Improving the Load-Carrying Capacity of Structures by Separation in Geometry

This chapter presents a very powerful method in structural engineering, referred to as ‘separation in geometry’. An important part of the separation in geometry is the method of aggregation, for increasing the load-carrying capacity of structures built with the same volume of material. A theorem has been proved that provides the foundation for the aggregation method in structures containing the same total volume of material. For an equal total volume, the ratio of the maximum tensile stresses in the non-aggregated and aggregated structure is equal to the scaling factor of the aggregated section along the depth of the beam, while the ratio of the deflections is given by the square of this scaling factor. These results hold regardless of the shape of the cross sections of the loaded beams. The reduction in material volume, deflection, and stress depends solely on the scaling factor of the cross section along the depth of the beam and is independent of the scaling factor along the width of the beam. This means that if the scaling factor along the depth of the beam is unity, aggregation into fewer load-carrying elements with larger cross sections will not result in any reduction in volume, deflection, or stress. The aggregation method was tested through finite element experiments, which confirmed that aggregating statically determinate cantilever beams and statically indeterminate frames leads to a drastic decrease in both the maximum von Mises stress and the maximum deflection.