Sensitivity Analysis of Influential Variables in Reinforced Concrete Ribbed Slabs Using Complex Variable Method

Abstract

This study presents a comprehensive sensitivity analysis of influential design variables in one-way reinforced concrete ribbed slabs, with particular emphasis on construction cost and carbon dioxide gas emissions as the primary objective functions. The Complex Variables Method (CVM) is employed and compared against the conventional Finite Difference Method (FDM) to evaluate the sensitivity numbers with respect to seven important design variables, including topping slab thickness, rib spacing, lower and upper rib widths, reinforcing bar diameter, rib depth, and concrete compressive strength. The results demonstrate that the CVM yields stable, step-size-independent sensitivity numbers across a wide range of extremely small step sizes. In contrast, the FDM fails to produce reliable estimates due to numerical instabilities and subtractive cancellation errors. Sensitivity analysis reveals that the variable rbd has the greatest influence on the objective functions, particularly carbon dioxide gas emissions, reinforcement weight (Wsteel), and cost, while certain variables exhibit zero sensitivity, indicating independence from specific objective functions. The Karush–Kuhn–Tucker (KKT) conditions are examined at the reported optimum point, and the non-zero sensitivity values are attributed to the discrete nature of the design variables. The findings underscore the robustness of CVM as a powerful computational tool for sensitivity analysis in structural optimization and provide practical insights for sustainable and cost-effective design of reinforced concrete ribbed slab systems.