Cross-laminated timber (CLT) is a popular construction material for low and medium-rise construction. However an architectural aspiration exists for tall mass timber buildings, and this is currently hindered by knowledge gaps and perceptions regarding the fire behaviour of mass timber buildings. To begin to address some of the important questions regarding the structural response of fire-exposed CLT structures in real fires, this paper presents a series of novel fire tests on CLT beams subjected to sustained flexural loading, coincident with non-standard heating using an incident heat flux sufficient to cause continuous flaming combustion. The load bearing capacities and measured time histories of deflection during heating are compared against predicted responses wherein the experimentally measured char depths are used, along with the Eurocode recommended reduced cross section method and zero-strength layer thickness. The results confirm that the current zero-strength layer value (indeed the zero-strength concept) fails to capture the necessary physics for robust prediction of structural response under non-standard heating. It is recommended that more detailed thermo-mechanical cross-sectional analyses, which allow the structural implications of real fire exposures to be properly considered, should be developed and that the zero-strength layer concept should be discarded in these situations. Such a novel approach, once developed and suitably validated, could offer more realistic and robust structural fire safety design.