authored by Ehsan Kazeminezhad*
Abstract
Base isolation is one of the ways to stabilize structures against earthquake. In general, two types of system for isolate are used: laminated rubber bearing and lead rubber bearing. In this paper, the laminated rubber bearing is used. These isolators are made of bonded steel and rubber sheets with vulcanization. One of the most important factors for their design is stability because they can cause damage to the upper structures due to instability. For stability check the buckling load calculated based on the theory relation and compared with the finite element method. The support rotation causes a significant reduction in the buckling load and critical displacement of the isolators. In this research, the buckling load of square and circular isolator is calculated and shows that the buckling load of square isolator is higher than the circular ones and also rotation decreases the critical displacement.
Keywords: Laminated rubber bearing; Buckling load; Critical displacement; Circular bearing; Square bearing
Introduction
The most important concern of civil engineers in design is the acceleration and relative displacement of stories of building. To limit these items in structures, the dimension and construction costs will increase. Separating the earthquake vibration from the structure is one of the best possible methods. The separation method is performed by an elastomeric bearing. These supports cause the spectrum acceleration to decrease dramatically by increasing the natural period of structure and also cause the base shear to be reduced up to fifty percent. In conventional and mid-height buildings, the rotation does not occur at the joint between isolator and structures, but in high rise buildings and bridges that rotation can be observed. Rotation causes a changing in the buckling modes and the critical force. The laminated rubber bearing (LRB) consists of rubber and steel sheets. These bearings have low horizontal stiffness and high vertical stiffness. Staudacher et al. [1] reviewed the isolation history. The first idea for base isolation was introduced by Klantarintz in England showing that if a building is constructed on free lubricated seams and soft sand or mica, the seismic forces to the building will be reduced. It should also be said that the first base isolation device for a third-floor building was constructed in Yugoslavia. Tarics et al. [2] shown that the first rubber with relatively high damping was manufactured in 1984 at Malaysian Tire Manufactures Research Institute in England which was used in a US-based legal and judicial building. The shear stiffness of these rubbers is high in low strain, but when the strain increases that will decrease by 4 to 6 times and when the strain reaches at about fifty percent, that will reach to its minimum amount. The shear stiffness will also increase when the strain is a more than 100%. The building design with the base isolation theory was presented by Naeim & Kelly [3] revealing that the relative displacement decreases in the first and higher modes of vibration due to higher modes’ normal to the first mode and ground motion. Higher modes do not also have any effect on the building displacement. Ravi et al. [4] showed that for the combined compression and shear loading case the numerical prediction matches well with the experimental result. The comparison is particularly good in the shear strain range from 50% to 150% which is of actual interest in design. The variation in the vertical compressive load from 0 to 200% of the design vertical load does not influence the horizontal displacement response due to the shearing loading. Kelly (1997) developed a base isolation theory and provided the relationships for critical loading and created a new isolator calculation. Warn & Weisman [5] studied the coupled horizontal – vertical behavior of elastomeric and lead rubber seismic isolation bearing and also investigated the mechanical properties of isolators. Tsai & Hsueh [6] indicated that rubber properties depend on strain amplitude and the loading frequency. Thus, they employed the viscoelastic treatment to indicate the effect of damping on the bearing response. Karbakhsh et al. [7] point out that the nonzero initial boundary condition changes the mechanical properties of laminated rubber bearing and the ending rotation decreases the horizontal stiffness. Kelly & Takhirov [8] examined the tension buckling in elastomeric bearing and reported the upward displacement. They also presented a theoretical relation for the tension and compression buckling. This research is presented in three main sections. In the first part, we ensure the accuracy of the modeling in the software. In the second part, the effect of the rotation on the critical load is investigated and the third part effect of the rotation on the critical displacement is evaluated. The ABAQUS software was also used for the finite element method. The innovation of the work is that so far, the effect of the support rotation on buckling load and critical displacement has not been investigated and empirical relationships are only able to calculate buckling load in non-rotational conditions.
Assumptions and Methodology
Base isolator structure
Base isolator bearing consists of rubber and steel sheets. These isolators have high vertical stiffness and low horizontal stiffness to resist against the vertical load and lateral displacement respectively. Steel and rubber are connected to each other by vulcanization process. Two end plates (flanges) are also used in up and down isolators.
Isolator and material modeling
Two materials were used in the isolator bearing: steel and rubber. In the base isolator bearing steel is linear and rubber is highly nonlinear. Full 3D models in geometry and loading conditions for each isolator were used in this study. The hybrid C3D8H element and full integration C3D8 of ABAQUS have been used to model the rubber and steel shims respectively. To simulate the experimental conditions of applying the load, a dummy node at the top of the isolator is modeled. The node is connected with all the nodes lying in top of the end plate by multipoint constraints so that the end plate is constrained to translate in the horizontal direction as a whole. The vertical and horizontal forces were applied through this dummy node.
Rubber-like material in ABAQUS
For modeling rubber-like material properties, there exist many options such as hyperelastic and viscoelastic in ABAQUS. The hyperelastic behavior is used which is described as a function of strain energy potential defining the strain energy stored in the material per unit of reference volume (initial volume) as a function of strain at that point in the material. There are several forms of stain energy potentials available in ABAQUS to approximately model the elastomers: Arruda-Boyce, Marlow, Mooney-Rivilin, Neo-Hookean, Poly-nominal, Reduced polynomial, Yeoh and Van der waals. These were described in the ABAQUS documentation and were briefly explained here. Arruda-Boyce model is based on molecular chain network, it is also called Arruda-Boyce 8-chain model because it was developed based on the representative volume (hexahedron) element where 8 chains emanate from the center to the corners of the volume. This is a two-parameter shear model based only on I1 which works well with the limited test data. Arruda-Boyce model is shown in Eq.(1):
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