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We analyse the effect on adiabatic stellar oscillation frequencies ofreplacing the near-surface layers in 1D stellar structure models with averaged3D stellar surface convection simulations. The main difference is an expansionof the atmosphere by 3D convection, expected to explain a major part of theasteroseismic surface effect; a systematic overestimation of p-mode frequenciesdue to inadequate surface physics.  We employ pairs of 1D stellar envelope models and 3D simulations from aprevious calibration of the mixing-length parameter, alpha. That calibrationconstitutes the hitherto most consistent matching of 1D models to 3Dsimulations, ensuring that their differences are not spurious, but entirely dueto the 3D nature of convection. The resulting frequency shift is identified asthe structural part of the surface effect. The important, typicallynon-adiabatic, modal components of the surface effect are not included in thepresent analysis, but relegated to future papers.  Evaluating the structural surface effect at the frequency of maximum modeamplitude, $\nu_{\rm max}$, we find shifts from $\delta\nu$=-0.8 microHz forgiants at $\log g$=2.2 to -35 microHz for a ($T_{\rm eff}=6901$ K, $\logg$=4.29) dwarf. The fractional effect $\delta\nu(\nu_{\rm max})/\nu_{\rm max}$,ranges from -0.1% for a cool dwarf (4185 K, 4.74) to -6% for a warm giant (4962K, 2.20).

The asteroseismic surface effect from a grid of 3D convection simulations. I. Frequency shifts from convective expansion of stellar atmospheres