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Stability issues and pressure–shear interaction in elastomeric bearings: the primary role of the secondary shape factor

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Abstract

Stability of isolation rubber bearings is a topic widely studied and concerns (1) the critical load capacity in the undeformed configuration, under long-term load (gravity) effects; and (2) the stability condition under short-term vertical pressure (due to gravity plus seismic loads) at large lateral deformations. In this paper the problem of elastomeric bearing stability under large lateral displacements is addressed through FEM parametric analysis; rubber bearings typical of current design practice, characterized by S1 = 20 are considered, with the value of the secondary shape factor S2 being varied between 1.5 and 6.2 in order to assess the effect of slenderness on the mechanical behavior, failure mode, and interaction vertical pressure–shear deformation. The analysis results show that the sensitivity of the shear response to the applied vertical pressure is directly related to the value of S2 and that S2 has an overwhelming effect on the stability behavior and shear response of the bearing, as compared to the effect of the primary shape factor and of the rubber shear modulus. Finally, S2 is the parameter which governs the failure mode of the bearing in the seismic condition (vertical pressure–shear deformation). On the basis of these results, design implications are discussed.

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Abbreviations

A:

Cross section area of the isolator

Ar :

Overlap (or reduced) area of the displaced bearing

As :

Shear area of the isolator

c:

Number of finite elements along the circumferential of half-isolator

d:

Shear displacement of the isolator

E:

Young’s modulus of the rubber

Ec :

Apparent compression modulus of the rubber-steel composite

(EI)s :

Effective bending stiffness of the composite system (steel plus rubber)

F:

Shear (horizontal) force acting on the isolator

G:

Shear modulus of the rubber

GAs :

Shear stiffness of the composite system (steel plus rubber)

h:

Height of the isolator

\(\bar{I}_{1}\) :

First deviatoric strain invariants

\(\bar{I}_{2}\) :

Second deviatoric strain invariants

Jel :

Ratio between the total volume strain J and the thermal volume strain Jth

Kth :

Theoretical horizontal stiffness of the isolator

Kγ=100% :

Horizontal secant stiffness of the isolator obtained from FE results at γ = 100 %

n s :

Number of steel shims

p:

Average vertical pressure

Pcr,0 :

Critical load of elastomeric bearings in absence of lateral deformations

pcr,0 :

Critical pressure of elastomeric bearings in absence of lateral deformations

Pcr,d :

Critical load of elastomeric bearings at the shear displacement d

pcr,d :

Critical pressure of elastomeric bearings at the shear displacement d

PE :

Euler buckling load

Ps :

Shear stiffness per unit length

r:

Number of finite elements in radial direction of half-isolator

s:

Number of finite elements in vertical directions of half-isolator

S1 :

First (or primary) shape factor of the isolator

S2 :

Second (or secondary) shape factor of the isolator

t:

Single rubber layer thickness

tr :

Total rubber thickness

t s :

Single steel shim plate thickness

t st :

External steel plate thickness

U:

Strain energy function per unit reference volume

Φ:

Diameter of isolator

ε:

Normal strain

γ:

Total shear strain in the rubber

γloc,FEM :

Local shear strain in the rubber layers provided by FEM analyses

γs :

Shear strain of the isolator due to shear force

γs,dam :

Shear deformation of the isolator corresponding to the first occurrence of shear damage in the rubber

γs,rupt :

Shear deformation of the isolator corresponding to the shear rupture in the rubber

γs,stab :

Shear deformation corresponding to isolator instability

φ:

Complementary half-angle subtended at the center of the intersection of the top and bottom circles

\(\overline{\lambda }_{i}\) :

Principal stretches

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Acknowledgments

This research has been partially supported by ReLUIS III—Research Project 2014 “Rete di Laboratori Universitari Ingegneria Sismica”, in the context of the activities of Task Seismic Isolation.

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Authors and Affiliations

  1. Department of Structures for Engineering and Architecture (DIST), University of Naples Federico II, P.le Tecchio, 80, 80125, Naples, Italy

    Giovanni Maria Montuori, Elena Mele, Giuseppe Marrazzo, Giuseppe Brandonisio & Antonello De Luca

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  1. Giovanni Maria Montuori
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Correspondence to Giovanni Maria Montuori.

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Montuori, G.M., Mele, E., Marrazzo, G. et al. Stability issues and pressure–shear interaction in elastomeric bearings: the primary role of the secondary shape factor. Bull Earthquake Eng 14, 569–597 (2016). https://doi.org/10.1007/s10518-015-9819-x

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