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Questions and Answers
In a partially constrained situation, why are the three equations of equilibrium not satisfied?
When is a rigid body considered improperly constrained?
What should be drawn to represent a particle isolated from its surroundings?
Which type of forces can act on a particle according to the text?
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In which case are statically determinate reactions present?
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What term describes a situation where the constraints provided by the supports are not enough to prevent movement?
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What type of reactions involve two unknowns and are usually represented by their x and y components?
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What type of reactions are caused by fixed supports that oppose any motion of the free body and constrain it completely?
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In a statically determinate situation, how many unknowns can be determined by solving the three equations of equilibrium?
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What is a situation where the number of unknowns exceeds the number of equilibrium equations available called?
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If a rigid body cannot move under any loading conditions, what is it said to be?
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What type of constraints involve more than three unknowns?
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What are the necessary and sufficient conditions for the equilibrium of a particle in terms of scalar equations?
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When both the force and the couple acting on a rigid body are zero, what state is the rigid body said to be in?
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How many unknowns can the three equilibrium equations in two dimensions be solved for?
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Which type of support or connection can prevent motion in one direction only?
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What type of reactions are exerted on a two-dimensional structure equivalent to a force with a known line of action?
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What term is used to describe the supports or connections that cause reactions equivalent to a force with a known line of action?
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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.
