In wide-decked bridges there is a tendency for the longitudinal in-plane displacements in the parts of the deck away from the edge girders/webs to lag behind those deck parts near the edge girders/webs. This phenomenon is known as shear lag. Shear lag is of particular concern in cable-stayed bridges because the spacing between supporting girders is usually large, thus causing the stresses at the girder-to-deck interface to be significantly higher than those estimated by elementary bending theories or simplified methods.

Shear lag can be observed in both the in-plane shear strain resulting from bending in the main longitudinal girders and in the action of the horizontal component of stay cable tension. To simplify our study and still obtain useful results, we focused on the latter. By doing so, we gained a clear understanding of the shear-lag behavior in this extremely wide bridge.

Finite Element Analysis

As part of the finite element analysis performed for the preliminary design, we investigated the shear lag that could be expected to occur, using LARSA for the steel and hybrid alternatives and GTSTRUDL for the concrete alternative.

Modeling. The steel superstructure was modeled using plate elements for the 254-millimeter-thick deck, and beam elements for the edge girders and floorbeams. For the concrete superstructure, the top and bottom slabs, webs and diaphragms were modeled using plate elements. The model for the hybrid alternative was a combination of these two.

Boundary conditions. Boundary conditions were defined to simplify the model as much as possible, yet allow the system to behave properly. For the steel and concrete alternatives, the boundary between the deck and the twoer was assumed to be fixed. For the hybrid alternative, however, the behavior of the tie beam, where the superstructure transitions from steel to concrete, was a concern. Therefore, the box-shaped tie beam, into which the main and back spans are framed, was modeled using plate elements. The ends of the tie beam frame into the tower legs and were assumed to be fixed. Additionally, the nodes at the cable attachment points at the deck were fixed against vertical translation.

Figure 1: Main Span, Deck Longitudinal Compressive Stress Contour.

Figure 2: Back Span—Top Slab, Deck Longitudinal Compressive Stress Contour.

Figure 3: Hybrid Alternative-Section Thru Tie-Beam.

Application of Cable Forces. The longitudinal and transverse components of the dead load cable forces were computed and applied at the cable support points in order to determine the shear lag behavior of the deck under dead load. Approximate live load effects were determined by proportioning the dead load effects.

Longitudinal stress. Longitudinal compressive stresses were plotted for deck cross sections taken at each cable
connection point and contour stress plots were generated. Examples of the contour stress plots for the hybrid alternative main span and back span are shown in Figures 1 and 2 below.

Results: Stress Variations Will Be Small

As expected, the stresses are highest at the cable anchor point and diminish toward the middle of the deck in the main span and the edges of the deck in the back spans. These stress variations will be small, indicating that the shear lag phenomenon will not create difficulties in the design.

Examination of shear stresses along the edge of the bridge deck at the girder deck interface and variation of shear stress perpendicular to the edge girder showed that shear stresses, highest at the girder to deck interface, can be handled by a reasonable amount of reinforcement.

Shear lag analysis of the hybrid alternative allowed us to investigate the behavior of the tie beam. With the compression from the back span distributed in the top slab, bottom slab and center spine, and the main span compression more or less concentrated in the deck slab, it was thought that high torsional forces would develop in the tie beam (Figure 3). The associated shear forces were extracted from the shear lag analysis, and combined as required in the AASHTO group loadings. The resulting torsional forces can be provided for by using reasonable shear reinforcement.