Flexural Strength to Mass Ratio Design Optimization.
Skills Used: Multivariable function analysis, design optimization, CAD: Fusion 360 design and simulation FEA (static modeling), technical drawing, failure analysis.
Keywords and topics: Bending, flexural strength, specific strength, stress concentrations.
Problem Statement: Build a design that supports the maximum load per unit mass when loaded in a three-point loading system. The design must only use the materials given; one oak beam, one poplar beam, one oak rod, and 10 nails. Predict the maximum load the design created can withstand before failing in the three-point loading system.
Summary: I quantitatively proved that the presumed ideal design, an I-beam, does not effectively maximize the strength to mass ratio for a three point loading configuration. The optimal design I created was a simple beam oriented vertically with the greatest height to base ratio possible. It was made of poplar which has the greatest specific strength and nails were avoided because they induce stress concentrations. Notably, the beam I designed won the mechanical engineering class competition to create a design with the greatest flexural strength (load) to mass ratio. My predicted failure load was also the most accurate of the class.
Approach
A system that supports the maximum load at failure per unit mass when subjected to a three-point load system was designed and built using only materials given. An equation created using an I-beam's dimensions (flange and web, height and width) to determine the most efficient flexural strength to mass ratio. The I-Beams dimensions were substituted into the flexural strength formula and graphed using 3D graphing calculator GeoGebra. From graphical analysis I determined the shape with the greatest strength to mass ratio was a classic beam with no flanges that had the greatest height to base ratio possible. Following this determination, a prediction of the maximum transverse load the beam could hold was made and was tested through an Instron test system and a three-point loading jaw.
