Inclined cut in a beam

Let us consider a thin homogeneous isotropic beam of thickness 2s. We assume that the beam mid-line coincides with the segment (0,1) of the axis X. At the point y = 1/2, the beam has an inclined cut as a segment having the angle a with the vertical line, 0 tana 2e). We look for the function % = (W, w) of horizontal displacements W(x) and vertical displacements w(x) provided that the external forces g(x),f(x) are given. The condition of clamped edges 

gG L fly). The equilibrium problem for the beam with the inclined cut is formulated as the following variational inequality  

There exists a unique solution % G iX of (3.199). At the cut edges we have 

Therefore, by Theorem 3.13, the problem (3.199) is equivalent to the following boundary value problem  

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