Transverse Schottky spectra and beam transfer functions (BTFs) of coasting ion beams were measured in the heavy ion synchrotron SIS-18 in order to study the impact of space charge on the transverse beam dynamics. The particle number in the beam was varied to investigate the intensity dependence of the space-charge effect. No cooling was applied to the beams throughout the experiment. The expected deformation of the Schottky spectra and BTFs is observed. An analytic model with linear space charge is employed to describe the deformed Schottky and BTF signals. In this model, the incoherent space-charge force and the coherent forces due to impedances are treated separately. Using the model, the space-charge induced tune shift is evaluated both from the position and the form of the signals. The data are well described by the model, only in the high-intensity BTFs deviations are observed. The stability diagrams are shifted according to the space-charge parameter obtained from the BTFs. In addition, the tune shift is estimated by virtue of measured beam profiles and particle numbers. The estimated tune shift is of the same order of magnitude but smaller than the measured one. Possible explanations for deviations between the measurements, the model, and the estimation are discussed.