SDOF models for reinforced concrete beams under impulsive loads accounting for strain rate effects

In this paper, reinforced concrete beams subjected to blast and impact loads are examined. Two single degree of freedom models are proposed to predict the response of the beam. The first model (denoted as “energy model”) is developed from the law of energy balance and assumes that the deformed shape of the beam is represented by its first vibration mode. In the second model (named “dynamic model”), the dynamic behavior of the beam is simulated by a spring-mass oscillator. In both formulations, the strain rate dependencies of the constitutive properties of the beams are considered by varying the parameters of the models at each time step of the computation according to the values of the strain rates of the materials (i.e. concrete and reinforcing steels). The efficiency of each model is evaluated by comparing the theoretical results with experimental data found in literature. The comparison shows that the energy model gives a good estimation of the maximum deflection of the beam at collapse, defined as the attainment of the ultimate strain in concrete. On the other hand, the dynamic model generally provides a smaller value of the maximum displacement. However, both approaches yield reliable results, even though they are based on some approximations. Being also very simple to implement, they may serve as an useful tool in practical applications

Punching of reinforced concrete slab without shear reinforcement: standard models and new proposal

Reinforced concrete (RC) slabs are characterized by reduced construction time, versatility, and easier space partitioning. Their structural behavior is not straightforward and, specifically, punching shear strength is a current research topic. In this study an experimental database of 113 RC slabs without shear reinforcement under punching loads was compiled using data available in the literature. A sensitivity analysis of the parameters involved in the punching shear strength assessment was conducted, which highlighted the importance of the flexural reinforcement that are not typically considered for punching shear strength. After a discussion of the current international standards, a new proposed model for punching shear strength and rotation of RC slabs without shear reinforcement was discussed. It was based on a simplified load-rotation curve and new failure criteria that takes into account the flexural reinforcement effects. This experimental database was used to validate the approaches of the current international standards as well as the new proposed model. The latter proved to be a potentially useful design tool

Collapse of prestressed reinforced concrete jetties: durabilityand faults analysis

Catastrophic collapses often are caused by minor details and lack of adequate precautionary measures. Such a case is presented in this paper, where the authors investigate the failure and collapse of jetties in a marina (built in 1974). The inquiry begins with collecting the original design documents and with the examination of the structural elements recovered from water. The original calculation report and drawings have been analysed in the light of the former and the current structural codes. Particular attention is drawn to the conceptual approach of the original designer. Back in the seventies, it was customary that a fully prestressed structural element did not have any ordinary reinforcement for bending. Therefore, the resistance depended only on the prestressing forces, and so the ratio between resistant bending moment and design bending moment MR/ME varied along with the positions of the strands. The calculations performed by the authors using up to date theories, have shown that the service life was almost adequate. The main cause of the failure was hidden behind a small detail: the external section of the strands, where bond between steel and concrete was prevented by a PVC duct, did not have an adequate protection. Hence, the sea water could penetrate the core of the element, causing severe corrosion

Theoretical models to predict the flexural failure of reinforced concrete beams under blast loads

This paper presents two alternative approaches for the study of reinforced concrete beams under blast loads. In the first approach, the beam is modeled by means of Euler–Bernoulli’s theory and its elastic–plastic behavior is expressed through a new nonlinear relationship between bending moment and curvature. In the second approach, instead, the beam is idealized as a single degree of freedom system. The effects of strain rate, which are of paramount relevance in blast problems, are taken into consideration by introducing time-variable coefficients into the equations of motion derived from the two models. The latter are employed to assess the time-history of the maximum deflection of a simply supported beam subjected to a uniformly distributed blast load. By comparing the theoretical results with some experimental findings available in literature and with the solution obtained from a commercial finite element software, it is found that the first approach is capable of accurately evaluating the maximum deflection of the beam at failure; on the other hand, the second approach provides a less precise prediction, however it is simpler to implement in practice because it requires less computational effort

Flexural models of reinforced concrete beams under blast load

Nowadays, the issue of structural safety under blast loading has become a dramatic problem. The tragic news of the terrorist attacks of recent years (9/11/2001, New York; 7/7/2005, London; 7/23/2005, Sharm El Sheik; 1/24/2011, Moscow; etc), raise important, urgent questions regarding the real safety and reliability of our buildings. Extreme loads such as impacts, explosions, etc., can occur in everyday life with unexpectedly high frequency. Actually, the problem of terrorist attacks, so important for strategic and military building design, has been linked to residential and industrial building explosion accidents. The present thesis deals with the flexural failure of Reinforced Concrete beams under blast loads. The main aim is firstly to develop dynamic and energy models capable of evaluating the response of R.C. under explosive load. Then a sensitivity analysis is obtained by means of the above mentioned models in order to determine what are the key parameters in the beam response. In this way it is possible to attain simple predictive polynomial formulations and, finally, simple table for early structural assessment of beams under blast load during the design procedure. The thesis is composed of three sections. Various dynamic models are developed in Section 1, taking into account the strain-rate sensitivity of both steel and concrete, as well as other nonlinearities in structural behaviour. Models with different levels of complexity are presented, from the simplest Single Degree Of Freedom (SDOF) system to Continuous Beam and Finite Element models. The characteristics, advantages and disadvantages of each approach are stated and discussed. The author compares his models with some experimental findings available in the scientific literature. The principal innovation that can be inferred from this section is the hypothesis of distributed plasticity along the beam (in the continuous model), represented by a non-linear smooth relationship between bending moment and curvature. This relationship, in addition to the Euler-Bernoulli beam equation, yields a non-linear Partial Differential Equation solved by means of the Finite Difference Method. In Section 2, the same problem is solved in a different way: starting from the principle of energy conservation, the innovative procedure, developed by the author, can calculate the displacement field of a R.C. beam under blast load. This procedure, less accurate than the previous one, produces very good results regarding midspan displacement, especially as it requires less computation time. In order to better understand the phenomenon, with the aim of identifying the key parameters in structural response, a sensitivity analysis is developed in Section 3. To this end, the author has performed a numerical investigation referring to the SDOF model presented in Section 1. Several numerical simulations are performed, with random variation of beam and load characteristics. Results are expressed in terms of maximum deflection and maximum velocity for each case. Then a least-squares interpolation has produced various polynomial curves and surfaces representing both a simplified tool to estimate structural response and a sensitivity analysis of the key parameters involved. One of the possible developments of this useful work is represented by simple tables that provide the response of the beam under blast load for early assessment in design procedures

On the whole spectrum of Timoshenko beams. Part I: a theoretical revisitation

The problem of free vibrations of the Timoshenko beam model is here addressed. A careful analysis of the governing equations allows identifying that the vibration spectrum consists of two parts, separated by a transition frequency, which, depending on the applied boundary conditions, might be itself part of the spectrum. For both parts of the spectrum, the values of natural frequencies are computed and the expressions of eigenmodes are provided. This allows to acknowledge that the nature of vibration modes changes when moving across the transition frequency. Among all possible combination of end constraints which can be applied to single-span beams, the case of a simply supported beam is considered. These theoretical results can be used as benchmarks for assessing the correctness of the numerical values provided by several numerical techniques, e.g. traditional Lagrangian-based finite element models or the newly developed isogeometric approach

On the whole spectrum of Timoshenko beams. Part II: Further applications

The problem of free vibrations of the Timoshenko beam model has been addressed in the first part of this paper. A careful analysis of the governing equations has shown that the vibration spectrum consists of two parts, separated by a transition frequency, which, depending on the applied boundary conditions, might be itself part of the spectrum. Here, as an extension, the case of a doubly clamped beam is considered. For both parts of the spectrum, the values of natural frequencies are computed and the expressions of eigenmodes are provided: this allows to acknowledge that the nature of vibration modes changes when moving across the transition frequency. This case is a meaningful example of more general ones, where the wave-numbers equation cannot be written in a factorized form and hence must be solved by general rootfinding methods for nonlinear transcendental equations. These theoretical results can be used as further benchmarks for assessing the correctness of the numerical values provided by several numerical techniques, e.g. finite element models

An analytical assessment of finite element and isogeometric analyses of the whole spectrum of Timoshenko beams

The theoretical results relevant to the vibration modes of Timoshenko beams are here used as benchmarks for assessing the correctness of the numerical values provided by several finite element models, based on either the traditional Lagrangian interpolation or on the recently developed isogeometric approach. Comparison of results is performed on both spectrum error (in terms of the detected natural frequencies) and on the l2 relative error (in terms of the computed eigenmodes): this double check allows detecting for each finite element model, and for a discretization based on the same number of degrees-of-freedom, N, the frequency threshold above which some prescribed accuracy level is lost, and results become more and more unreliable. Hence a quantitative way of measuring the finite element performance in modeling a Timoshenko beam is proposed. The use of Fast Fourier Transform is finally employed, for a selected set of vibration modes, to explain the reasons of the accuracy decay, mostly linked to a poor separation of the natural frequencies in the spectrum, which is responsible of some aliasing of modes

Seismic and Thermal Retrofitting of Masonry Buildings with Fiber Reinforced Composite Systems: A State of the Art Review

Old masonry buildings represent the largest part of traditional constructions. Generally, they are both seismically vulnerable and thermally dispersive. Therefore, the need for seismic and thermal retrofitting aimed at reducing their vulnerability and environmental impact has motivated research efforts towards sustainable retrofitting solutions. This study presents a literature review of the approaches currently available for masonry retrofitting. Specifically, it highlights the use of fiber in textile form i.e., Textile Reinforcement Mortar (TRM), as Fiber Reinforced Polymer (FRP) and natural fibers (animal and plant sources) to masonry retrofitting. In addition, specific attention is devoted to the integrated (structural and thermal) fiber-based integrated retrofitting techniques that are becoming very important in the last years