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
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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Research Article
Modeling of Steady-State Creep Deformation in an Orthotropic Composite Thick-Walled Rotating Cylinder Subjected to a Thermal Gradient
Temesgen Alemu Godana*
,
Indu Bala
Issue:
Volume 15, Issue 3, June 2026
Pages:
45-55
Received:
8 September 2026
Accepted:
20 September 2026
Published:
14 October 2026
DOI:
10.11648/j.pamj.20261503.12
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Views:
Abstract: The objective of this research is to use Lebesgue strain measure theory and Seth's transition theory to build a mathematical model of steady state creep deformation of an orthotropic thick-walled rotating cylinder subjected to a thermal gradient. Because Seth's theory does not require any assumptions, such as the creep deformation is infinitesimally small, creep strain laws and the associated flow rules, it is crucial for calculating creep stresses based on generalized strain measure theory and asymptotic solution at the turning points of the differential equations defining the deformed field. This theory's consideration of the material's nonlinear character is one of its advantages. The combined effects of temperature and angular speed have been presented numerically and graphically using examples of thick-walled cylinders made of orthotropic, transversely isotropic, and isotropic materials. It is observed that near the cylinder's outer surface, cylinders composed of orthotropic materials (boron-aluminum and graphite-magnesium) have a larger radial creep stress value than those made of titanium and steel. From the inner to the outer surface of the cylinder the tangential creep stress for isotropic material (steel) and transversely isotropic material (titanium) is greater than the tangential creep stress of the cylinder composed of orthotropic boron-aluminum and graphite-magnesium materials. At the outer surface of the cylinder, titanium and steel material has higher axial creep stress value than orthotropic materials. The findings of this paper can be useful in the analysis and design of a cylinder that is exposed to high temperatures, such as high-speed structures involving aerodynamic heating, chemical plants and nuclear plants.
Abstract: The objective of this research is to use Lebesgue strain measure theory and Seth's transition theory to build a mathematical model of steady state creep deformation of an orthotropic thick-walled rotating cylinder subjected to a thermal gradient. Because Seth's theory does not require any assumptions, such as the creep deformation is infinitesimall...
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