|Session 5.2 - Structural Modelling|
Mass-eccentric Building Structures: Effects of Asymmetric Distribution of Axial Forces in Vertical Resisting Elements
Torsional behavior of asymmetric buildings is one of the most frequent sources of structural damage and failure during strong ground motions. Plan irregularity of buildings frequently involves the asymmetric distribution of mass which results in rotational motions of the floor slab in addition to the translational motions, even for stiff, strong symmetric systems. As a consequence, both force and displacement demands on vertical resisting elements can be larger then those they would experience in the presence of mass symmetry. Moreover, asymmetric distributions of mass leed to an asymmetric distribution of axial forces in resisting elements, presenting different lateral strength capabilities because of the influence of interaction phenomena. However, simple single storey asymmetric models used so far are not capable to show the influence of these aspects. They have in fact been developed under the assumption that resisting elements are able to sustain uni-directional horizontal forces only, and no allowance for vertical forces is usually made. Therefore, a refined advanced numerical model of one-storey asymmetric building structures has been developed which is able to overcome limitations of the above-mentioned simplified models. This new idealization can take into account the presence of vertical forces due both gravity loads and vertical input ground motion as well as effects of inelastic interaction between axial force and bi-directional horizontal forces. Results obtained from this new model are compared to those from previous models. It is evident of the significant effects of plan-asymmetry of axial forces due to gravity loads on the overall lateral-torsional inelastic behaviour.
Keywords: irregular buildings, mass eccentricity, torsional response, inelastic interaction.
Key elements in the seismic assessment of an existing reinforced concrete structure are the identification of the non-linear deformation sources of a member, and consequent adequate modelling of the identified non-linear behaviour. Tests on as-built reinforced concrete components with plain round longitudinal bars shows that the major non-linear deformation is due to flexural cracks of beams at beam-column interface, which is referred to as the fixed-end rotation of the beams. Beam deformation at the fixed-end occurs mainly due to severe bond degradation along the longitudinal reinforcement within the joint core, and it is associated with beam force transfer across the joint core - and therefore also with the other members framing into the same joint. All the existing member models assume that post-elastic behaviour of a member is fully determined by the considered member. Hence, there is a need for incorporating other members at the same joint in adequately modelling member behaviour at the fixed-end. Subsequently, a tentative member model is proposed.
Keywords: member model,post-elastic seismic behaviour, seismic assessment, bond slip, fixed-end rotation, beam-column joint
S.C. Fan and Z.N. Yin
Laboratory tests of structural elements, in particular the reinforced concrete beam-column joints, subjected to cyclic loading provide useful information of the structural damage and post-damage ductile behaviour during an earthquake. With the advent of computer technology, it is possible to study the complicated phenomena through numerical simulations. However, the major hindrance lies in the establishment of a sound constitutive model for concrete. This paper puts in place a multi-surface strength model for concrete, which accounts for the elastic, plastic, damage and post-damage behaviour. It is a semi-theoretical model, in which the strength envelope is derived from experimental meridians and completed through strength theory. Different from those popular but over-simplistic strength criteria, such as Tresca and Mises, the present strength model takes into account all stresses. Eventually, the strength model is presented in multi-surface form in the 3-dimensional stress space (p-space) for different phases. The key one is the maximum strength surface, which is subsequently used to derive the elastic-limit surface and series of plastic loading surfaces. In addition, evolution of stress states is governed by known rules for the loading-unloading-reloading processes. In the pre-damage phase, non-associate plasticity and hardening rule are employed to govern the behaviour of concrete. In the post-damage phase, anisotropic damage theory is used to describe the stiffness degradation. The numerical simulation of a beam-column joint is presented and compared with experimental results
Keywords: strength theory, concrete, constitutive law, cyclic loading
N.H.T. To, J.M. Ingham, B.J. Davidson and S. Sritharan
Nonlinear cyclic force-displacement responses of three concrete cantilever beams and three large-scale concrete bridge knee-joint systems were analysed using nonlinear cyclic strut-and-tie models. Existing element models in the computer program RUAUMOKO were employed for performing the nonlinear analyses. The analytical results were found to compare satisfactorily with the experimental data.
Keywords: cyclic structural response, strut-and-tie model
In 1960 Newmark showed that the displacements of inelastic structures subjected to earthquake excitation were similar to those of the same structure when it behaved elastically. Code writers have taken this to develop the equal displacement concept that has been the mainstay of seismic design codes for the past 40 years. Modifications have been made to the approach for structures with short natural periods of free vibration, to use the equal energy and equal acceleration concepts when deriving the inelastic design spectra. It will be shown in this paper that many of these assumptions are not particularly true even for the earthquake accelerograms used by Newmark. With all the advances in the analysis methods and design philosophies, such as capacity design and performance based design, made over the past 40 years that it is appropriate than the basic assumptions used in deriving the inelastic design spectra need to be re-appraised. This paper will outline a method of deriving the inelastic design spectra for any earthquake excitation allowing for almost any stiffness and strength degradation models to be used to represent the structural behaviour.
Keywords: inelastic response spectra, analysis, design spectra