An experimental and numerical study of hot-rolled steel I-sections under combined compression and bending moment is presented herein. A total of two stub column tests and 12 mono-axial or bi-axial eccentric compression tests on HEB 160 cross-sections with two different material grades (S235 and S355) were carried out. The tested cross-sections were of stocky proportions to enable the influence of material strain hardening on the strength and behaviour of hot-rolled steel I-sections to be investigated. The loading eccentricities for the eccentric compression tests were varied in order to achieve different axial compression-to-bending moment ratios. Measured geometric and material properties, together with the full load-deformation histories from the test specimens, were reported. Finite element (FE) models were developed and validated against the experimentally obtained load-deformation curves, as well as the failure modes. The FE results successfully captured the experimental structural performance of hot-rolled steel I-sections and the validated FE models were then used for parametric studies in the companion paper to generate additional numerical results, considering different cross-section slendernesses, material grades and combinations of loading. The experimental and numerical results are employed in the companion paper for the assessment of the design rules given in EN 1993-1-1 (2005) and AISC-360-16 (2016) and for the extension of the deformation-based continuous strength method to the case of hot-rolled steel I-sections under combined loading.