Most previous treatments of problems of bonded materials in linear elastostatics do not establish the possible functional relationship between the fields in the single and composite material. In this paper, the interior of one of two orthotropic semi-infinite plate strips joined end-on and simply-supported along the longitudinal edges is subjected to an arbitrary transverse load. Using a real-function approach, it is shown that the fields for the composite plate are directly computable from the corresponding fields for the homogeneous infinite plate, and that the connecting relations remain unchanged irrespective of the shape of the loaded area. A knowledge of this fact gives important advantages in economy and simplicity.