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Boundary conditions of a beam with a rotationnal spring support

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(@franky87)
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Joined: 10 years ago

If a have a beam (ij) (as shown in the picture) and i have to solve its differential equation (EI Y(x)=0). In the general case we take the following boundary conditions:

-For end deformation:

vi = -Y[0]

Thetai = Y[0]

vj = Y[L]

Thetaj = Y[L]

-For end forces:

Vi = -EI*Y[0]

Mi = -EI*Y[0]

Vj = -EI*Y[L]

Mj = EI*Y[L]

What are the boundary conditions to take if a have a rotational spring in both sides (i and j) (see picture).

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