Superstructure stiffness

Effect of Superstructure Stiffness on Liquefaction-Induced Failure Mechanisms... 

Madabhushi SPG, Haigh SK (2010) Effect of superstructure stiffness on liquefaction-induced failure mechanisms. Int J Geotech Earthq Eng 1 71-87, ISSN 1947-8488... 

FIG. 8 Phase diagram of a Langmuir monolayer in a model of grafted stiff Lennard-Jones chains. LE denotes a disordered expanded phase, LC-U a condensed phase with untilted chains, LC-NN and LC-NNN condensed phases with collective tilt towards nearest neighbors and next-nearest neighbors, respectively, and LC-mod a phase which has a superstructure and an intermediate direction of tilt. (From Stadler and Schmid [151].)... 

The lateral bending stifihess ofthe plate girder bridge is quite small in comparison to the axial stiffness (1 x EA = 3.255 GNm ) or the Euler buckling load of each span. So when the piers try to rotate about their cross-sectional axis, the superstructure i.e. bridge deck offers least resistance. 

To model the superstructure, five different oscillators were used. Two types of columns (aluminium, steel) were selected in order to vary pier stiffness. AU columns had a rectangular cross section, 3x12 mm. The aluminium and steel piers have a flexural stiffness, /, of 1.89 x 10 kNm and 5.67 x 10 kNm, respectively. 

The first step in determining the thermal forces on the substructures for a bridge with monolithic bents is to determine the point of no movement. After this point is determined, one can calculate the relative displacement of any point along the superstructure to this point by the distance to this point times the temperature range and times the coefficient of expansion. With known displacement at the top and known boundary conditions at the top and bottom, the forces on the pier due to the temperature change can be calculated by using the displacement times the stiffness of the pier. 

The contribution of the superstructure to the transfer of loads to adjacent substructure units depends on the capacity of the connection of the superstructure to substructure and the relative stiffness of the substructure at the location of the impact. However, in order to consider partial transfer of lateral forces to the superstructure, positive steel or concrete connections of superstructure to substructure such as shear keys must be provided. Similarly, for partial transfer to the superstructure of the longitudinal component of the impact force, the shear capacity of the bearings must be adequate. When elastomeric bearings are used their longitudinal flexibility may be added to the longitudinal flexibility of the piers. If the ultimate capacity of the bearings is exceeded, then the pier must take the total longitudinal force and be treated as a cantilever. 

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