Limiting self-weight is a primary requirement in the design of most types of bridges. Self-weight is among the most significant loads on the bridge and its reduction creates a reserve available for live loads. Self-weight also governs the cost of construction equipment, which is a primary component of the construction cost of a bridge. The density of normal-weight concrete does not vary much with the concrete strength, the weight of a prestressed-concrete (PC) bridge depends linearly on the cross-sectional area, and the most influencing parameters are therefore related to the cross-sectional geometry.

**Prestressed Composite Bridges with Steel Corrugated-Plate Webs **analyzes the influence of the different parameters with a database of 165 constant-depth PC box-girder highway bridges with continuous spans ranging from 19 to 96-m. The depth of the cross-section governs the shear and flexural capacity and therefore increases regularly with the span.

The cost of materials and specialized construction equipment depends on the weight of the cross-section, *i.e.* on its area. The moment of inertia is the main indicator of the flexural capacity of the cross-section and is inversely proportional to the cost of post-tensioning. The design efficiency of a PC bridge can therefore be evaluated in terms of radius of gyration of the cross-section.

Since moment of inertia and area depend on the deck width, their increase with the span is scattered. Their ratio does not depend much on the deck width, and the increase of the radius of gyration with the span is therefore more regular. The maximum radius of gyration is achieved when the area is positioned at the edges, and the efficiency of the cross-section can therefore be expressed as flexural efficiency. The closer the latter is to the ideal value of 1, the better the flexural efficiency and the lower the quantity of post-tensioning.

The cross-section of a PC box girder includes top slab, bottom slab and webs, and these three components can be treated separately to increase the flexural efficiency. The thickness of the top slab depends on localized wheel-load bending and on the demand for punching strength and adequate concrete cover, and cannot be reduced excessively. The thickness of the bottom slab is often governed by technological requirements of internal post-tensioning, but its design is generally less restrained. Using internal post-tensioning, the web thickness is governed by the need to contain and deviate the tendons, and in a narrow box girder the webs can reach 30% of the cross-sectional area.

The webs reduce the flexural efficiency of the cross-section with a small contribution to the moment of inertia due to their position close to the neutral axis. The webs also increase the cost of materials and labor, as they are the most difficult element to form and to cast of the cross-section. The webs are necessary for shear transfer, and their shear efficiency depends on the mechanical properties of the material used for the webs.

The efficiency of a material can be evaluated with its strength-to-density ratio. A concrete with 45-MPa compressive strength has a compressive efficiency of about 1800-m and a much smaller tensile efficiency. A steel plate with 355-MPa yielding strength has a tensile efficiency of about 4600-m at first yielding and is 2.5 times more efficient than concrete in optimum work conditions. The composite bridges with concrete slab and steel girders are therefore more efficient than the PC bridges, as their masses are more distant from the gravity axis and the materials perform better.

Prestressing strand, however, is definitely more efficient. Commercial 7-wire strand reaches a tensile efficiency of about 21500-m at the 0.1%-load, and a cable is generally the most effective way to use steel in tension. By relating the efficiency of materials in their optimal work conditions to the efficiency of prestressing steel, 45-MPa concrete reaches only 8.4%, and medium-grade steel plates reach 21.4%.

A PC bridge is mainly designed for bending. Prestressing is the most efficient and cost-effective solution to control the edge tensile stresses generated by bending, and in a continuous beam this requires the presence of two flanges to compress without instability. The use of reinforced concrete for the two flanges offers compressive strength at low cost, and the use of external post-tensioning allows web design for principal stresses without geometry restraints. Once the flexural demand has been met, tendon deviation reduces the tangential stresses in the webs, with beneficial effects on web thickness and the flexural efficiency of the cross-section.

The efficiency of concrete can be improved by increasing the strength with the same density (*i.e*., by using high-performance concrete) or by reducing the density with the same strength (*i.e*., by using lightweight concrete). The next step in the search for maximum flexural efficiency is abandoning the concrete webs and using two or more steel I-girders to connect the concrete slabs. Steel webs offer the same shear capacity as concrete webs with only 5-8% of their weight, tendon deviation diminishes the shear demand on the webs, the flexural efficiency of the cross-section increases because of the better mass distribution, and these sections are also fast and easy to build.

The prestressed composite bridges may be grouped into two categories, the main difference between them consisting in the transmission of shear. The **space-frame decks** eliminate material not working in the Mörsch shear-lattice scheme, and the diagonals between the concrete slabs may be made with steel shapes, steel pipes with or without concrete infill acting compositely, or precast PC members. The box girders with steel-plate webs benefit from the higher shear efficiency of the steel plates compared with concrete webs.

The combined use of external prestressing, concrete slabs and steel-plate or trussed webs results in efficient cross-sections that make the most out of prestressing and are light and easy to build. Compared with a conventional PC box girder, the cross-sectional area diminishes without affecting the moment of inertia much, and the flexural efficiency increases. On a 40-m span, a PC box girder with internal tendons requires about 0.55 cubic meters of concrete per square meter of deck surface, which decreases to 0.45 cubic meters per square meter with the use of external tendons. A prestressed composite box girder with steel-plate webs requires only 0.35 cubic meters per square meter and is 25-35% lighter.

Concrete is located at the edges of the cross-section, the radius of gyration increases, and the flexural efficiency increases with quadratic ratio. The cross-sectional area of concrete to be compressed decreases, and prestressing diminishes because of the combined effect of smaller area and higher cross-sectional efficiency.

The contribution of materials specializes. The concrete slabs resist bending thanks to prestressing, whose deviation reduces shear to values that can be resisted with light steel-plate or trussed webs. Each material works in uniform rather than triangular stress pattern (the concrete slabs are uniformly compressed, the web plates resist uniform shear stress, the truss diagonals resist axial compression and tension, and the prestressing tendons are subject to axial tension), which further enhances the efficiency of design.

A prestressed composite box girder with steel-plate webs is a hybrid between a PC box girder and a non-prestressed steel-composite deck that takes the best from the two technologies. Compared with a non-prestressed composite deck with two or multiple I-girders, the webs are thinner, the flanges are smaller, less cross frames and no lateral braces are necessary, the weight of steelwork is only 15-20%, the unit cost of steelwork is similar, field assembly is simpler, the geometry tolerances are less stringent, and the maintenance costs are lower. Compared with a PC box girder, the absence of concrete webs saves labor and post-tensioning and accelerates construction, reinforcement is simpler and easier to fabricate, and casting cell and erection equipment are less expensive.

The flexural efficiency of prestressed composite box girders with steel-plate webs has been evaluated by subtracting the concrete webs from the cross-sectional area and moment of inertia of the bridge database, and by increasing the net area thus determined by 5% to account for the weight of the steel webs. The increase in flexural efficiency is substantial, and the result is particularly interesting on longer spans because of the progressive increase in the web depth with the span. Better structural performance and savings in labor, concrete, reinforcement, prestressing and construction equipment balance the cost of steel webs and the risks of innovation, and open new perspectives in the design and construction of medium-span bridges.

The most intuitive way to replace the concrete webs of a PC box girder with steel webs is the use of stiffened-plate webs. The deck has a conventional aspect, as the prestressing tendons are hidden within the box cell. The behavior of the individual materials is well known, and the combined use of reinforced concrete slabs and steel I-girders has been amply tested in hundreds of composite bridges. However, this simplicity is only apparent, and several reasons discourage the use of this structural solution.

The steel webs resist a significant portion of the prestressing force applied to the composite section. Under the axial force imparted by post-tensioning, strain compatibility at the web-slab nodes governs the distribution of the axial force between the concrete slabs and the steel girders. The initial portion of post-tensioning resisted by the steel girders increases with time due to the time-dependent behavior of concrete and soon reaches 20-25% of the total prestressing force. This force is wasted and requires additional stiffeners to prevent web buckling, which increases the fabrication cost of the webs and may reduce their fatigue life due to cracks initiating at the stiffener welds.

If the webs were devoid of axial stiffness, the webs would resist shear force only, and the concrete slabs would resist the entirety of bending. The axial stiffness of the webs must therefore be diminished without affecting their shear capacity, and this requires anisotropic behavior.

Orthotropic plates with different stiffness in the orthogonal directions are commonly used in steel bridges. Webs and bottom flange of steel box girders are heavily stiffened in the direction of the principal compressive stresses, and less stiffened in the orthogonal direction. This concept may be extended to the axial stiffness of a plate by folding the plate to reduce its capability of resisting axial stress without affecting the shear capacity.

Trapezoidally- or sinusoidally-corrugated steel or aluminum plates are commonly accepted in naval and aeronautical applications. Several fuselages and wing structures have been built with undulated or corrugated plates. Skins of F-15 and wings of AV-8B and F-22 adopt corrugated panels. Aircraft designers have realized long ago that the corrugated panels have larger buckling strength in the direction perpendicular to the corrugation. Corrugated metal panels have long been recognized as excellent shear carrying members. This is attributed to two characteristics of the panels: the transverse stiffness provided by the corrugation depth, and the in-plane stiffness due to narrow spaced folds that act as vertical stiffeners.

In civil structures, the advantages of structural anisotropy may be exploited by replacing the stiffened-plate webs of steel or composite girders with corrugated-plate webs. Vertical corrugation by cold folding creates the in-plane flexibility necessary to minimize the longitudinal axial capacity of the web panels and amplifies the transverse flexural capacity needed to resist transverse bending and cross-sectional distortion and to prevent buckling of web panels devoid of welded stiffeners.

The idea of using corrugated-plate webs in civil structures was first introduced for the steel beams of buildings, where the web thickness varies from 2 to 5-mm and the height-to-thickness ratio of the web panels varies between 150 and 260. In the past three decades there has been increasing interest in prestressed composite box-girder bridges with steel corrugated-plate webs, where the web thickness varies between 8 and 12-mm and the height-to-thickness ratio of the web panels typically ranges between 220 and 375 and has reached 445.

The corrugated-plate webs have symmetrical regular shape with constant wavelength in the longitudinal direction. Load tests on specimens of corrugated plates, finite-element numerical analyses and studies on the behavior of corrugated-plate webs in prestressed composite bridges have been conducted in Britain, Canada, China, Egypt, France, Germany, Hungary, Italy, Japan, Sweden and the USA, and the first actual bridges confirmed many advantages of the prestressed composite box girders with steel corrugated-plate webs over the stiffened-plate ones.

- The longitudinal flexibility of the webs minimizes the initial and time-dependent loss of prestress into the webs. Fewer tendons are needed to prestress the slabs, and fewer shear connectors are needed at the web flanges to transfer longitudinal interface shear. Internal tendons in a slab compress only that slab and do not affect the other slab.
- The state of stress in the central region of the web panels is an almost pure shear one. The thickness of the web plates is chosen for shear strength, and the corrugation is designed to control buckling. The webs may often be made with 8-mm plates, while stiffened-plate webs are rarely thinner than 12-mm. In addition to savings in weight, this opens new perspectives for the efficient use of high-grade steels.
- Shear is mostly carried by tendon deviation, the residual shear is carried by the webs, bending is carried by the concrete slabs, torsion is carried with hollow-section behavior, resistance to cross-sectional distortion is higher and more uniform throughout the length of the bridge, and the interaction between bending and shear is minimal. Every material works with optimal stress distribution.
- The transverse stiffness of the corrugated plates avoids the need for welded stiffeners, reduces the number of cross frames and diaphragms within the box cell, and saves material and labor. These savings, along with the reduced plate thickness, are often enough to cover the cost of plate corrugation.
- Higher transverse stiffness, closely spaced folds, and the boundary restraint provided by the concrete slabs increase web stability from buckling. Buckling depends on shear only, while in a stiffened-plate web it depends on combined shear and axial stresses. Longitudinal axial stresses do arise in the corrugated-plate webs in proximity of the concrete slabs, and vertical axial stresses arise in the support regions of the bridge; these local stresses, however, do not affect web stability.
- The sensitivity to premature buckling due to geometry defects is definitely lower. The defects of planarity are compared with the amplitude of the folds instead of the plate thickness, and their effects are 10-20 times lower. Local distortion due to welding is limited to the edges of the panels, which are restrained by the concrete slabs. The plastic strains due to cold folding are uniform over the web depth and do not affect the elastic equilibrium of the panel.
- The flexibility of the web panels facilitates fabrication and field assembly and avoids the need for trial assembly and tight geometry tolerances. The web panels are overlapped and fillet-welded on either side; in-place casting of the concrete slabs compensates for the residual geometry irregularities.

Prestressed composite box-girder bridges with corrugated-plate webs have been built by incremental launching on spans ranging from 40 to 55-m, and as balanced cantilevers on longer spans. Corrugated-plate webs have been used in extradosed and cable-stayed bridges, and research is in progress to extend their use to long-span arches. Combined with the use of high-performance concrete for the rib slabs, corrugated-plate webs could lighten the arch ribs, diminish the cost of foundations and temporary support systems prior to crown closure, avoid labor-intensive staged casting of concrete webs, and accelerate construction.

In 32 pages in full A4/letter format, **Prestressed Composite Bridges with Steel Corrugated-Plate Webs** explores the design and construction of prestressed composite bridges. Statistical analysis of 165 bridges shows substantial gains in structural efficiency. The eManual explains state of stress in the webs, torsion-distortion interaction, and the design of the web-slab nodes for local bending and shear.

The eManual provides exhaustive coverage of local, global and interactive buckling of corrugated-plate webs, the resistance factors suggested by the international research for the different buckling modes in relation to their different post-critical domain, and web crippling due to the traveling patch loads of incremental launching construction. It also explores numerous case studies and includes a comprehensive bibliography with 79 references that identify the state-of-the-art of prestressed composite bridges.

The eManual discusses a step-by-step procedure for the design of the plate corrugation parameters for factored (ULS) and non-factored (SLS) load combinations with a spreadsheet, and includes an Excel spreadsheet that implements the procedure. The spreadsheet calculates the factored and non-factored shear capacity of steel corrugated-plate webs with user-selected resistance factors for the different buckling modes, and optimizes the plate corrugation parameters for a given plate thickness and panel depth.

Spreadsheet and eManual are indispensable sources of information and design tools for bridge owners, designers and constructors interested in light bridge superstructures that are less expensive, more efficient and simpler to maintain than steel multi-girder and girder-substringer systems.