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EXCEPTIONAL ACTIONS: BLAST LOADS ON REINFORCED CONCRETE STRUCTURES
No full textThe paper deals with the flexural failure of Reinforced Concrete elements under
blast loads. The main topics and results of a PhD thesis are here summarized, whose
aim was to develop theoretical dynamic and energy models capable of evaluating the
dynamic response of R.C. elements under explosive load.
In the original work, models with different levels of complexity were presented, but
for sake of simplicity only the simplest Single Degree Of Freedom (SDOF) system has
been here discussed. Strain-rate effects are also accounted for.
A sensitivity analysis to determine the key parameters in beam response under
blast load has been developed by means of the SDOF model. Results of numerical
simulations obtained in terms of deflection and velocity have been fitted by proper
polynomial least-square interpolation.
Among the various interpolations considering several parameters (peak load,
positive phase duration, slenderness, span length, concrete strength, reinforcement
ratio etc.) slenderness (corresponding to stiffness) and peak load prove to be the most
important parameters, but span length (corresponding to mass) is also a key
parameter. Other variables such as concrete strength and reinforcement ratio do not
seem to have a high correlation with results.
Lastly some suggestions for blast-resistant bridge design are presented
INCREMENTO PRESTAZIONALE DI EDIFICI IN C.A. RESISTENTI AD ESPLOSIONE E RELATIVA VALUTAZIONE ECONOMICA
No full textIl lavoro ha come obiettivo quello di valutare l’incremento del costo complessivo di un edificio sismo-resistente affinché questo sia in grado di sopportare anche un carico da esplosione. Si sono valutati diversi scenari di carico in cui la struttura è costituita da un sistema intelaiato monopiano in C.A. (tipico dell’edilizia industriale) localizzato in zone con differente pericolosità sismica. Si è prima calcolato il costo della struttura sottoposta alle combinazioni di carico usuali (anche quelle sismiche) quindi quello della stessa costruzione sottoposta alla combinazione di carico eccezionale riferita ad un evento esplosivo. Dai risultati è possibile desumere semplicemente il costo per incrementare la robustezza strutturale necessaria per un dato livello di sicurezza. Si fornisce anche un’indicazione su quale deve essere la minima distanza di sicurezza dalla costruzione (distanza di stand-off) economicamente accettabile da garantire attraverso l’utilizzo di elementi di arredo urbano o opportuni dissuasori
Azioni Esplosive sulle strutture in C.A.
No full textThis paper deals with the effect of blast
loading on R.C. structures. After depicting load
and materials characteristics in blast event,
different alternative structural models are
proposed. The first approach idealizes the beam
as a single degree of freedom system, the second
models it by means of Euler-Bernoulli’s theory and
its elastic-plastic behaviour is expressed through a
nonlinear relationship between bending moment
and curvature. The effects of strain rate are taken
into consideration by introducing time-variable
coefficients into the equations of motion derived
from the two models. The comparison with some
experimental results assesses the reliability of the
approach, and a sensibility analysis of the
different involved parameters is then developed.
Slenderness and span length proved to be the key
parameters and let the Authors to find a
polynomial relation between them and the
maximum displacement/velocity of the beam
Theoretical models to predict the flexural failure of reinforced concrete beams under blast loads
Full text linkThis 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
Evaluation of the structural response of reinforced concrete beams failing in flexure under blast loads
No full textIn this paper, the structural responses of reinforced concrete (RC) beams subjected to blast loading are investigated.
In particular, RC beams with a low reinforcement ratio are examined, which are more likely to fail in flexure than in
shear. In order to assess the response of the beam, two analytical approaches are developed. In the first one, the
beam is modeled as a continuous element by means of Euler-Bernoulli’s theory, which neglects the contributions of
shear deformation and rotary inertia. The nonlinear behaviour of the beam in the elastic-plastic range is approximated
by a single smooth relationship between bending moment and curvature, which allows to derive an original
expression of the differential equation of motion of the beam. The parameters appearing in the latter are easily determined
from the geometric and constitutive properties of the beam. The second approach described in this paper
consists in evaluating the response of the beam through an equivalent single degree of freedom (SDOF) system. The
latter is a mass-spring oscillator, and its constitutive behaviour is expressed through a bilateral relationship between
force and displacement. The main drawback of this simplified approach is the need to introduce empirical quantities,
such as the equivalent mass and the length of the plastic hinge. In both approaches, strain rate effects are taken into
account. In fact, these effects should not be ignored in problems concerning blast loads, since the mechanical properties
of both concrete and steel strongly depend on the rate of deformation. In this paper, strain rate effects are considered
by changing the parameters related to the material properties during time, in accordance with the rules provided
by the CEB Information Bulletin n. 187 and the fib Bulletin n. 55. Finally, in order to test the validity of the
two approaches, the theoretical results are compared with some experimental data found in literature. In particular,
the time-histories of the maximum deflections of several simply supported RC beams under uniformly distributed
loads generated by explosions are analyzed. It is shown that the first approach is capable of predicting both the maximum
displacement time-history and the deflection at collapse of any beam accurately. On the other hand, the
second approach gives a less precise assessment of the structural response of the beam; nonetheless, the method
based on the equivalent SDOF model is simpler to use and its differential equation of motion is faster to integrate
SDOF models for reinforced concrete beams under impulsive loads accounting for strain rate effects
Full text linkIn 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
RELIABILITY OF ANCIENT RC STRUCTURES BY MEANS OF NUMERICAL MODELING
No full textIn sustainability theme it is very important to know if the historical existing buildings may be used nowadays or they must be refurbished or, even, demolished and reconstructed. Among them may be included even reinforced concrete structures. The paper deals with the steps that plan out the understanding of the behaviour of such structures: critical approach, original documents research and interpretation, paraphrase of former calculations, safety assessment by means of current calculation methods and codes. As an exemplification of the above mentioned procedures two significant cases, both in Cagliari, are presented in this work. The CasMez pavilion, a folded plate RC structures, and the San Domenico Church, a meaningful example of the interaction between modern and ancient architecture
Ottimizzazione di piastre in C.A. allo SLU
No full textNel presente lavoro si affronta lo studio di strutture bidimensionali costituite da piastre inflesse in C.A. L’articolo illustra le tecniche ed i risultati ottenuti in un concreto problema di ottimizzazione strutturale. Nell’analisi sono utilizzati il metodo delle linee di rottura, il principio dei lavori virtuali, l’algoritmo Simulated Annealing (SA) e una originale procedura degli autori implementati in ambiente MATLAB. L’obiettivo è la determinazione della migliore disposizione delle armature e la definizione dello spessore ottimale dell’elemento che consentano di ottenere maggiori benefici sul piano economico nel rispetto dello Stato Limite Ultimo. In conclusione i risultati ottenuti evidenziano che la scelta ottima non viene influenzata (se non marginalmente) dalle variazioni dei prezzi del mercato o delle caratteristiche dei materiali rivelando una notevole stabilità della soluzione trovata
Modal analysis of laminated composite plates by a new hybrid assumed strain finite element
No full textFibre reinforced plates and shells are funding an increasing interest in engineering applications;
in most cases dynamic phenomena need to be taken into account. Consequently effective
and robust computational tools are sought in order to provide reliable results for the analysis of such
structural models. In this paper the laminate hybrid assumed-strain plate element presented in [1],
and used there in a static analysis, has been extended to the dynamic realm. This model is derived
within the framework of the so called First-order Shear Deformation Theory (FSDT) [2], [3]. What
is peculiar in this assumed strain finite element is the direct modelling of the in-plane strain components;
the corresponding stress components are deduced via constitutive law. By enforcing the
equilibrium equations for each lamina, account taken of continuity requirements, the out-of-plane
shear stresses are computed and, finally, constitutive law provides the corresponding strains. The
resulting global strain field depends on a fixed number of parameters, regardless of the total number
of layers. Since the proposed element is not locking prone even in the thin plate limit and provides
an accurate description of inter-laminar stresses, an extension to the dynamic range seems to be
particularly attractive. The same kinematic assumptions will lead to the formulation of a consistent
mass matrix. The element, developed in this way, has been extensively tested for several lamination
sequences and comparison with analytical solutions are presented
AZIONI ESPLOSIVE SU TRAVI IN ACCIAIO
No full textIn this paper, the structural responses of steel beams subjected to air-blast loading are investigated.
In order to assess the response of beams, two Single Degree of Freedom models are
developed. In the first model (denoted as “dynamic model”), the dynamic behaviour of the
beam is simulated by a simple spring-mass oscillator. The second model (named “energy
model”) is developed from the equation of energy balance. In both formulations, the strain
rate dependencies of the constitutive properties of the beams are considered. In fact, these effects
should not be ignored in problems concerning blast and impulsive loads, since the mechanical
properties of steel strongly depend on the rate of deformation. In this paper, strain
rate effects are considered in accordance with the espression provided by Cowper-Symonds
strain rate model. Finally, in order to test the validity of the two approaches, the theoretical
results produced by the latter ones are compared with some experimental data found in literature.
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
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