# Constraints and Statical Determinacy

• sami23
In summary, the conversation discusses different loading conditions and the possibility of redundant constraints. It is mentioned that F_1 and F_2 are applied, known forces. The first and third choices seem to have redundant constraints, while the second choice is not agreed upon.
sami23

## Homework Statement

Which of these bodies has redundant constraints for the given loading conditions? F_1 and F_2 are applied, known forces. In the first choice, the support at A is fixed and a cable connects points B and C. In the second choice, the support at A is a smooth pin, and a cable connects points B and C. In the third choice, the support at A is a single thrust bearing, and a cable connects points B and C.
Check all that apply.

## Homework Equations

Redundant constraints - when a body has more supports than necessary to hold it in equilibrium it becomes statically indeterminate.

## The Attempt at a Solution

the first and last seem to have redundant constraints.

#### Attachments

• constraints a.jpg
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• constraints b.jpg
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• constraints c.jpg
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## What is the difference between constraints and statical determinacy?

Constraints are restrictions placed on a system that limit its motion or behavior. Statical determinacy refers to a system in which all forces and reactions can be determined using equations of static equilibrium. In other words, the equations of static equilibrium are sufficient to solve for all the unknown forces in a statically determinate system.

## What are some examples of constraints in a system?

Some examples of constraints include fixed supports, rollers, and hinges. These are physical connections or restrictions that limit the motion of a system.

## How do constraints affect the analysis of a system?

Constraints can affect the analysis of a system by adding additional unknown forces and reactions. These unknowns must be solved for using additional equations or techniques, such as the method of virtual work.

## Can a system be both constrained and statically determinate?

Yes, a system can be both constrained and statically determinate. The constraints may limit the motion of the system, but the equations of static equilibrium are still sufficient to solve for all the unknown forces and reactions.

## What happens if a system is over-constrained?

If a system is over-constrained, it means that there are more constraints than necessary to limit the motion of the system. This can lead to a statically indeterminate system, where the equations of static equilibrium are not enough to solve for all the unknown forces and reactions. Additional information or assumptions may be needed to analyze an over-constrained system.

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