The shear center of a rectangular, thin-walled, and closed cross section with a constant thickness coincides with its center of gravity. If the profile is not closed but opened at one side of the rectangle, the shear center moves from the inside to the outside of the cross section. In high-rise buildings stiffening cores are often used as elevator shafts which require wall openings in each floor. Thus alternating sections of closed and opened profiles occur along the height of the core. In this work, seven 1:50 scaled models of high-rise cores have been investigated, where numbers, positions, and sizes of the perforations have been varied. A set-up for the measurement of the movement of the shear center along the height has been developed. Physical measurements and numerical simulations have been carried out. A general coincidence is observed regarding the geometric patterns of the perforations and the periodicity of the shear center movements. In addition, the eccentricity of the shear center seems to decrease with decreasing distance to the rigid clamping. This relationship is more pronounced in the simulations as compared to the experimental results.