reinforced concrete beam design using catenary theory

Catenary theory was first proposed by robert hooke in 1675, originally presented as an anagram. in brief, catenary theory is the study of a draping chain, its application to efficient arches and understanding how stress flows naturally in structural members. a draping chain is in pure tension, and free of bending and shears. if inverted, the stresses change to pure compressions, and therefore recognized by hooke as ideally suited for arches. however, since the initial discovery, it took 16 years to understand the mathematics of the catenary, and ever since, the application of catenary theory to structures has been meagre. compression arching in beams, however, is a well-known concept, and has been applied to structures for thousands of years. nevertheless, the actual geometry of the arch has never been identified, nor connected to catenary theory. this study begins by first establishing the actual geometry of the compression arch in a beam, which is catenary, using a recently developed equilibrium technique called funicular arch theory (or segmental equilibrium method). having established the geometry of the compression arch, catenary theory was applied to reinforced concrete beam design, to determine the flexural and shear steel. the theory is developed from first principles, and compared to codes of practice, such as bs8110 and sans 10100. the prediction of the required flexural and shear steel is similar, establishing catenary theory as an alternative method to design reinforced concrete beams. in addition, the catenary equations were mathematically manipulated to solve for the scaling factor “a” (a component of the catenary equation), without requiring the equations to be iterated. this mathematical manipulation was necessary to make the proposed method more usable as a design tool.