What is the formula for calculating frame deflection in a beam problem?

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SUMMARY

The formula for calculating frame deflection in a beam problem is definitively established as (4F(L^3))/3EI. This conclusion arises from considering the contributions of deflection at points E and F, where the total deflection at point C is derived by summing the individual deflections. The initial miscalculation of (2FL(^3))/3EI was corrected by accounting for the deflection due to the applied force F and the reaction force Ra. The discussion emphasizes the importance of accurately applying beam deflection equations in structural analysis.

PREREQUISITES
  • Understanding of beam deflection principles
  • Familiarity with the variables in the equation: F (force), L (length), E (modulus of elasticity), I (moment of inertia)
  • Knowledge of standard beam problem simplifications
  • Ability to analyze deflections at multiple points in a beam
NEXT STEPS
  • Study the derivation of beam deflection formulas in structural engineering
  • Learn about the impact of varying load conditions on beam deflection
  • Explore the application of the moment of inertia in beam design
  • Investigate advanced topics in beam theory, such as composite beams and their deflection characteristics
USEFUL FOR

Structural engineers, civil engineering students, and professionals involved in beam design and analysis will benefit from this discussion, particularly those focused on accurately calculating deflections in structural frameworks.

hatchelhoff
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Homework Statement


X_FRAME.PNG


Homework Equations


The answer in the book is (4F(L^3))/3EI

The Attempt at a Solution


I felt the above question could be simplified into a standard beam problem. I choose the following beam.
Simple Support.PNG


I used the Yc equation, but when I replace a with L I get an answer of (2FL(^3))/3EI
[/B]
 

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You seem to be ignoring the deflection of E in the y direction. That will increase the deflection at C.
hatchelhoff said:

Homework Statement


View attachment 215748

Homework Equations


The answer in the book is (4F(L^3))/3EI

The Attempt at a Solution


I felt the above question could be simplified into a standard beam problem. I choose the following beam.
View attachment 215749

I used the Yc equation, but when I replace a with L I get an answer of (2FL(^3))/3EI[/B]
 
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pongo38 said:
You seem to be ignoring the deflection of E in the y direction. That will increase the deflection at C.
Thanks pongo38. I have taken into account the deflection at E due to F and due to Ra. this gives me 2FL(^3))/3EI.
I then add this to the deflection at F. This gives me a total of 4FL(^3))/3EI.
 

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