An Approximate Formula for Asymmetrical Lateral-Impact Forces: A Residuals Margin and Laplace Transform Approach

Abstract

Calculating impact forces in asymmetrical lateral structures has been a complex challenge that spans decades in engineering. Traditional models often fall short due to the inherent complexity of asymmetrical members and the need for significant computational resources or a vast pool of training data. This paper develops an approximate formula for accurately calculating the impact force of asymmetrical lateral-impact members under lateral impact. Existing methods for assessing impact forces have been limited in their application due to the inherent complexity of asymmetrical members and the significant computational resources or extensive training data they often require. Our approach employs the residuals margin method, and Laplace transforms to derive an efficient and accurate formula for impact force calculation. The paper rigorously validates this Formula through experimental testing, demonstrating high precision with an error margin of less than 5%. Further validation against diverse impact data from multiple studies on different materials and loadings under static and dynamic conditions confirmed the Formula’s consistency. Despite simplifying assumptions, this research contributes a novel and computationally efficient approach for calculating impact forces. The formula offers engineers a practical tool while advancing a fundamental understanding of asymmetric impact dynamics. Rigid experimentation verified its significant accuracy, establishing the formula as a valuable structural impact analysis and design resource. This research presents an analytical formula for calculating impact forces on structures like buildings, bridges, and vehicles experiencing asymmetrical lateral impacts. Such impacts commonly occur due to falling debris, vehicle collisions, seismic pounding, and derailed train strikes. However, existing design formulas often oversimplify impact mechanics or require complex simulations. The proposed method provides engineers with a simple spreadsheet-compatible equation relating impact force directly to tangible mechanical quantities like momentum. This enables rapid impact load assessments essential for performance-based design against accidental hazards. The formula was validated through laboratory impact tests on reinforced concrete slabs, demonstrating precision within 5% of measured forces. Additional validations against published experimental and simulation data on different construction materials confirmed accuracy. The proposed formula equips structural engineers and safety analysts with a practical impact analysis tool by offering a computationally efficient approach with proven reliability. It facilitates assessing design performance for asymmetrical impact load scenarios, helping improve resilience for critical facilities subjected to hazardous lateral impacts.