any axis.
It is unable to experience any form of motion. (correct)

What distinguishes statistically determinate systems from statistically indeterminate systems?

<p>Determinate systems have exactly as many unknowns as equations of equilibrium. (D)</p> Signup and view all the answers

What is true about pin connections in a rigid body?

<p>They allow rotation but develop only forces, not moments. (C)</p> Signup and view all the answers

Flashcards

What is a rigid body in statics?

A rigid body is an object that is assumed to maintain its shape and size under the influence of forces. It means that the relative positions of all the particles making up the rigid body don't change when forces are applied.

What are the conditions for rigid body equilibrium?

For a rigid body to be in equilibrium, both the net force and the net moment acting on it must be zero. This means the object isn't moving in any direction (translation) or rotating (rotation).

What are support reactions?

A support reaction is a force or moment exerted by a support on a rigid body to prevent its motion or rotation. The type of support determines the number of unknown reactions.

What is the difference between statistically determinate and indeterminate structures?

A structure is considered statistically determinate if the number of unknown forces or moments can be solved using the equations of equilibrium. If the equations are insufficient to solve for unknowns, then the structure is statistically indeterminate.

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Explain 'completely constrained' and 'partially constrained' structures.

A completely constrained rigid body has enough supports to prevent any possible motion. A partially constrained body has insufficient supports and can move. We want our structures to be completely constrained and statistically determinate for a stable solution.

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Study Notes

Rigid Body Statics

Statics calculates external forces on rigid bodies at equilibrium.
A rigid body is a combination of many particles fixed relative to each other.

Conditions of Rigid-body Equilibrium

Concurrent forces act on a particle.
Non-concurrent forces are also considered for rigid body equilibrium, ensuring it doesn't rotate.
Net force and moment about any point must equal zero for equilibrium.

Support Reactions

Supports preventing translation create a reaction force in that direction.
Supports preventing rotation create a couple moment.

Types of Supports and Unknown Reactions

Cables: 1 unknown
Contacting Surfaces: 1 unknown
Roller Support: 1 unknown
Pin Support: 2 unknowns
Slider/Constrained Pin: 1 unknown
Fixed Support: 3 unknowns

Reactions and Constraints

Completely Constrained: Rigid body cannot move
Partially Constrained: Constraints aren't sufficient to prevent the body from moving
Statically Determinate: When enough equilibrium equations can solve for unknowns.
Statically Indeterminate: When more unknowns than equilibrium equations.
Structures should be optimally constrained and determinate.