The automatic generation of elastic-plastic stress fields (EPSF) for structural concrete members by means of the finite element method has been demonstrated as a suitable approach for the design and assessment of D regions. This methodology allows accounting for an elastic-plastic behaviour of the materials. For concrete, no tensile strength is considered, and the compression softening hypothesis of Vecchio & Collins is incorporated to take into account the effect of the transversal cracking on the compressive strength of concrete. In this paper, the application of this tool for the analysis of the failure load and cracking conditions at serviceability is investigated over a series of experimental tests on dapped-end beams (DEB). The failure of DEB occurred in most cases by spalling of the concrete cover on top of the suspension reinforcement. The models with the EPSF predicted also consistently this failure mode. Contrary to classical approaches of stress fields, where the tensile strength of the concrete cover is neglected (leading thus to conservative estimates of the strength for members failing by cover spalling), it is shown in this paper that EPSF can be suitably adapted to reproduce this failure mode by introducing a fictitious reinforcement in the cover. This reinforcement is introduced to reproduce cover spalling for a critical opening of the spalling cracks developing. With this assumption, a very good estimate of the experimental ultimate loads is consistently obtained, also for prestressed elements and for steel-fibre reinforced members (for which the contribution of the fibres is introduced in the model as an equivalent plastic tensile strength of the concrete). A methodology for the determination of the crack width in the critical regions of DEB for service load levels by using EPSF is also investigated. It is assumed a rigid-plastic approximation for the bond stresses near the crack. The methodology gives also reasonable and consistent estimates of the crack widths for DEB specimens, particularly for those with diagonal reinforcement, in which the cracking process is more stable.