The development of composite materials is a major issue in sustainable construction regarding the exhaustion of natural resources. The environmental impact of concrete favours the development of alternative solutions such as inorganic phosphate cement (IPC) matrix composite, which presents significant advantages. The manufacturing of unidirectional glass-fibre-reinforced IPC matrix composite by pultrusion shows shear weaknesses, leading to premature failure of load-bearing elements under shear effects. Thus, composite beams are strengthened by braiding and circumferential wrapping to increase their load-carrying capacity by bridging shear cracks. Nevertheless, the optimization of the strengthening and the later development of design rules targeting engineers involve the identification of dimensioning parameters. To bridge quantitative and qualitative analyses of the bending behaviour of strengthened beams, we propose here the use of a 3D finite element model and experimental data. The strengthening enhancement is discussed, and the numerical model is validated at the global scale. The bending stiffness and the failure are well predicted for ultimate and serviceability limit states. The braiding brings additional stiffness regardless of the characteristics of braiding, but the fibre volume ratio and the nature of the fibres (glass or carbon) have a significant influence on the failure load. At the local scale, the numerical results diverge from the experimental ones. A more detailed analysis of the local damaging phenomena is necessary. (C) 2016 Elsevier Ltd. All rights reserved.