Number of total reactions in a structure

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SUMMARY

The total number of reactions in a structure, as discussed, is determined by analyzing the support types and internal reactions. In the given example, there are 3 reactions from the internal structure, 2 from a pin support, and 1 from a roller support, leading to a total of 9 reactions. The method involves counting unique internal reactions only once and adding them to the reactions from supports. This systematic approach ensures accurate calculation of total reactions in structural analysis.

PREREQUISITES
  • Understanding of structural analysis concepts
  • Familiarity with support types (pin and roller)
  • Knowledge of internal reaction forces in closed loops
  • Basic principles of equilibrium in mechanics
NEXT STEPS
  • Study the principles of static equilibrium in structures
  • Learn about different types of structural supports and their reactions
  • Explore methods for calculating internal reaction forces in frames
  • Investigate advanced topics in structural analysis, such as finite element methods
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Students and professionals in civil engineering, structural engineering, and mechanics who are involved in analyzing and calculating reactions in structural systems.

fonseh
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Homework Statement


In the example A , Why the author stated the total reactions = 9 only ? How to determine the total reactions for this type of questions ?

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The Attempt at a Solution


we can see that there is a total of 3 reactions (vertical , horizontal and moment) at the cut of the 4 parts , right (circled part) , and 3 reactions below . So , the total reactions is 4x3 + 3 = 15.
 

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When ever you have a closed loop as in this frame, you cut it, and you count the set of internal reactions (only once) as reaction forces.

Looking at the loop we get a total of 3+3 reactions (note that the internal reactions of AD and DA are the same and we do not count them as 6 , but 3 unique ones)
Looking at the supports , one is a pin ∴ 2 reactions and the other is a roller ∴ 1 reaction.

In conclusion, we have 3+3+2+1 =9 reactions
 
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