Abstract
Some composite beam problem requires the different boundary conditions in each beam. The degree of freedom in each node becomes three by permitting split-off action, and it becomes possible to treat the boundary conditions independently for the each beam terminal. The author develops new composite beam theory permitted this action and shows the effectivity of this theory by applying it to the problem of the composite floor slab smeared with the flexural cracks in the tension zone of the concrete portion. The solution of this illustrative problem also gives the explanation of the phenomenon of the observed poor composite action when we use some group of steel deck plates.