Improving the load-carrying capacity of structures consisting of multiple elements

The paper presents a very powerful method in structural engineering, referred to as the method of aggregation, for reducing the weight and increasing load capacity of structures. Rigorous results have been stated and proved, forming the foundation of the aggregation method for structures composed of beams with arbitrarily shaped cross-sections. The essence of this method, overlooked in modern stress analysis, lies in consolidating loaded elements into a reduced number of elements with larger cross-sections, thereby significantly decreasing the material required to support a given total load. For instance, in a five-to-one aggregation of cantilever and simply supported beams, material usage can be reduced by a factor of 1.71. For cantilever and simply supported beams, the reduction in material volume, deflection, and stress depends only on the scaling factor of the cross-section along the y-axis and is independent of the scaling factor along the x-axis. The aggregation method was tested by a case study and finite element experiments involving structures built on statically determinate cantilever beams and statically indeterminate portal frames. These studies confirmed that aggregating elements loaded in bending leads to a drastic increase of the load capacity of the structures and a drastic decrease of both the maximum von Mises stress and the maximum deflection.