Beam deflection derivation

In summary, The person is trying to mathematically derive the beam deflection formula for a double cantilever simple beam, but is unsure how to link the formulas y= (FL^3)/(48—Iε), M ymax / I, and 1/p = M/EI together. They are seeking help and the suggestion to Google the derivation and to consider the two beams as springs in parallel or series.
  • #1
***ALLI***
1
0

Homework Statement


hi i am currently trying to mathcamatically derive the beam deflection formula for a double cantilever simple beam. i have the beam deflection formula y= (FL^3)/(48—Iε) as well as M ymax / I as well as 1/p = M/EI but am not sure how to link them together. any help will be apprecieated
Thanx :)
 
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  • #2
***ALLI*** said:

Homework Statement


hi i am currently trying to mathcamatically derive the beam deflection formula for a double cantilever simple beam What's that? Do you mean a beam on two simple supports? i have the beam deflection formula y= (FL^3)/(48—Iε)what's this? It looks something like the deflection at centerline of a simply supported beam with a concentrated load F at its center, but your denominator makes no sense. as well as? = M ymax / I as well as 1/p = M/EI but am not sure how to link them together. any help will be apprecieated
Thanx :)
See my questions noted in red. Are you looking for the derivation of the beam deflection formula [tex] d^2y/dx^2 = M/EI [/tex] ? You might want to google it.
 
  • #3
you definitely need to consier the two beams as springs in parallel or series, then get the effective spring constant
 

1. What is beam deflection derivation?

Beam deflection derivation is the process of calculating the amount of deflection or bending that occurs in a beam when a load is applied. It involves using mathematical equations and principles of mechanics to determine the deflection at different points along the beam.

2. Why is beam deflection important?

Beam deflection is important because it affects the structural integrity and stability of a beam. Too much deflection can lead to failure or collapse of the beam, while too little deflection can cause it to be too stiff and unable to withstand loads.

3. What factors affect beam deflection?

The amount of beam deflection is influenced by several factors, including the load applied, the length and shape of the beam, the material properties of the beam, and the support conditions at the ends of the beam.

4. What are the common methods used for beam deflection derivation?

The two most common methods for beam deflection derivation are the double integration method and the moment-area method. The double integration method involves solving differential equations, while the moment-area method uses the area under the bending moment diagram to determine deflection.

5. How can beam deflection be minimized?

Beam deflection can be minimized by using stiffer materials, increasing the beam's cross-sectional area, reducing the length of the beam, or adding additional support points. Properly designing and reinforcing the beam can also help prevent excessive deflection.

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