Fundamental Engineering Problems (Solid Mechanics)

Hand calculations are an important asset to develop problem-solving skills for a mechanical engineer. FEA simulation in solid mechanics provides the manifold advantage of evaluating a design for structural integrity, identifying failure modes, and ultimate strength without the need for initial prototyping.

While FEA principles are applied predominantly in mechanical design, hand calculations are an excellent elementary tool to understand a mechanical structure's essential parameters. One can use their engineering aptitude of fundamental solid mechanics to assess loading conditions and calculate stress, deformation, and strain expressions for simple beam geometries, such as cantilever and simply-supported beams. These analytical methods do not require FEA tools, which might not be readily available to students. Furthermore, one can validate hand calculations with simulation data to refine and optimize the design for mitigating any structural irregularities and enhancing its quality.

Below, you will find a few of my academic thesis research utilizing hand calculations for solving fundamental beam bending problems, namely:

1. calculating the optimum structural weight and thickness of a rectangular sandwich beam with a concentrated load at the center (for a specified bending stiffness)

2. determine bending stress and shear stress of a rectangular sandwich beam in 3-point bending

3. solve the maximum deflection of a cantilever beam with an applied load at the free end

Note: This work on sandwich beam bending is based on deflection and weight analytical formulas obtained from Gibson and Ashby - Cellular Solids (See references at the end)

Hand calculations of bending stress and shear stress of sandwich beams in 3-point bending test (according to ASTM C393 Standard [2])

Thank you for taking the time to visit. Please feel free to contact me for feedback or if you have any questions. I would love to hear from you.