COMPARATIVE NUMERICAL ACCURACY OF EULER AND RUNGE–KUTTA METHODS FOR REINFORCED CONCRETE BEAM DEFLECTION USING A DOUBLE-INTEGRATION ANALYTICAL BENCHMARK - Iola Abi Gail; Indra Rio Saputro; Via Azizul Saputri Khalifah; Erik Wahyu Palguna; Diajeng Sekar Shaliha (Jurnal Teknik SILITEK, 2026)
Beam deflection is a critical parameter in reinforced concrete design because it governs structural serviceability. Analytical solutions are often limited to simplified cases; therefore, accurate numerical methods are required for practical analysis. This study evaluates the accuracy of the Euler, second-order Runge-Kutta (RK2), and fourth-order Runge-Kutta (RK4) methods in predicting reinforced concrete beam deflection against an analytical benchmark obtained using the double-integration method. A quantitative approach was applied to a simply supported reinforced concrete beam with a 6 m span, a uniformly distributed load of 1200 kg/m, and flexural rigidity (EI) of 3.97 x 107 kg/cm2. The governing differential equation was solved numerically and compared with the exact analytical solution. Pointwise relative error and root mean square error (RMSE) were used to evaluate numerical accuracy. The results show that the Euler method has the lowest accuracy, with an initial error of 100% decreasing to approximately 9% at mid-span and a maximum deflection of 0.0002790 m. RK2 improves the prediction substantially, reducing the error to below 1% and producing a maximum deflection of 0.00030620 m. RK4 provides the highest accuracy, with errors approaching 0% after rounding and a maximum deflection of 0.0003057 m, closely matching the exact value of 0.000306 m. Step-size sensitivity analysis confirms first-order convergence for Euler and second-order convergence for RK2, while RK4 remains at machine-precision level for the adopted polynomial model.