A Spreadsheet Environment for Force, Torque and Strength of Materials Modeling: Bridging Analytical Mathematics and Engineering Practice
Abstract
This paper presents and validates a unified spreadsheet-based framework for engineering mechanics education and preliminary design. Three modules are integrated within a single openly available workbook: multi-point resultant force and moment computation; axial normal stress with stress concentration effects for three geometric configurations (plate with hole, shoulder plate, stepped shaft); and beam deflection for simply supported and cantilever configurations under point loads. All governing equations are implemented as explicit closed-form expressions validated against analytical reference solutions for six independent cases; relative errors fall below 10−10 in all cases. Three worked exercises demonstrate the practical scope of the framework. A biomechanical multi-point force system yields joint moments of −6880, −33,421, and −58,241 N·mm at the wrist, elbow, and shoulder, respectively. A tensile shoulder plate with Kt≈1.85 produces σmax=232 MPa against σy=200 MPa, identifying a design failure; a parametric redesign with fillet radius r=10 mm reduces Kt to approximately 1.59 and σmax to approximately 198.7 MPa, restoring structural safety. A cantilever beam subjected to a 20,000 N tip load yields a maximum deflection of 13,133 μm. The framework constitutes a validated intermediate layer between manual analytical derivations and high-fidelity numerical simulations, applicable to preliminary design, parametric sensitivity studies, and engineering education at the linear elastic level.
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BibTeX
@article{munich2026spreadsheet,
title = {{A Spreadsheet Environment for Force, Torque and Strength of Materials Modeling: Bridging Analytical Mathematics and Engineering Practice}},
author = {Elisa Munich and Jérémie Schutz and Christophe Sauvey and Yves Gillet},
journal = {Mathematics},
year = {2026},
month = jun,
doi = {10.3390/math14122213},
url = {https://hal.science/hal-05762356v1},
note = {CC BY},
}
RIS
TY - JOUR
TI - A Spreadsheet Environment for Force, Torque and Strength of Materials Modeling: Bridging Analytical Mathematics and Engineering Practice
AU - Elisa Munich
AU - Jérémie Schutz
AU - Christophe Sauvey
AU - Yves Gillet
PY - 2026
DA - 2026/06/19
JO - Mathematics
DO - 10.3390/math14122213
UR - https://hal.science/hal-05762356v1
AB - This paper presents and validates a unified spreadsheet-based framework for engineering mechanics education and preliminary design. Three modules are integrated within a single openly available workbook: multi-point resultant force and moment computation; axial normal stress with stress concentration effects for three geometric configurations (plate with hole, shoulder plate, stepped shaft); and beam deflection for simply supported and cantilever configurations under point loads. All governing equations are implemented as explicit closed-form expressions validated against analytical reference solutions for six independent cases; relative errors fall below 10−10 in all cases. Three worked exercises demonstrate the practical scope of the framework. A biomechanical multi-point force system yields joint moments of −6880, −33,421, and −58,241 N·mm at the wrist, elbow, and shoulder, respectively. A tensile shoulder plate with Kt≈1.85 produces σmax=232 MPa against σy=200 MPa, identifying a design failure; a parametric redesign with fillet radius r=10 mm reduces Kt to approximately 1.59 and σmax to approximately 198.7 MPa, restoring structural safety. A cantilever beam subjected to a 20,000 N tip load yields a maximum deflection of 13,133 μm. The framework constitutes a validated intermediate layer between manual analytical derivations and high-fidelity numerical simulations, applicable to preliminary design, parametric sensitivity studies, and engineering education at the linear elastic level.
SN - 2227-7390
ER -