Statically indeterminate (deflection)

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SUMMARY

The discussion centers on the application of deflection equations in statically indeterminate structures, specifically when to use maximum deflection equations versus simple deflection equations. It is established that one should utilize the most general deflection formula applicable to the beam and loading arrangement. In cases such as propped cantilevers, the maximum deflection formula can be derived from the general deflection equation by substituting the length of the cantilever. This approach ensures accurate calculations for reactions in statically indeterminate problems.

PREREQUISITES
  • Understanding of statically indeterminate structures
  • Familiarity with deflection equations in structural engineering
  • Knowledge of cantilever beam mechanics
  • Ability to evaluate loading arrangements on beams
NEXT STEPS
  • Study the general deflection equations for various beam types
  • Learn about propped cantilever beam analysis
  • Research specific maximum deflection formulas for different loading conditions
  • Practice solving statically indeterminate problems using deflection equations
USEFUL FOR

Structural engineers, civil engineering students, and professionals involved in the analysis and design of beams and load-bearing structures will benefit from this discussion.

feedingjax
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For these types of question, I know deflection equation is needed to find the reaction.
However, my question is that when should i use the max. deflection equation and when should i use only simple deflection equation for my calculation ?

Thank you very much!
23hrd5v.png

w18t5e.jpg


beam-deflection-formulae-1-728.jpg
 
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feedingjax said:
For these types of question, I know deflection equation is needed to find the reaction.
However, my question is that when should i use the max. deflection equation and when should i use only simple deflection equation for my calculation ?

Thank you very much!
23hrd5v.png

w18t5e.jpg


beam-deflection-formulae-1-728.jpg

I think you are trying to be too choosy with your equations here.

Don't worry about which particular cases to use the max. deflection formula to solve an indeterminate problem. Pick the most general deflection formula for a particular beam and loading arrangement. If the location of the redundant support in question requires the use of a max. deflection formula, as in the case of the propped cantilever, then substituting the length of the cantilever into the general deflection equation should give the same equation as that for the max. deflection.

The max. deflection formulas in the table above are all special cases of the general deflection equation for the type of loading indicated for the cantilever. You should be able to verify this by evaluating the cantilever formulas above for x = L.
 

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