Constraints and Statical Determinacy

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SUMMARY

This discussion focuses on identifying redundant constraints in mechanical systems under specific loading conditions. The scenarios presented involve a fixed support at A with a cable between B and C, a smooth pin support at A with the same cable, and a single thrust bearing at A. It is concluded that the first and last configurations exhibit redundant constraints, rendering them statically indeterminate, while the second configuration does not.

PREREQUISITES
  • Understanding of statics and equilibrium in mechanical systems
  • Familiarity with concepts of redundant constraints and static indeterminacy
  • Knowledge of support types: fixed supports, smooth pins, and thrust bearings
  • Ability to analyze loading conditions and their effects on structures
NEXT STEPS
  • Study the principles of static indeterminacy in mechanical systems
  • Learn about different types of supports and their implications on structural analysis
  • Explore methods for determining redundancy in constraints
  • Review case studies involving fixed supports and cables in engineering applications
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Mechanical engineers, structural analysts, and students studying statics who need to understand the implications of redundant constraints in load-bearing systems.

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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.
 

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agree about a and b, but not about c.
 

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