Hydrodynamic flow of materials, initiated by shock waves, is determined by their equation of state EOS. For comparatively weak shocks, the zero-temperature isotherm and thermal motion of ions, mainly, determine the EOS. However, in processes involving high energy density, as in inertial confinement fusion, astrophysical phenomena, nuclear explosion, etc., very strong shocks (P> few megabars, T> few eV) are encountered. Such shocks give rise to many thermal effects leading to dissociation of molecules, ionization of electrons, radiation emission, etc., in addition to the quantum-mechanical pressure ionization in materials. Therefore, hydrodynamics due to strong shocks crucially depend on the behavior of electrons and the radiation emitted by the electrons. This paper aims at developing a simple but quantitative model of electronic binding in plasmas and its effects on compressibility of materials. An improved version of the screened hydrogenic model is developed for this purpose. The effect of radiation emission is incorporated using Stefan-Boltzmann law. The Hugoniot of various elements such as Al, Be, Fe, etc., are, then, computed. These are in excellent agreement with those obtained using sophisticated self-consistent field calculations, and the oscillations in Hugoniot are shown to be due to ionization of electrons from different shells. Shell effects are also reflected in the variation of electronic specific heat with temperature and the relation between shock velocity and fluid velocity. Further, at very high temperature and pressure, equilibration between radiation and matter increases the compressibility of materials. The limiting compression of all materials, via a strong shock, is found to be 7 unlike 4, which is the limit for free-electron gas or ideal monoatomic gas. The model reported here can be employed in lieu of Thomas-Fermi-type theories used in global EOS packages such as quotidian equation of state (QEOS).