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

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hatchelhoff
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Homework Statement


Textbook diagram of an X-shaped frame in the xz plane with members of length 2l meeting at point E at angle θ, supports RA, RB, RD, and load F downward at C.


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.
Textbook page titled 'Simple supports—overhanging load' showing a beam diagram with supports A and B, load F at overhang C, reactions R1 and R2, shear force V and bending moment M diagrams, and deflection formulas for yAB, yBC and yC.


I used the Yc equation, but when I replace a with L I get an answer of (2FL(^3))/3EI
[/B]
 
Attachments
  • Textbook diagram of an X-shaped frame in the xz plane with members of length 2l meeting at point E at angle θ, supports RA, RB, RD, and load F downward at C.
    X_FRAME.PNG
    9.8 KB · Views: 1,498
  • Textbook page titled 'Simple supports—overhanging load' showing a beam diagram with supports A and B, load F at overhang C, reactions R1 and R2, shear force V and bending moment M diagrams, and deflection formulas for yAB, yBC and yC.
    Simple Support.PNG
    4.7 KB · Views: 1,286
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.