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The physical and mechanical properties of a Σ5(310)[001] symmetrical tilt grain boundary (STGB) in body centred cubic (bcc) Fe are investigated by means of ab-initio calculations with respect to the effect of a varying number of C and H atoms at the grain boundary. The obtained results show that with increasing number of C atoms the grain boundary energy is lowered, and the segregation energy remains negative up to a full coverage of the grain boundary with C. Thus, in a bcc Fe-C system with a sufficient amount of interstitial C, the C segregated state should be considered as the ground state of this interface. Ab-initio uni-axial tensile tests of the grain boundary reveal that the work of separation as well as the theoretical strength of the Σ5(310)[001] STGB increase significantly with increasing C content. The improved cohesion due to C is mainly a chemical effect, but the mechanical contribution is also cohesion enhancing. The presence of hydrogen changes the cohesion enhancing mechanical contribution of C to an embrittling contribution, and also reduces the beneficial chemical contribution to the cohesion. When hydrogen is present together with C at the grain boundary, the reduction in strength amounts to almost 20% for the co-segregated case and to more than 25% if C is completely replaced by H. Compared to the strength of the STGB in pure iron, however, the influence of H is negligible. Hence, H embrittlement can only be understood in the three component Fe-C-H system.