Volume 23, Issue 59, January - June, 2026

Development of an Empirical Correction Model for Improving Single-Degree-of-Freedom Predictions of Beam Response Under Impact Loading

Ali M. Lafta^1♦, Salih Meri Al-Absi^2,3, Ahmed Raad Al- Adhadh⁴

¹Civil Engineering Department, College of Engineering, Al-Muthanna University, Al-Muthanna, Iraq
²Department of Refrigeration and Air-Conditioning, College of Technical Engineering, Sawa University, Al-Muthanna, Iraq.
³Iraqi Cement State Company, Ministry of Industry and Minerals, Baghdad, Iraq.
⁴Civil Engineering Department, College of Engineering, Al-Muthanna University, Al-Muthanna, Iraq.

^♦Corresponding author
Ali M. Lafta, Civil Engineering Department, College of Engineering, Al-Muthanna University, Al-Muthanna, Iraq

ABSTRACT

This study investigated the response of a reinforced concrete beam subjected to drop-weight impact using both a single-degree-of-freedom (SDOF) model and a multi-degree-of-freedom (MDOF) model. The study examined the displacement response in both models and then developed a correction factor to bring the SDOF displacement results closer the corresponding MDOF values. Both models were analyzed under various realistic conditions relevant to structural applications. The main advantages of the SDOF model ARE its simplicity, speed, and low computational cost; however, its accuracy under impact conditions remains questionable, whereas the MDOF model does not suffer from this limitation. We created and analyzed a simply supported beam and built the MDOF model using the finite element method (FEM). The study focused on four main variables: drop mass, drop height, span length, and section depth. The accuracy of the results was also verified by comparing these results with published experiments and Abaqus simulations, and the agreement was very close. Additionally, a parametric investigation determined the conversion factor. The results showed that the SDOF model gave higher maximum mid-span displacement values than the MDOF model. Where the difference between the two models are 44.6% for effect of span length and 43% for effect of section depth. After applying the correction factor, the results showed a high correlation with MDOF values (R2 = 0.9866) with a maximum error of less than 2% in most simulated cases. Therefore, the proposed conversion factor provides a practical and computationally efficient tool for preliminary design and structural evaluation.

Keywords: Single-degree-of-freedom (SDOF) model; multi-degree-of-freedom (MDOF) model; Finite element method (FEM); Impact loading; Displacement prediction; Empirical correction model

Indian Journal of Engineering, 2026, 23(59), e8ije1716

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DOI: https://doi.org/10.54905/disssi.v23i59.e8ije1716

Published: 18 May 2026