Pemodelan Matematika Distribusi Tegangan Dan Regangan Pada Struktur Balok Beton Bertulang

Abstract

Reinforced concrete beams are structural elements widely used in construction due to their ability to effectively resist bending loads. The analysis of stress and strain distribution in reinforced concrete beams is a crucial aspect in ensuring structural safety and performance. This study aims to develop and analyze a mathematical model of stress and strain distribution in reinforced concrete beams subjected to bending loads. The research methodology employs an analytical approach based on bending theory and constitutive relationships of concrete and reinforcing steel materials, complemented by verification through numerical analysis. The mathematical model is formulated under the assumptions that plane sections remain plane after bending and that perfect bond exists between concrete and steel reinforcement. The results indicate that strain distribution is linear, while stress distribution exhibits nonlinear behavior in compressed concrete and elastic–plastic behavior in reinforcing steel. Variations in reinforcement ratio and concrete strength significantly affect the flexural capacity and deformation response of the beam. A comparison between analytical and numerical results shows good agreement, indicating that the developed model is sufficiently accurate for preliminary analysis and design of reinforced concrete beams. This study is expected to contribute to the development of more rational and efficient analysis methods for reinforced concrete structures.