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The shielding capabilities of five different glass systems, namely 60TeO$_2$–(30-x)ZnO–5Bi$_2$O$_3$–5TiO$_2$-xB$_2$O$_3$, where x varies from 0 to 10 mol\%, against photons, protons, alpha particles, neutrons, and carbon ions were investigated. The study involved the theoretical analysis and Monte Carlo simulations of various shielding parameters such as attenuation coefficients, mean free path, value layers, effective atomic number, effective electron density, and build-up factors, spanning an energy range from 1 keV to 1 GeV. Additionally, rapid neutron removal cross-sections and effective conductivity for the transport properties of the glass compositions were examined. The simulation utilized the glass samples as shielding materials and subjected them to bombardment by photons emitted from Cs-137 and Co-60 sources. Stopping potentials and projected range of photons, alpha particles, and ions were also analyzed using the Stopping and Range of Ions in Matter (SRIM) software. The results indicated that the glass composition 60TeO$_2$–30ZnO–5Bi2O3–5TiO$_2$ exhibited superior attenuation capabilities against gamma rays, protons, alpha particles, and carbon ions in comparison to other samples. Conversely, the glass composition 60TeO$_2$–20ZnO–5Bi2O3–5TiO$_2$-10B$_2$O$_3$ displayed excellent neutron shielding behavior owing to its higher boron atom concentration. By comparing the calculated attenuation parameters, potentials, and ranges with previously reported data and recommended glass systems for nuclear applications, it is concluded that the selected glass sample demonstrated effective and comparable shielding properties. This study provides valuable insights into the shielding properties of different glass compositions against diverse radiation types. These findings are crucial for the development of shielding materials for nuclear applications and environments with potential radiation exposure.