Rigid Body Constraints Quiz

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Questions and Answers

In a partially constrained situation, why are the three equations of equilibrium not satisfied?

There are fewer unknowns than equations (correct)

The object is not at rest

The supports are excessive

The object is too heavy

When is a rigid body considered improperly constrained?

When the supports must be either concurrent or parallel (correct)

When there are no supports provided

When the object is free to move in any direction

When there is an excess of constraints

What should be drawn to represent a particle isolated from its surroundings?

Outlined shape (correct)

Dotted outline

Solid shape

No shape needed

Which type of forces can act on a particle according to the text?

Active forces and reactive forces Signup and view all the answers

In which case are statically determinate reactions present?

When all equilibrium equations are satisfied Signup and view all the answers

What term describes a situation where the constraints provided by the supports are not enough to prevent movement?

Partially constrained Signup and view all the answers

What type of reactions involve two unknowns and are usually represented by their x and y components?

Reactions equivalent to a force of unknown direction and magnitude Signup and view all the answers

What type of reactions are caused by fixed supports that oppose any motion of the free body and constrain it completely?

Reactions equivalent to a force and a couple Signup and view all the answers

In a statically determinate situation, how many unknowns can be determined by solving the three equations of equilibrium?

Three unknowns Signup and view all the answers

What is a situation where the number of unknowns exceeds the number of equilibrium equations available called?

Statically indeterminate Signup and view all the answers

If a rigid body cannot move under any loading conditions, what is it said to be?

Completely constrained Signup and view all the answers

What type of constraints involve more than three unknowns?

Partial constraints Signup and view all the answers

What are the necessary and sufficient conditions for the equilibrium of a particle in terms of scalar equations?

Fx = 0, Fy = 0 Signup and view all the answers

When both the force and the couple acting on a rigid body are zero, what state is the rigid body said to be in?

Equilibrium Signup and view all the answers

How many unknowns can the three equilibrium equations in two dimensions be solved for?

Three Signup and view all the answers

Which type of support or connection can prevent motion in one direction only?

Rollers Signup and view all the answers

What type of reactions are exerted on a two-dimensional structure equivalent to a force with a known line of action?

Horizontally opposite reactions Signup and view all the answers

What term is used to describe the supports or connections that cause reactions equivalent to a force with a known line of action?

Partial constraints Signup and view all the answers

Study Notes

Types of Reactions

Reactions Equivalent to a Force of Unknown Direction and Magnitude:
- Caused by frictionless pins in fitted holes, hinges, and rough surfaces
- Involve two unknowns, usually represented by their x and y components
Reactions Equivalent to a Force and a Couple:
- Caused by fixed supports that oppose any motion of the free body and thus constrain it completely
- Involve three unknowns, usually consisting of the two components of the force and the moment of the couple

Statically Indeterminate Reactions and Partial Constraints

Completely Constrained and Statically Determinate:
- Rigid body is completely constrained and cannot move under the given loads or any other loading conditions
- Reactions involve three unknowns and can be determined by solving the three equations of equilibrium
Statically Indeterminate:
- Number of unknowns exceeds the number of equilibrium equations available
Partially Constrained:
- Constraints provided by the supports are not sufficient to keep the object from moving
- Three equations of equilibrium are not satisfied, and there are fewer unknowns than equations
Improperly Constrained:
- Rigid body is improperly constrained whenever the supports are arranged in such a way that the reactions must be either concurrent or parallel

Drawing a Free-Body Diagram

Draw outlined shape of the particle
Imagine the particle to be isolated or cut "free" from its surroundings
Show all forces, including active forces and reactive forces
Identify each force with its proper magnitude and direction

Equilibrium of a Particle

Resolving each force F into rectangular components, we have (Fxi+ Fyj)= 𝟎 or (Fx)i+(Fy)j = 𝟎
Necessary and sufficient conditions for the equilibrium of a particle are Fx = 𝟎 and Fy = 𝟎
When the force and the couple are both equal to zero, the external forces form a system equivalent to zero, and the rigid body is said to be in equilibrium

Equations of Equilibrium in Two Dimensions

Fx = 𝟎, Fy = 𝟎, and M=𝟎, where A is any point in the plane of the structure
These three equations can be solved for no more than three unknowns

Reactions for a Two-Dimensional Structure

Reactions fall into three categories that correspond to three types of supports or connections
Reactions Equivalent to a Force with a Known Line of Action:
- Caused by rollers, rockers, frictionless surfaces, short links and cables, collars on frictionless rods, and frictionless pins in slots
- Each of these supports and connections can prevent motion in one direction only

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Description

Test your knowledge on partially constrained and improperly constrained rigid bodies, where supports may not provide enough constraints or are improperly arranged. Understand when the equations of equilibrium are not satisfied in these scenarios.