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Fire resistance of composite slab of steel deck and concrete is numerically examined. The model takes into account of the heat and mass transfer, the desorption of physically adsorbed water, and the thermal decomposition of water of crystallization. The accuracy of the model is verified by comparing with the fire test data. By using the model, the dependence of the thermal responses on the cross sectional shapes are derived. While the average thickness is kept constant (1 15mm), the rib sizes are changed. The fire resistance time is determined for each shape. In case of small ribs, the fire resistance time is determined by the average temperature rise of the unexposed surface. On the contrary, as the rib becomes large, the fire resistance time is determined by the maximum temperature rise. Between these rib sizes, the two criteria are exceeded at the same time. We call these shapes as 'thermally optimum' in the sense that there is no redundancy of concrete. By extrapolating the results for 115mm average thickness, thermally optimum shapes for different average thickness can be guessed.