Dynamic and static response of beam-like hyperbolic paraboloid concrete elements: A numerical, analytical, and experimental study

Abstract

Beam-like hyperbolic paraboloid (HP) elements carry loads primarily through membrane action, enabling thinner cross-sections and up to 70% less material compared to bending-active slabs and beams. Their doubly ruled geometry permits reinforcement and prestressing with straight elements, simplifying construction and lowering cost relative to other shell typologies. Experimental verification of their structural response remains limited—yet it is essential to support a broader adoption of these elements. This thesis investigates the static and dynamic behaviour of an existing HP prototype element using analytical modelling, finite element analysis (FEA), experimental modal analysis (EMA), and static load testing. Dynamic properties, including natural frequencies, damping ratios, and mode shapes, were identified using a roving hammer test. Static behaviour was evaluated under uniform pressure loading and a four-point bending test to failure, with strain data obtained via distributed fibre optic sensing (DFOS) and digital image correlation (DIC). EMA identified six flexural modes below 220 Hz, with a fundamental frequency of 50.9 Hz and damping ratios between 0.56% and 1.1%. Numerical sensitivity studies explored the effects of boundary conditions, reinforcement, and modelling approaches on modal characteristics. Calibrated numerical models predicted resonance frequencies within 3% of experimental values and demonstrated strong mode shape correlation. Strain data obtained from DFOS and DIC provided insight into the strain evolution under static loading conditions. Non-linear FEA enabled the prediction of deformations, crack patterns, and ultimate load capacity. Sensitivity studies were performed to assess the influence of boundary conditions, reinforcement configurations, and concrete– reinforcement interface modelling. The degree of longitudinal restraint was found to significantly affect both the structural response and the load-bearing capacity. Preliminary comparisons indicated that the numerical models reasonably captured the observed strain and crack patterns. Through these static and dynamic assessments the thesis contributes to a deeper understanding of the structural behaviour of HP elements. It provides experimental validation and builds confidence in how these elements can be reliably modelled. Key words: Hyperbolic paraboloid (HP) shell structures, Reinforced concrete, Experimental modal analysis (EMA), Experimental stress analysis (ESA), Non-linear finite element analysis (NLFEA), Roving hammer testing, Distributed fibre optic strain sensing (DFOS), Digital image correlation (DIC)