Research Article
Mathematical Modeling of Integrated Wind, Thermal, and Tectonic Stress Analysis on Cantilever Balconies Using Ordinary Differential Equations
Issue:
Volume 15, Issue 3, June 2026
Pages:
35-44
Received:
4 April 2026
Accepted:
25 April 2026
Published:
11 May 2026
DOI:
10.11648/j.pamj.20261503.11
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Abstract: Cantilever balconies are widely used in modern buildings due to their architectural flexibility and efficient use of space. However, their structural performance is highly sensitive to environmental loading because their bending resistance is concentrated at the fixed support. In real service conditions, these structures are simultaneously subjected to static loads, wind-induced aerodynamic forces, seasonal thermal effects, and seismic ground acceleration. Most conventional analyses treat these effects independently, which may underestimate cumulative deflection and lead to inaccurate serviceability predictions. This study develops a unified mathematical model to quantify the total tip deflection of a cantilever balcony subjected to combined static, wind, thermal, and seismic loading. The formulation is based on Euler–Bernoulli beam theory and linear elasticity assumptions. Closed-form analytical expressions are derived for each loading component and integrated using the principle of superposition to obtain a compact total deflection equation. Numerical simulations are performed for aluminum, steel, reinforced concrete, and carbon fiber composites under representative environmental conditions. Results show that thermal effects become dominant in high-temperature environments for materials with large coefficients of thermal expansion, while seismic effects become significant in regions with high peak ground acceleration. Among the materials considered, carbon fiber composites consistently exhibit the smallest total deflection due to their high stiffness and low thermal sensitivity, while reinforced concrete shows the largest deformation due to its lower elastic modulus. The proposed model provides a mathematically consistent framework for evaluating cantilever balcony performance under multi-hazard environmental loading and offers a useful decision-support tool for preliminary structural design and material selection.
Abstract: Cantilever balconies are widely used in modern buildings due to their architectural flexibility and efficient use of space. However, their structural performance is highly sensitive to environmental loading because their bending resistance is concentrated at the fixed support. In real service conditions, these structures are simultaneously subjecte...
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Beatrice Adhiambo Odero Obiero
