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This paper presents measurements of the voltages, the magnetic fields and the magnetic-field derivatives inside a structure simulating reinforced concrete buildings. The test structure comprises a cubic cage of 2-m side length with single- or double-layer reinforced grids. The injected lightning currents simulate the positive, the negative first and the negative subsequent return strokes with amplitudes of ∼ 77, 16, and 4.8 kA, respectively. Three distinct points of the lightning stroke impact to the structure roof are considered, namely, the center, the mid-edge and the corner. In the case of a single-layer cage, the results reveal that slow-rising magnetic-field components are generated inside the structure for various lightning currents. This effect becomes dominant for the case of the double-layer cage. For all the simulated currents, striking to the structure corner induces the lowest voltage across it, but gives the highest values for both the resultant magnetic fields and the magnetic-field derivatives. For all striking points, the magnetic fields have the highest values for positive strokes, while the negative subsequent strokes give the highest amplitude of the resultant magnetic-field derivatives and roof-to-floor voltages. Compared to the case of a single-layer cage for the negative subsequent strokes, the use of a double-layer cage shows a considerable mitigation of the voltage across the structure, and a moderate mitigation of both the resultant magnetic fields and the magnetic-field derivatives.