Jason Beecher, URS Corporation, received the 2009 GT STRUDL Users Group "Award for Excellence" for his presentation on the "Sub-Modeling Bridge Components Using GTSTRUDL Superelement Functionality"  (use the link here to view).  A brief summary of this presentation is shown below.

The Girard Point Bridge, located in Philadelphia, PA is a 1500’ double-deck three-span, suspended-span truss bridge supporting a stacked deck, stringer, floorbeam superstructure.  Instrumentation of recently applied retrofits to the transverse floorbeam web connection to the truss on the lower deck indicate that out-of-plane stresses to the point of yield are being seen by the web material due to thermal expansion/contraction of the bridge.  This thermal effect is a global phenomenon whereby the truss system and the deck stringer system behave in a manner that is incompatible with the system boundary conditions.  This incompatibility is resolved through the longitudinal deflection of the floorbeam top flange relative to the truss system through an 8” long ‘dogbone’ web cut connection to the truss.  This out-of-plane deformation results in large double-curvature stress build-up in this ‘dogbone’ cut.

The job of the URS design team was to assess the behavior of the floorbeam web retrofit under this global loading phenomenon.  A local floorbeam model using shell elements was developed to establish the areas of the web that are experiencing this high stress.  A global finite element model was developed to determine the thermal response of the truss sys-tem relative to the superstructure system.  However, the global response of the bridge is dependent on the characteristics of this superstructure-to-truss connection which is one that is neither a fully fixed connection, nor a fully pinned connection, and one that behaves differently for in-plane versus

out-of-plane loading.  Therefore, it was decided that the actual geometry of the connection must be applied to the model in order to get an accurate assessment of the global behavior.  However, given the multiple connections to the truss using a significantly refined floorbeam mesh makes modeling all but impossible.

The GTSTRUDL Superelement (SE) sub-modeling approach was used to overcome this difficulty by only inputting the stiffness characteristics of the floorbeam local mesh and modeling the remaining bridge components in the global model.  The superelement could now account for the connection geometry, without the software having to handle 23 floorbeam meshes with 12,000 shell elements each in a global model that already has 13,000 elements, and 15,000 members.  Various SE’s were developed from local models to account for differences in floorbeam connection geometries.

Using consistent coordinate systems between local and global models is good practice when developing the SE; otherwise it is necessary to perform matrix transformations on the SE matrices before placing into the global model.  Boundary node definitions must also be coincident with the global model in order for the stiffness and load matrices to be properly reflected in the model.  Other issues relative to software limitations (GTS or windows) have to be considered.

This modeling approach proved to be an effective way to accurately represent the characteristics of relatively small details contained within large structural systems whose global behavior relies on those details.  Applying the GTSTRUDL SE modeling technique in this project brought forth issues that must be properly addressed when considering its use.