Cantilever with matlab (timoshenko, euler bernoulli, reduced integration)

[Batzo]

Hi!
I am writing a code in Matlab for cantilever beam with point load at the end and linear shape functions.
I can change beam's height and number of elements.
The thing I dont understand is:

Why reduced integration merged with timoshenko for deflection but merged with euler bernoulli for rotation? Both deflection and rotation are affected from shear deformation.

 

[Celt83]

for a fixed-free beam with a point load at the end the cross section rotations are equivalent between a Timoshenko and Euler Bernoulli Beam.

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[Batzo]

1.But if I want to develop a formula for timoshenko beam's deflection with point load, this is how (file attached). And i got the same as the article.

https://www.researchgate.net/public...tions_of_a_Tapered_Cantilever_Timoshenko_Beam

2. So i need to neglecte addition rotation from shear deformation?

 

[Celt83]

Wikipedia-Timoshenko Beam

For a prismatic beam because The boundary condition is a rotation of 0 @ x=0 the coupling of the Timoshenko formulas has no impact.
(the sign change for theta in the below comes because I use a different sign convention than the wiki formula is based on)

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[Celt83]

I assume in your derivation y'=theta, your derivation includes P0/k_sGA while the research papers formula does not include this term:

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[Batzo]

Thank you for you explanation!
I will Look at it

 

[Celt83]

I'd really have to dig into my notes but I think if you have a vertical shearing force the cross section rotations are consistent between Timoshenko and EB beams.

We had a "fun" discussion on point moments in the Structural Forum: Link

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