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To date I have been reading about Euler Bernoulli Beam and Timoshenko Beam Theory desribed by the following equations respectively

EBT ##\displaystyle \frac{d^2}{dx^2}\left( EI \frac{d^2 w}{dx^2}\right )+c_fw=q(x)##

Timoshenko ##\displaystyle -\frac{d}{dx} \left[GAK_s \left(\Psi+\frac{dw}{dx}\right)\right]+c_fw=q## and ##\displaystyle - \frac{d}{dx} \left(EI \frac{d \Psi}{dx}\right)+GAK_s \left(\Psi+\frac{dw}{dx}\right)=0##

These expressions seem to be for straight beams. Where in the above PDE's is the geometry of the beam defined?

For example, if one wants to analyse a quadrant of a ring say (from ##\pi/2## to ##\pi##) where it is constrained at ##\pi## position and a point load applied at ##\pi/2## position....

How is the PDE formulated?

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# Where is the Geometry Defined in the EBT and Timoshenko PDE's

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