Browsing by Author "Chopra, Anil K."

Now showing 1 - 11 of 11
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    A macro-element model for inelastic building analysis
    (2000) Llera Martin, Juan Carlos de la; Vásquez P., Jorge; Chopra, Anil K.; Almazán Campillay, José Luis
    A three-dimensional model for approximate inelastic analysis of buildings is presented herein. The model is based on a single macro-element per building storey. The inelastic properties of the model are characterized by the so-called ultimate storey shear and torque (USST) surfaces. Different algorithms for the construction of these surfaces, as well as their applications in building modelling, are presented and discussed. Two alternative procedures are developed to integrate the force-deformation constitutive relationship of the macroelements. The first one follows the exact trajectory of the load path of the structure on the USST, and the second uses linear programming without ever forming the USST surface. The accuracy of the model and integration procedure is evaluated by means of the earthquake response of single-storey systems. The model and integration procedure developed is finally used to compute the inelastic response of a seven-storey R/C building. The results of this investigation show that the model proposed, although approximate, can be effective in estimating the inelastic deformation demand of a building. It also enables the engineer to capture and interpret important features of the three-dimensional inelastic response of a structure even before performing any inelastic dynamic analysis. Copyright (C) 2000 John Wiley & Sons, Ltd.
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    A simplified model for analysis and design of asymmetric-plan buildings
    (1995) Llera Martin, Juan Carlos de la; Chopra, Anil K.
    A new simplified model for analysis and design of multistorey buildings is developed. The model is based on a single super-element per building storey capable of representing the elastic and inelastic properties of the storey. This is done by matching the stiffness matrices and ultimate yield surface of the storey with that of the element; this surface relates storey shear and storey torque. For practical convenience, these surfaces are parametrized in terms of seven important physical parameters controlling the seismic response of asymmetric structures. Several numerical studies showed that the accuracy of the super-element model is satisfactory for most design purposes; the errors in peak responses are expected to be less than 20 per cent for most practical structures. Among the important advantages of this simplified model is that the time required in formulating, analysing and interpreting the structural model and its response is at least an order of magnitude smaller than for any conventional 3-D inelastic model. This enables the engineer to try different structural configurations and, thus, produce designs that have the desired seismic behaviour and are cost-effective. Furthermore, it has been shown through a multistorey building example that the super-element model is a powerful tool for conceptual design of a building. In spite of its simplicity, the model uses an accurate representation of the storey-shear and torque surfaces, which enables it to capture the fundamental features controlling the inelastic behaviour of the building.
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    Accidental torsion in buildings due to base rotational excitation
    (1994) De La Llera Martin, Juan Carlos; Chopra, Anil K.
    This investigation is concerned with accidental torsion in buildings resulting from rotational excitation (about a vertical axis) of the building foundations as a result of spatially non-uniform ground motions. Because of this accidental torsion, the displacements and deformations in the structural elements of the building are likely to increase. This increase in response is evaluated using actual base rotational excitations derived from ground motions recorded at the base of 30 buildings during recent California earthquakes. Accidental torsion has the effect of increasing the building displacements, in the mean, by less than 5 per cent for systems that are torsionally stiff or have lateral vibration periods longer than half a second. On the other hand, short period (less than half a second) and torsionally flexible systems may experience significant increases in response due to accidental torsion. Since the dependence between this increase in response and the system parameters is complex, two simplified methods are developed for conveniently estimating this effect of accidental torsion. They are the ‘accidental eccentricity’ and the ‘response spectrum’ method. The computed accidental eccentricities are much smaller than the typical code values, 0.05bb or 0.1b, except for buildings with very long plan dimensions (b ≥ 50 m). Alternatively, by using the response spectrum method the increase in response can be estimated by computing the peak response to each base motion independently and combining the peak values using the SRSS rule.
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    Accidental torsion in buildings due to stiffness uncertainty
    (1994) Llera Martin, Juan Carlos de la; Chopra, Anil K.
    Discrepancies between the computed and actual values of the structural element stiffness imply that a building with nominally symmetric plan is actually asymmetric to some unknown degree and will undergo torsional vibration when subjected to purely translational ground motion. Such accidental torsion leads to increase in structural element deformations which is shown to be essentially insensitive to the uncoupled lateral vibration period of the system but is affected strongly by the ratio of uncoupled lateral and torsional vibration periods. The structural deformations increase, in the mean, by at most 10 and 5 per cent for R/C and steel buildings, respectively, and by much smaller amounts for a wide range of system parameters. The increase in structural deformations due to stiffness uncertainty is shown to be much smaller than implied by the accidental torsional provisions in the Uniform Building Code and most other building codes.
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    Accidental torsion in buildings: analysis versus earthquake motions
    (2001) Lin, Wen-Hsiung; Chopra, Anil K.; Llera Martin, Juan Carlos de la
    A simplified analysis procedure has been developed to consider accidental torsion in building design that is rational and convenient relative to building codes. This procedure is extended and evaluated in this paper against measured accidental torsion determined from motions of 12 buildings-with nominally-symmetric plan-recorded during Northridge (1994), boma Prieta (1989), Whittier (1987), and Upland (1990) earthquakes. The selected buildings include structures in reinforced concrete and in steel that cover a wide range of structural systems, including moment resisting frames, shear walls, braced frames, and hybrid systems. After the measured torsion is interpreted and compared to analytical estimates, it is demonstrated that this procedure is sufficiently accurate to be used in design applications.
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    Estimation of accidental torsion effects for seismic design of buildings
    (1995) Llera Martin, Juan Carlos de la; Chopra, Anil K.
    A procedure is developed for including the effects of accidental torsion in seismic design of buildings. It has four steps. First, the ratio between the fundamental frequencies of uncoupled torsional and lateral motions of the building is computed. This ratio and plan dimensions are then used to estimate the increase in displacements at the edge of the building resulting from all sources of accidental torsion. Third, from these edge displacements the increase in displacements at the location of interior resisting planes are estimated. Finally, the design forces in structural members are computed by amplifying the forces ignoring accidental torsion by the increase in building displacements determined previously. This procedure has several advantages over the code-specified static and dynamic analysis procedures to include accidental torsion, such as: (1) The elimination of cumbersome static or three-dimensional dynamic analyses to account for accidental torsion effects in building design; and (2) the inclusion of the effects of all sources of accidental torsion. Two building examples are presented to illustrate these advantages as well as the computational steps required to implement the new procedure.
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    Evaluation of code accidental‐torsion provisions from building records
    (1992) Llera Martin, Juan Carlos de la; Chopra, Anil K.
    A procedure is presented for evaluating building‐code provisions for accidental torsion from analysis of earthquake‐induced motions of nominally symmetric‐plan buildings. This procedure is used to analyze the motions of three buildings recorded during recent California earthquakes. Two alternative approaches to evaluate the code accidental torsion provisions are developed. The first One considers the response histories of base shear and base torque in the building, and the second, the “actual” forces in the structural elements during the earthquake. The results show that base rotational motions cause between 25% and 45% of the total accidental torsion in the buildings. They also demonstrate that the accidental torsional moments specified by the Uniform Building Code are sufficient in representing the torsion in the recorded motions of the three buildings. Further, it is shown that accidental torsion need not be considered in the design of two of the three buildings studied. This observation, however, may not necessarily apply to other structures, such as buildings with torsional vibration periods much longer than their lateral vibration periods.
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    Inelastic behavior of asymmetric multistory buildings
    (1996) Llera Martin, Juan Carlos de la; Chopra, Anil K.
    Studied in this paper is the inelastic seismic behavior and design of asymmetric multistory buildings emphasizing, primarily, the use of story shear and torque histories. The following six different structural characteristics and their effect on the torsional response of buildings are analyzed: strength of orthogonal resisting planes, stiffness asymmetry, strength asymmetry, planwise distribution of strength, number of resisting planes, and intensity of the ground motion component in the orthogonal direction. As a result of these analyses several techniques and conceptual guidelines are developed to correct the planwise unbalance in deformation demands typical of asymmetric structures. The two most important are to increase the torsional capacity of the system by introducing resisting planes in the orthogonal direction, and to modify the stiffness and strength distribution to localize yielding in selected resisting planes. Using these guidelines the undesirable earthquake response of a very asymmetrical building is effectively corrected by changing slightly the strength of a few key resisting planes. Finally, it is concluded that the use of the story shear and response histories in conjunction with the corresponding story yield surfaces is a powerful tool for conceptual understanding of the earthquake behavior of asymmetric structures.
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    Three-dimensional inelastic response of an RC Building during the Northridge earthquake
    (2001) Llera Martin, Juan Carlos de la; Chopra, Anil K.; Almazán Campillay, José Luis
    The three-dimensional inelastic earthquake response of a seven-story reinforced-concrete building during the 1994 Northridge earthquake is studied herein. The objectives of this investigation are as follows: (1) to understand the, inelastic behavior of the building using recorded motions; and (2) to propose a simplified inelastic model that could explain the lateral-torsional coupling observed in this nominally symmetric building. Because several two-dimensional inelastic models of the building have been reported by other researchers, this paper focuses on the three-dimensional behavior of the structure. Response results of a simplified inelastic stick model that uses the story-shear and torque surfaces are compared with the results obtained from a conventional elastic three-dimensional building model, These results suggest that damage in the building occurred in the first few cycles of the response, and that the building showed markedly inelastic torsional behavior in spite of its nominal symmetry in plan. Such torsional behavior could also occur in other symmetric-plan buildings with strong perimeter frames, and constitutes a rather new phenomenon that should be studied further. It is proposed herein that such behavior be foreseen in design by using the concept of the ultimate story-shear and torque surface.
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    Understanding the inelastic seismic behaviour of asymmetric-plan buildings
    (1995) Llera Martin, Juan Carlos de la; Chopra, Anil K.
    Studied in this paper is the inelastic seismic behaviour of asymmetric-plan buildings using the histories of base shear and torque. The first step in understanding this behaviour is to construct the base shear and torque surface (BST) for the building, which represents all combinations of shear and torque that applied statically lead to collapse of the structure. Several factors controlling the shape of this surface, such as strength eccentricity and bidirectional ground motion, are identified. Also, their effects on the building responses are studied considering several structural configurations. The results obtained show that the BST surface, in conjunction with the base-shear and torque histories, provides a useful conceptual framework for understanding the behaviour of asymmetric systems. Furthermore, using these surfaces, relevant aspects of the behaviour and design of such buildings become apparent even before dynamic analysis of the structure.
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    Using accidental eccentricity in code-specified static and dynamic analyses of buildings
    (1994) Llera Martin, Juan Carlos de la; Chopra, Anil K.
    The differences between the increase in building response due to accidental eccentricity predicted by code-specified static and dynamic analyses are studied for symmetric and unsymmetric single and multistorey buildings. The increase in response computed from static analysis of the building is obtained by applying the equivalent static forces at distance ea, equal to the storey accidental eccentricity, from the centre of mass at each floor. Alternatively, this increase in response is computed by dynamic analysis of the building with the centre of mass of each floor shifted through a distance ea from its nominal position. A parametric study is performed on single-storey systems in order to evaluate the differences in response predicted by both analysis procedures. It is shown that these results are essentially the same as the ones obtained for a special class of multistorey systems. Upper and lower bounds for the differences in response computed from static and dynamic analyses are obtained for general multistorey systems. These differences in response depend primarily on the ratio of the fundamental torsional and lateral frequencies of the building. They are larger for small values of the frequency ratio and decrease to zero as the frequency ratio becomes large. Further, these discrepancies are in many cases of the same order as the code-intended increase in response due to accidental eccentricity. This implies that the code-specified static and dynamic analyses to account for accidental torsion should be modified to be mutually consistent.