Shear and Bending Solution

To complete the anal3dical solution for the simplified case outlined in Remark 9.1, the remaining four equilibrium equations for shear and bending need to be considered. The external line loads contained therein are again provided by Eqs. (9.2), and the internal loads are supplied by the right one of Eqs. (8.4) in conjunction with Eq. (9.1). Further on, the beam shear angles are eliminated by virtue of Eq. (7.29). 

With the above substitutions, the equilibrium relations of Eqs. (8.36b) and (8.36d) as well as Eqs. (8.36c) and (8.36e) may be combined such that each resulting equation contains the axial derivative of one of the sought inclination angles of the cross-section. Integration in consideration of the clamped boundary conditions at one end, then yields 

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