Abstract: This article presents a 3-D modified non-linear elastic model in the strain space. The Helmholtz free energy function is introduced with the existence of a dissipation potential surface in the space of thermodynamic conjugate forces. The constitutive equation and the damage evolution were derived as well. The modified damage has been examined to model the nonlinear behavior of reinforced concrete (RC) slabs with an opening. A parametric study with RC was carried out to investigate the impact of different factors on the behavior of RC slabs. These factors are the opening area, the opening shape, the place of opening, and the thickness of the slabs. And the numerical results have been compared with the experimental data from literature. Finally, the model showed its ability to be applied to the structural analysis of RC slabs.
Abstract: In construction industry, reinforced concrete (RC) slabs
represent fundamental elements of buildings and bridges. Different
methods are available for analysing the structural behaviour of
slabs. In the early ages of last century, the yield-line method has
been proposed to attempt to solve such problem. Simple geometry
problems could easily be solved by using traditional hand analyses
which include plasticity theories. Nowadays, advanced finite element
(FE) analyses have mainly found their way into applications of
many engineering fields due to the wide range of geometries to
which they can be applied. In such cases, the application of an
elastic or a plastic constitutive model would completely change the
approach of the analysis itself. Elastic methods are popular due to
their easy applicability to automated computations. However, elastic
analyses are limited since they do not consider any aspect of the
material behaviour beyond its yield limit, which turns to be an
essential aspect of RC structural performance. Furthermore, their
applicability to non-linear analysis for modeling plastic behaviour
gives very reliable results. Per contra, this type of analysis is
computationally quite expensive, i.e. not well suited for solving
daily engineering problems. In the past years, many researchers have
worked on filling this gap between easy-to-implement elastic methods
and computationally complex plastic analyses. This paper aims at
proposing a numerical procedure, through which a pseudo-lower
bound solution, not violating the yield criterion, is achieved. The
advantages of moment distribution are taken into account, hence the
increase in strength provided by plastic behaviour is considered. The
lower bound solution is improved by detecting over-yielded moments,
which are used to artificially rule the moment distribution among
the rest of the non-yielded elements. The proposed technique obeys
Nielsen’s yield criterion. The outcome of this analysis provides a
simple, yet accurate, and non-time-consuming tool of predicting the
lower-bound solution of the collapse load of RC slabs. By using
this method, structural engineers can find the fracture patterns and
ultimate load bearing capacity. The collapse triggering mechanism is
found by detecting yield-lines. An application to the simple case of
a square clamped slab is shown, and a good match was found with
the exact values of collapse load.
Abstract: The aim of this paper is to perform experimental
modal analysis (EMA) of reinforced concrete (RC) square slabs.
EMA is the process of determining the modal parameters (Natural
Frequencies, damping factors, modal vectors) of a structure from a
set of frequency response functions FRFs (curve fitting). Although,
experimental modal analysis (or modal testing) has grown steadily in
popularity since the advent of the digital FFT spectrum analyzer in
the early 1970’s, studying all types of members and materials using
such method have not yet been well documented. Therefore, in this
work, experimental tests were conducted on RC square slab
specimens of dimensions 600mm x 600mmx 40mm. Experimental
analysis was based on freely supported boundary condition.
Moreover, impact testing as a fast and economical means of finding
the modes of vibration of a structure was used during the
experiments. In addition, Pico Scope 6 device and MATLAB
software were used to acquire data, analyze and plot Frequency
Response Function (FRF). The experimental natural frequencies
which were extracted from measurements exhibit good agreement
with analytical predictions. It is showed that EMA method can be
usefully employed to investigate the dynamic behavior of RC slabs.
Abstract: This paper focuses on the dynamic behavior of
reinforced concrete (RC) slabs. Therefore, the theoretical modal
analysis was performed using two different types of boundary
conditions. Modal analysis method is the most important dynamic
analyses. The analysis would be modal case when there is no external
force on the structure. By using this method in this paper, the effects
of freely and simply supported boundary conditions on the
frequencies and mode shapes of RC square slabs are studied. ANSYS
software was employed to derive the finite element model to
determine the natural frequencies and mode shapes of the slabs.
Then, the obtained results through numerical analysis (finite element
analysis) would be compared with the exact solution. The main goal
of the research study is to predict how the boundary conditions
change the behavior of the slab structures prior to performing
experimental modal analysis. Based on the results, it is concluded
that simply support boundary condition has obvious influence to
increase the natural frequencies and change the shape of the mode
when it is compared with freely supported boundary condition of
slabs. This means that such support conditions have the direct
influence on the dynamic behavior of the slabs. Thus, it is suggested
to use free-free boundary condition in experimental modal analysis to
precisely reflect the properties of the structure. By using free-free
boundary conditions, the influence of poorly defined supports is
interrupted.