{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "name": "Elisa Munich"
    },
    {
      "name": "Jérémie Schutz"
    },
    {
      "name": "Christophe Sauvey"
    },
    {
      "name": "Yves Gillet"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0fanxqa2wtcgd.bib",
  "cited_by": 0,
  "doi": "10.3390/math14122213",
  "fulltext_url": null,
  "id": "0fanxqa2wtcgd",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://hal.science/hal-05762356v1",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "2205|Engineering Applied Research"
    ]
  ],
  "openalex": "W7165656543",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-19",
  "publisher": "MDPI",
  "ris": "https://research.draconitic.com/paper/0fanxqa2wtcgd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:40Z",
      "native_id": "hal-05762356",
      "source": "hal",
      "url": "https://hal.science/hal-05762356v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "A Spreadsheet Environment for Force, Torque and Strength of Materials Modeling: Bridging Analytical Mathematics and Engineering Practice",
  "title_text": "A Spreadsheet Environment for Force, Torque and Strength of Materials Modeling: Bridging Analytical Mathematics and Engineering Practice",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:40Z",
  "url": "https://research.draconitic.com/paper/0fanxqa2wtcgd",
  "venue": "Mathematics",
  "versions": []
}