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Vincent Chu answers......
How to determine the size of elastomeric bearings?
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Vincent T. H. Chu is renowned internationally Photograph of vincent chuas walking encyclopedia of civil engineering. Author of a number of widely acclaimed civil engineering books, Mr Chu is recipient of various reputed awards including Young Engineer of the Year Award 2008 (Merit) by the Hong Kong Institution of Engineers &  Ombudsman’s Award 2007 (under complaint-related category). He is also listed in 11th Edition of Marquis Who's Who in Science and Engineering. ConcreteBasics.org thanks him for his exemplary contribution to the cause of civil engineers around the world.
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For  elastomeric  bearing,  the  vertical  load  is  resisted  by  its  compression  while  shear resistance of the  bearing controls the horizontal movements. The design of elastomeric bearings is based on striking a  balance between the provision of sufficient stiffness to resist  high  compressive  force  and  the  flexibility  to  allow  for  translation  and  rotation movement.

The cross sectional area is normally determined by the allowable pressure on the bearing support.  Sometimes, the plan area of bearings is controlled by the maximum allowable compressive stress arising from the consideration of delamination of elastomer from steel plates.

In addition, the size of elastomeric bearings is also influenced by considering the separation between the structure and the edge of bearing  which may occur in rotation because tensile stresses deriving from separation may cause delamination.

The thickness of bearings is designed based on the limitation of its horizontal stiffness and is controlled by movement requirements. The shear strain should be less than a certain limit to avoid the occurrence of rolling over and fatigue damage. The vertical stiffness of bearings is obtained by inserting sufficient number of steel plates.

Reference: 200 Questions and Answers on Practical Civil Engineering Works by Vincent Chu
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