TORSIONAL COUPLING EFFECTS FOR STRUCTURES EXPOSED TO VRANCEA EARTHQUAKES Ruxandra Enache 1* , Sorin Demetriu 1 and Emil Albot1 1 Depart ment of Theoretical Mechani cs, St atics and Dynamics of Structures Technical University of Civi l Engineering Bd. Lacul Tei 124, sector 2, 38RO-020396 Bucharest, Romani a E-mail: [email protected][email protected][email protected]Keywords: torsion, coupling, eigenmodes ABSTRACT The dynamic response of a system with coincidence between mass and stiffness center is a translational one. Natural torsion appears in systems where these two centers don’t lie in the same point. The dynamic response couples torsion and translation on one or two orthogonal directions, depending on the existence of a symmetry axis. The natural modes of vibration for single level dynamic systems with eccentricities on two orthogonal directions in plan are studied in this paper. There are outlined some parameters which have influence upon the modal coupling. The normalized eccentricities and the natural frequencies of the uncoupled system decide if the fundamental mode of vibration is in translation, in torsion or a coupled one. The nature of the fundamental mode of vibration influences the dynamic response of the system. The considered systems are acted by accelerograms recorded durin g 1977 Vran cea earthquake. 1. INTRODUCTION Torsion usually refers to non-symmetrical structural systems (the mass center and the stiffness center lie in different points). The phenomenon is named natural torsion and the systems are torsional coupled systems. It is possible to appear torsion even in symmetrical buildings, known as accidental torsion, which may be induced by the rotational component of the ground motion during an earthquake or uncertainties in mass or stiffnesses distribution. In this paper it i s studied the response of torsional coupled systems in free vi brations (the natural modes of vibration). The character of the fundamental eigenmode has a great influence
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The dynamic response of a system with coincidence between mass and stiffness center is atranslational one. Natural torsion appears in systems where these two centers don’t lie in the
same point. The dynamic response couples torsion and translation on one or two orthogonal
directions, depending on the existence of a symmetry axis.
The natural modes of vibration for single level dynamic systems with eccentricities on two
orthogonal directions in plan are studied in this paper. There are outlined some parameters
which have influence upon the modal coupling. The normalized eccentricities and the natural
frequencies of the uncoupled system decide if the fundamental mode of vibration is in
translation, in torsion or a coupled one. The nature of the fundamental mode of vibration
influences the dynamic response of the system. The considered systems are acted by
accelerograms recorded during 1977 Vrancea earthquake.
1. INTRODUCTION
Torsion usually refers to non-symmetrical structural systems (the mass center and the stiffness
center lie in different points). The phenomenon is named natural torsion and the systems are
torsional coupled systems. It is possible to appear torsion even in symmetrical buildings,
known as accidental torsion, which may be induced by the rotational component of the ground
motion during an earthquake or uncertainties in mass or stiffnesses distribution.
In this paper it is studied the response of torsional coupled systems in free vibrations (the
natural modes of vibration). The character of the fundamental eigenmode has a great influence
on the behaviour of the dynamic system. A simple method for identifying this character is
developed.
2. THE DYNAMIC SYSTEM
The linear considered system is a single story structure as it is presented in Figure 1. It is made
the assumption that the mass is distributed to the rigid floor supported by massless columns orshear walls. The coordinate axes have the origin in the mass center (CM). The translational
stiffness of the vertical elements is non-symmetrical distributed on the two axis X and Y. The
stiffness center CR is that point of the floor where, if applied, a horizontal force produces only
translation. The distance between the stiffness and the mass center is defined by the static
eccentricities ex and ey :
∑=i
i yi
y
x R x
Re
,
1 and ∑=
i
i xi
x
y R y
Re
,
1 (1)
where R x,i and R y,i are the translational stiffnesses of the ith element and xi and yi define the position of this element about the mass center and R x and R y are the translation stiffnesses on x
and y:
∑=i
i x x R R , and ∑=i
i y y R R , (2)
The dynamic coordinates associated to the three degrees of freedom are two horizontal
translations and a rotation about a vertical axis.
3. NATURAL MODES OF VIBRATION
For the analysed system, the characteristic equation is: