A Spreadsheet Environment for Force, Torque and Strength of Materials Modeling: Bridging Analytical Mathematics and Engineering Practice

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.