Description of an exemplary cross-section

Here those branches will be considered that do not participate in the formation of a closed cell. They possess one free end, and the same reasoning as in the 

The connection of closed cells through the sharing of a common branch represents a statically indeterminate system. Due to the excess of branches with regard to cells and junctions respectively, the unknown warping resultants may only be determined by both continuity requirements of the cells and axial equilibrium conditions at the junctions. 

Such equilibrium conditions are only relevant for the case of multiple adjoined cells, since the warping resultants of open branches and separate cells are effectively determined by Eq. (7.49), respectively by Eq. (7.50). The axial equilibrium at the junctions j requires the consideration of the coordinate direction in the cross-sectional plane of every involved branch i captured by the association function /j. Thus, the following may be formulated  

Further on, the continuity requirement, as imposed by Remark 7.13, also applies to the warping displacements of all branches meeting at a junction, which thus have to be identical there. Since an arrangement like Eq. (7.41) can be made only for one branch, the integration constants C j(x) of the remaining branches may be determined. 

To illustrate the rather abstract formulation of the general cross-section outlined above, the essential relations for two examples will be given. The first is a closed cross-section with two cells and thus represents the elementary case of a statically indeterminate system. The second examines the differences induced by a slit in one of these cells and therefore is concerned with the combination of a closed cell and two open branches. 

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Fig. 7.2. Description of an exemplary cross-section with two adjoined cells k, formed by two junctions j and three branches i. With the optional slit at the dashed Hne, it may be converted into a combined cross-section consisting of a single closed cell and two branches with free ends.

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