Trusses Instead of Solid Webs?

Trusses instead of solid webs ?

Whatever the construction method of a bridge may be, the limitation of self-weight is a primary requirement. Self-weight is the most important loading on the structure, and its reduction creates a reserve available for live loads. Self-weight also governs the design of construction equipment, whose amortization is a primary component of the construction cost of a bridge.

The self-weight of a prestressed-concrete box girder is the sum of the weight of the top slab, the bottom slab and the webs, and these three components can be treated separately to lighten the cross-section. The thickness of the top slab depends on the live load and the need to assure adequate punching strength, and therefore cannot be reduced excessively. The thickness of the bottom slab often depends on the need to contain internal tendons, but its design is generally less restrained.

When internal post-tensioning is used, the web thickness is often governed by the need to contain and deviate the tendons, and in narrow box girders the web area can reach 30% of the cross-sectional area. The webs reduce the cross-sectional flexural efficiency because of their position close to the gravity axis and increase the cost of labor and materials, as they are the most difficult element to cast of the whole cross-section. However, webs are necessary for shear transfer, and their shear efficiency mainly depends on the mechanical properties of the material.

The efficiency of a material can be evaluated with the ratio of its strength to density. A 45-MPa concrete has a compressive efficiency around 1800-m and a low tensile efficiency; consequently, shear efficiency is low as well. The tensile efficiency of a Fe 510 EN-10025 steel plate is much higher, around 4600-m at yielding, although instability diminishes the compressive efficiency.

Prestressing steel is definitely more efficient. A T15S EN-10138 strand reaches 21.500-m at the 0.1%-load, and the cable is generally the most effective way to use tension steel. By relating the efficiency of the structural materials in their optimum work conditions to the one of prestressing steel, 45-MPa concrete reaches 8.4% and high-grade steel plates reach 21.4%.

Beam bridges are mainly designed for flexural stresses, and prestressing steel is used to create an eccentric compression that controls the edge stresses. This requires the presence of two wide flanges to compress without instability, and the use of reinforced concrete offers reasonable compressive efficiency at low cost. Once the flexural demand has been met, tendon deviation can reduce the longitudinal shear force in the webs, with beneficial effects on the web thickness and, consequently, on the flexural efficiency of the cross-section.

External post-tensioning enhances the cross-sectional efficiency, reduces the cost of labor and materials, and accelerates and simplifies construction. In addition, the compressive efficiency of reinforced-concrete can be improved by increasing the strength with the same density (i.e., with the use of high-performance concrete), or by reducing the density with the same strength (i.e., with the use of structural lightweight concrete).

The next step toward higher structural efficiency is abandoning the prestressed-concrete box girder concept for the use of non-prestressed steel girders completed with a reinforced concrete slab. A few-millimeter steel plate resists the same shear force as a many-decimeter concrete web with less than 10% of the weight. However, instability penalizes the use of steel in compression, and the use of a concrete bottom slab for double composite action in the negative bending regions is generally limited to the longest spans. In most cases, therefore, the torsional stresses are resisted with cross frames and lateral bracing, thick steel bottom flanges carry negative bending, and the lateral stability of compression flanges becomes a main concern.

A similar efficiency may be attained with prestressed composite box girders that combine the use of external post-tensioning, reinforced concrete slabs, and steel corrugated-plate webs or light trussed webs and space-frames. These solutions offer efficient cross-sections (composed of masses far from the gravity axis and prestressed in an effective way) that make the most out of prestressing steel and are light and easy to build. Published on ACI Concrete International in May 2001, Trusses Instead of Solid Webs provides a thorough introduction of these innovative structural solutions.

Compared with a conventional prestressed-concrete box girder, self-weight decreases without penalizing moment of inertia and flexural capacity, and the structural efficiency increases immediately. On a 40-m span, a prestressed-concrete box girder with internal post-tensioning requires about 0.55 cubic meters of concrete per square meter of deck surface, which decrease to 0.45-m with the use of external prestressing. A prestressed-concrete box girder with trussed webs or steel corrugated-plate webs requires only 0.35-m of concrete, and lightening is 25 to 35%.

Since concrete is concentrated at the edges of the cross-section, the radius of gyration increases, the cross-sectional flexural efficiency increases with quadratic ratio, and the demand for post-tensioning decreases significantly. The flexural efficiency is even higher than that of conventional non-prestressed composite sections.

The contribution of materials specializes: the concrete slabs resist bending thanks to prestressing, whose deviation reduces the shear force to values that can be resisted with light steel or concrete trusses or steel corrugated-plate webs. Each material works in uniform rather than triangular stress pattern, with enhanced individual efficiency.

Compared with non-prestressed composite bridges, the weight of steelwork is 15 to 20% and its unit cost is similar as the trusses can be fabricated with commercial shapes and the steel corrugated-plate webs do not require welded stiffeners.

Field activities are simplest. Compared with prestressed-concrete bridges, casting of the concrete webs is avoided. Compared with steel-composite bridges, field splicing is simpler and the dimensional tolerances are less stringent. Construction duration decreases and the erection equipment is lighter and less expensive.

The prestressed composite bridges may be grouped into two categories, the main difference between them consisting in the longitudinal transmission of the shear force. The space-frame bridges eliminate material not working in the Moersch lattice scheme, while the box girders with steel corrugated-plate webs benefit from the higher shear efficiency of steel plates compared with reinforced concrete webs.

The advantages over conventional prestressed-concrete box girders can be significant, and the interesting aspects of these structural solutions are not limited to the savings in labor and materials, as many qualitative aspects are also involved.

Most prestressed-concrete box girders have only two webs due to the weight and complexity of multi-cellular sections, and the longitudinal axial stresses in the slabs are different from the average values of two-dimensional longitudinal analysis because of shear-lag. A space-frame superstructure uses multiple truss planes to attain three-dimensional load distribution, to increase redundancy and ductility, and to diminish the longitudinal shear forces transferred through the nodes between diagonals and the slabs, and the results of analysis are more reliable. The uniform transverse deflections of a space frame also make the results of two-dimensional longitudinal analysis more realistic.

In a conventional box girder, differential shrinkage due to the different thickness of webs and slabs causes stress gradients at the cross-sectional nodes. In a space-frame bridge with concrete diagonals, these effects are reduced by the similar thickness of the structural elements. Finally, load dispersal occurs through several paths, and in case of failure of a member, the stresses are redistributed due to the higher grade of redundancy.

In relation to the construction method, the migration of the support reactions does not suggest the incremental launching of trussed-web and space-frame bridges. When the longitudinal spacing of the bottom slab nodes is smaller than the pier cap width, movable launch bearings may be used under the bottom nodes, although this requires a discontinuous launch sequence and frequent jacking operations.

To date, the most significant applications of these structural systems have been built by segmental precasting with self-launching gantries, in-place casting on falsework, and balanced cantilever casting with form travelers.

The second edition of Bridge Launching and Prestressed Composite Bridges with Steel Corrugated-Plate Webs compare the efficiency of prestressed composite bridges (steel corrugated-plate webs and space frames) with the efficiency of conventional prestressed-concrete box girders with a statistical analysis of 76 highway bridges with constant-depth single-cell cross section and internal post-tensioning. The average improvement in the flexural efficiency is about 22%, while the improvement in the structural efficiency ranges from 15% for 30-m spans to 27% for 70-m spans.