4.4.2.1 Concrete

The compressive strength of concrete is denoted by concrete strength classes that relate to the characteristic (5%) cylinder strength f_ck at 28 days (or the cube strength f_ck,cube) in accordance with EN 206‐1 [2]. The strength classes for concretes frequently used in bridges are presented in Table 4.1.

The mean tensile strength f_ctm refers to the highest stress reached under concentric tensile loading. The flexural tensile strength can be increased for members with depths h up to 0.6 m, by using the relationship: f_ctm,fl = max {(1.6 – h) f_ctm; f_ctm}.

The elastic deformations of concrete largely depend on its composition (especially the aggregates). Therefore, values for the secant modulus of elasticity E_cm, between σ_c = 0 and 0.4 f_cm, given in Table 4.1 for concretes with quartzite aggregates, should be regarded as indicative and specifically assessed if the structure is likely to be sensitive to deformations. For limestone and sandstone aggregates, the values should be reduced by 10 and 30%, respectively. For basalt aggregates, the values should be increased by 20%. Poisson's ratio may be taken equal to 0.2 for uncracked concrete and 0 for cracked concrete. The linear coefficient of thermal expansion is usually taken equal to 10⁻⁵ C⁻¹. The value of the design compressive is defined from these values as f_cd = f_ck/γ_c, where γ_c is the partial safety factor for concrete, usually 1.50.

Finally, for executing the structural analysing and computing the resistance of concrete cross sections under compression the stress–strain diagrams of Figure 4.7a and b may be respectively adopted, using the properties from Table 4.1.

4.4.2.2 Reinforcing Steel

Reinforcing steel can take the form of bars, de‐coiled rods or welded fabric. Figure 4.7c presents the typical stress–strain diagram for reinforcing hot rolled steel (dashed) with the characteristic yield strength f_yk and tensile strength f_tk, and the correspondent strain, ε_su. The same figure also includes the stress–strain diagram usually used for design (for tension and compression), with a yield strength f_yd = f_yk/γ_s and γ_s = 1.15, the partial safety factor for reinforcing steel at ULS (Ultimate Limit State).

The design value of the modulus of elasticity E_s is assumed to be 200 GPa. Typical values of strains ε_s1 and ε_ud are, respectively, 2.174‰ and 10‰ for reinforcing steel B500 (in accordance with the EN 10080), the most frequently used in bridges.

4.4.2.3 Prestressing Steel

Prestressing steel usually appears in concrete decks as wires, bars or strands, with low level of relaxation (class 2) and susceptibility to corrosion. Additionally, prestressing steel should be adequately and permanently protected against corrosion in sheaths or ducts. These ducts are grouted with cement grout (both bonded and external tendons), with petroleum wax or mineral‐oil‐based grease (for external unbounded tendons only).

Figure 4.7d presents the typical stress–strain diagram for prestressing steel (dashed) with the characteristic 0.1% proof stress f_p0.1k and tensile strength f_pk and the correspondent strain, ε_uk. The properties of prestressing steels are given for example in EN 10138. The same figure includes also the stress–strain diagram usually used for design, with a strength f_pd = f_p0.1k/γ_s, with γ_s = 1.15 at ULS.

The most commonly prestressing steel used in concrete bridges consists of a bundle of seven‐wire strands, 15.3 or 15.7 mm nominal diameter (designated T15 normal or T15 super), with nominal tensile strengths of 1770 or 1860 MPa, respectively.

The design value for the modulus of elasticity E_p may be assumed equal to 195 GPa for strands, although the actual value can range from 185 to 205 GPa, depending on the manufacturing process. Typical values of strains ε_s1 = 0.75‰, ε_ud = 10‰ and proof stress f_p0.1k = 0.9 f_pk = 1680 MPa for the prestressing steel Y1860 (in accordance with the EN 10138‐3 [3]).

The maximum forces in each strand should be obtained with the stressing limit at tension stage f_po = min {0.8 f_pk; 0.9 f_p0.1k}. Bars have usually lower stress limits due to higher susceptibility to fatigue and brittle failure.

4.5.2.1 Materials and Weldability

Steel materials for metal bridges should have sufficient resistance, ductility and good weldability characteristics. The ultimate resistance of steel materials may be reached by plasticity, brittle fracture or fatiguering.

Plasticity occurs after a steel specimen reaches the elastic limit strength associated with yielding, while brittle fracture (inducing a crack like in fatigue failure, Figure 4.37) may occur at low stress levels usually associated with low temperatures and high strain rates induced by impact loading. Lamellar tearing (Figure 4.38) is a kind of brittle fracture occurring across the thickness of a steel specimen induced by deformation in the direction perpendicular to the surface of a steel plate.

The plastic resistance is characterized by yielding and ultimate failure stresses defined from tensile tests (f_y and f_u, respectively). Resistance to brittle fracture is defined by the Charpy test [8] where the toughness of the steel is defined as its capacity to resist to crack propagation, usually associated with high tensile stresses or multiaxial tensile stresses. Lamellar tearing occurs in the direction perpendicular to hot rolling and is characterized from specific tensile tests according to [9].

From tensile tests, one defines stress–strain diagrams (Figure 4.39) and from the Charpy test, one defines the steel toughness. This last mechanical characteristics, is defined in terms of capacity to absorb energy required to propagation of a crack. The stress intensity factor K at the vicinity of a certain crack depends on the geometry and dimensions of the crack and stress level. Under increasing stresses, a critical value K_v is reached at a certain temperature giving rise to a brittle fracture. From low to high temperatures, the steel behaviour passes from brittle to ductile. A nominal transition temperature may be defined (Figure 4.40). The toughness is measured by impact bending tests on a specimen with a V‐notch, usually by using a Charpy Pendulum machine. The impact energy is measured by a certain mass M with weight P falling from a certain height, h. The impact energy is measured as A_v = P h in Joules (1 J = 1 N × 1 m). On the other hand, it is possible to define the temperature associated to a nominal brittle fracture impact energy specified as 27 J in Part 1‐10 of EN 1993 [10]. Figure 4.40 shows a diagram where the K_V is defined (Charpy V‐Notch) as the value of impact energy A_V (T) in Joules (J) required to fracture a Charpy V‐Notch specimen at a given test temperature, T. Toughness tends to reduce under decreasing temperatures. Sufficient toughness is particularly required for welded bridges to prevent cracks from appearing or to increase rapidly under fatigue loading. Fracture mechanics adopts the concepts of stress intensity facture K [11] for a certain nominal crack (Figure 4.41) and toughness at certain temperature. If a crack amplitude is measured by a certain geometrical parameter a (Figure 4.41) and if that crack exists at service conditions of a steel bridge, the propagation of the crack dimension a has a typical diagram as shown in Figure 4.41. The propagation ratio (gradient) of the crack dimension da/dN may be correlated with the variation of the stress intensity factor ΔK. Paris law [12, 13], represented in Figure 4.42, gives the simplest correlation. The constants D and n defining the linear correlation in the stable range of the crack are material dependent only. If the variation of the stress intensity factor does not exceed a certain value defined in Figure 4.41 by ΔK_th, the crack does not tend to increase or may increase in a very slow fashion during the life of the structure. This is important to know for cracks detected during maintenance inspections of steel bridges. From this limit ΔK_th on, the crack tends to progress in a stable fashion according to Paris law. However, if a certain limit is exceeded, the propagation gradient da/dN is very high and the crack increases rapidly. It is possible [11] to define the critical dimension of a fatigue crack not inducing local failure by unstable crack propagation. In this case, the stress intensity factor remains smaller than its critical value K_c. This critical value is called toughness and is approximately dependent on the material only and independent of the geometry of the detail. However, it is temperature and strain rate (impact loading) dependent. Brittle fracture and fatigue crack is in steel bridges are usually induced by weld details. The detail of the plate welded joint to the lower flange in Figure 4.37 induces a high stress intensity factor inducing a crack in the flange propagated to the web.

Yield strength is specified in design by the steel grade while toughness is fixed by steel quality. Hence, steel for bridges may be specified in the design according to EN 1993‐2 and EN 1993‐1‐10. The following steels are usually adopted for bridges [14]:

1. Non‐alloy steels, according to EN10025‐2 – Steel grades S235, S275 and S355 with qualities J0, J2 e K2 the last one is usually for S355 only.
2. Fine grain weldable steels according to EN10025‐3 – Steel grades S275, S355, S420 and S460 with qualities N or NL.
3. Thermomechanical steels according to EN10025‐4 – Steel grades S275, S355, S420 and S460 with qualities M or ML.

Qualities J and K are associated with 27 and 40 J. The numbers 0 and 2, associated with J and K, represent a temperature of 0 and −20°C, respectively. Hence, a steel of quality J2 has a toughness of 27 J at −20°C while a steel of quality K2 has 40 J at −20°C. In EN 10025‐2 [14], there is also a lower quality steel designated JR (27 J at +20°C) that should only be adopted for secondary elements. Steels for the main structural bridge elements, specified according to EN 10025‐2, should be at least S355 J2 or S355 K2.

Steels may be subjected to a normalizing treatment, a thermal treatment during steel fabrication improving its qualities. The normalized delivery condition should be required for steel for bridges and steel specification is written as +N, as, for example, S355 J2 + N or S355 K2 + N. However, for fine grain weldable steels specified according to EN10025‐3 [14], the normalizing delivery condition is already included and steels are denoted just as N. For ‘N steels’, the toughness is defined as 40 J at −20°C or 27 J at −50°C for NL steels (L – stand for low temperature).

Thermomechanical steels (‘steels M’) are subjected specific thermal treatments during the rolling process and for the same mechanical characteristics of other steels; they have less carbon in its chemical composition. For weldability, it is important to define the equivalent carbon, C_e, defined as:

(4.4)

where the several terms C, Mn, Cr and so on define the chemical composition of the steel material as a percentage of weight. Structural steels always have less than 0.25% of carbon (C), as, for example, a maximum of 0.18% for S355 steels. The remaining elements of the chemical composition defining the C_e value are manganese (Mn), chromium (Cr), molybdenum (Mo), vanadium (V), nickel (N) and copper (Cu). Other elements, such as sulfur (S), phosphorus (P) and hydrogen (H), have an adverse effect on the mechanical characteristics of steel materials.

The C_e value has an important role in the weldability of steel components. In design specifications for welded structures, this value should be specified. Steels with C_e values less than 0.4% may be welded with fewer or even no risks of cracking. Cracks appearing after are due to the appearance of martensite or cracking may be due to presence of hydrogen in the designated Heat Affected Zone (HAZ) at the welding zone.

The cooling velocity is an important factor to avoid cracking development due to welding. Thick plates are more susceptible of cracking due to hydrogen than thin plates. To reduce susceptibility to cracking, preheating before welding is usually required, at least for thick welds. One advantage of thermomechanical steels (‘M steels’) is reducing or even totally avoiding preheating for welding. These steels, developed in last decade of the last century, or fine grain weldable steels (‘N steels’), are nowadays the preferred ones for bridges. They are less susceptible to brittle fracture at least if the thickness of the plates exceeds 30 mm. Flange plates for bridge girders nowadays may reach 150 mm or even more, if necessary.

Resistance to brittle failure is considered in Part 1‐10 of EN 1993 [10]. Minimum steel quality in bridge design may be defined from Fracture Mechanics but a simplified procedure is predicted in EN 1993‐1‐10 by defining maximum allowable plate thickness to be welded at a minimum design service temperature. An accidental combination of actions is defined where the leading action is the reference temperature, T_Ed in EN 1993‐1‐10. The temperature T_Ed is obtained from the minimum air temperature at the bridge site, which is defined as T_md associated to a certain return period (usually 50 years) defined in EN 1991‐1‐5, and from ΔT_r an adjustment for radiation lost, usually −3 or −5°C. For most cases T_Ed = T_md + ΔT_r.

The stress level at the referred load combination, as a ratio of the service load stress σ_Ed to the yield stress f_y, is taken in EN1993‐1‐10 with its frequent load value. Table 4.3 present the maximum thicknesses as a function of steel qualities, T_Ed and σ_Ed/ f_y(t).

Additional values are given in EN 1993‐1‐10 [10] for other steel grades. If one takes, for example, T_Ed = –10°C and σ_Ed = 0.5f_y, the allowable maximum thicknesses for a steel plate are, from Table 4.3: t_max = 65 mm for steel S355JO; t_max = 110 mm for steels S355 K2 or S355 N and t_max = 155 mm for steel S355NL.

Finally, concerning lamellar tearing (Figure 4.38), this is dependent on:

1. susceptibility of the steel material
2. deformation across the thickness of the steel plates induced by shrinkage due to welding
3. welding orientation
4. loading type (cycle load or impact load)

Lamellar tearing, when it occurs, is usually, but not always, in the base material and outside of the HAZ, as a result of a stress state perpendicular to the plate thickness.

For design, it is important for thick plates (say above a thickness of 30 mm) to specify properties across the thickness of the plate element. These properties are defined according to EN 10164:2004 [9]. A tensile test of a specimen according to EN 10002‐1 [12], where tensile stresses are applied perpendicular to the surface of the specimen with an initial area S_o. At ultimate stress, the area S_o is reduced to S_u and the relative deformation is defined by the Z parameter

(4.5)

The quality classes Z15, Z25 and Z35 are defined from minimum values of Z = 15%, Z = 25% or Z = 35%, respectively, obtained from average values in three tests. The minimum Z value for the steel plates is defined in the steel specification of welded structures with thick plates. The design verification may be done according to EN 1993‐1‐10 [10] by defining a ‘design value’ for Z_Ed

(4.6)

where the several terms are taken from Table 3.2 of EN 1993‐1‐10. Lamellar tearing may be neglected if Z_Ed < Z_Rd where Z_Rd is defined from the quality class, that is:

(4.7)

The terms Z_a to Z_e in Eq. (4.6) may have positive or negative values depending, for example, on connection detail and conditions for restrained or free shrinkage due to welding. Another aspect is the beneficial effect of pre‐heating for thick welds that is associated with Z_e. For example, Z_e = 0 without pre‐heating and Z_e = −8 with preheating (>100°C). Hence, pre‐heating reduces the Z_Ed and consequently the required Z_Rd. An example of calculation of Z_Ed is given in Figure 4.43 for a cross‐girder welded connection to a bottom chord of a truss girder bridge.

4.5.2.2 Corrosion Protection

With respect to maintenance requirements in steel and composite bridges, one of the main issues is usually corrosion protection. The protection schemes have been very improved in the last decades. Nowadays, it is usual to specify a corrosion protection scheme with a durability of at least 20 years for steel bridges. The improvement of modern coating systems may guarantee bridges in excess of 30 years without requiring the first major maintenance. The atmospheric corrosion categories are defined according to EN ISO 12944‐2 [15] as C1 very low, C2 low, C3 medium, C4 high, C5I very high (industrial) and C5M very high (marine).

The coating scheme may be defined according to EN ISO 12944, but the minimum total dry film thickness of paint system (primer, intermediate and finish coat) may vary from 200 up to 1000 μm. The primer is applied on steel after abrasive blasting cleaning defined by a standard grade of cleanliness from EN ISO 8501‐1 as SA1, SA2 SA2 ½ and SA3, from light blast cleaning to blast cleaning to visually clean steel. Grades Sa2 ½ and SA3 are usually specified for bridges.

For bridges in environments of high corrosivity, a ‘duplex’ scheme for coating may be adopted were paints are applied over thermal metal spraying coatings.

Weathering steels (‘Corten’), avoiding any type of coatings, is a common practice in several European countries (Figure 4.44).

The influence of design detailing on corrosion is quite meaningful. The handling of structural steelwork to bridge site may induce severe damage to the corrosion protection system. Site connections and splices are potential aspects to be taken into consideration, also because they may induce corrosion problems. The reader is referred to references [15, 16] for further information on corrosion protection systems.

4.5.3.1 Concrete Slab Decks

Concrete slab decks are adopted in general with thicknesses between 0.20 and 0.30 m, connected to deck steelwork through one of the types of shear connectors shown in Figure 4.45. The longitudinal shear flow, q_s, between concrete and steel (Figure 4.46) is resisted by the shear connectors and, if so, the concrete slab works in composite action with the steelwork. An equivalent homogeneous cross section in steel is taken by considering a reduced slab width, b_h, working in composite action with the steel girder, b_h = b/n where n = E_s/E_c is the ratio between steel and concrete elastic modulus. The shear flow, q_s, is a force per unit length dF/dx, and is determined by the well‐known formula from Strength of Materials:

(4.8)

where V_z is the vertical shear force at the cross section, S_hy is the static moment of the homogenized concrete part as shown in Figure 4.46 and I_hy is the moment of inertia with respect to the bending neutral axis (yy) of the homogenized transverse cross section.

Shear connectors of one of the types shown in Figure 4.45 may be classified as rigid or flexible. In rigid connectors, the shear flow q_s (a force per unit length) is considered to be taken at each section, even at ULS. If a is the longitudinal distance between shear connectors, the force acting at each group of connectors located at the same cross section is q_sa. Flexible connectors may redistribute the longitudinal forces between them at ULS and longitudinal equilibrium is resisted by a set of connectors between two transverse cross sections of the composite girder. If the forces due to bending stresses in the concrete part are denoted as F_A and F_B, at cross sections A and B, the longitudinal equilibrium requires ΔF = F_B − F_A = n F_R where F_R is the resistant shear force of each connector. Flexible connectors, head stud type, are the most adopted ones and are specified in Europe by ISO 13918 [17]. The most common diameters for head studs in bridges are 16, 19, 22 and 25 mm. Steels adopted in Europe for head studs usually have:

• yield strength f_y – minimum value of 350 N mm⁻²;
• ultimate strength f_u – minimum value of 450 N mm⁻²;
• minimum strain of 15%, measured in a normalized specimen with a length , where A_o is the initial cross section area of the specimen.

The geometrical characteristics of head studs (Figure 4.47a) should satisfy the following relationships – D > 1.5d and H > 0.4d. The height of a shear stud is usually h_sc = 75, 100, 150 or 175 mm and in any case should not be less than three times the nominal diameter, d.

In general, head studs are welded to girder flanges by arc welding, applied at the head of the stud by inducing an electrical discharge by a ‘pistol’. By this reason, the height L of the head stud cannot be specified arbitrarily. The lower end section has a ceramic ring to protect the weld during fusion of the material. The nominal diameter d should not be greater than 2.5 times the plate thickness to which the head stud is welded.

The geometrical arrangement of head studs in flanges should satisfy minimum distances specified, for example, in [18] as shown in Figure 4.47b.

Maximum longitudinal and transverse distances e_L and e_T shall take into consideration local plate buckling between shear connectors and are approximately 18t_s and 28t_s, respectively, for e_L and e_T for S355 steel grade where t_s is the plate thickness.

4.5.3.2 Steel Orthotropic Plate Decks

Main advantage of steel orthotropic plate decks, are reduced weight, as previously mentioned. They are the preferred option for long span bridges, say spans above 300 m, like cable‐stayed and suspension bridges. However, in cable‐stayed bridges even with long spans, say 500 m or even more, steel‐concrete composite decks are possible options taking into consideration high axial forces induced by stay action in the deck.

Increasing the span length above 600 m, steel orthotropic plate decks are generally the preferred option, even if they have a high initial cost and increased maintenance cost. However, the steel slab deck may represent a saving in self‐weight of 2.5–4 times the self‐weight of a concrete slab deck and this has a large impact on savings for main deck steel structure, either a plate girder or a box girder.

The design examples of steel orthotropic plate decks, shown in Figure 4.48, are integrated as slab deck of an open section superstructure made of two truss girders (Figure 4.48a) and in a closed section (box girder) of a modern suspension bridge (Figure 4.48b). Another example of an orthotropic plate deck is presented in Figure 4.33 for the Millau cable‐stayed Viaduct, in France.

An orthotropic plate deck is composed by a plate with longitudinal stiffeners (stringers) and transverse cross beams supporting the stringers, as shown in Figure 4.49. The deck plate should have a minimum thickness of t 14 mm for durability and resistance to local concentrated loads due to traffic and a maximum of 20 mm. Minimum thickness is defined by bending deflections under local load effects, usually restrained to e/300, where e is the transverse distance between stringers.

Stringers may be of open or closed cross section (Figure 4.50) but its transverse distance e should not be greater than 25 t for open section stiffeners and 50 t for closed sections, for durability of surfacing. This yields 350 and 700 mm for maximum distance between stringers, respectively, for open and closed cross sections e measured between stringer axes. For pedestrian bridges, one may adopt t ≥ 10 mm and e/t ≤ 40 with e ≤ 600 mm.

Cross beams, spaced apart 1–2 m for open section stringers and 1.5–4.5 m for closed section stringers, transfer to longitudinal main girders or to webs of box girders, the vertical forces induced by permanent and traffic loads on the slab deck. The behaviour of the slab deck as an orthotropic plate is discussed in Chapter 6.

Open section stiffeners should be adopted with a depth b_s < 10t_s to avoid torsional buckling (Figure 4.50). Torsional buckling is a column‐like buckling mode involving torsional rotations of the cross sections and transverse displacements in the plane of the cross sections (see Annex A). In general, only open sections elements are susceptible of torsional buckling modes. A stiffener is attached to the plate where transverse cross sections are restricted but not torsional rotations. Open stringers may be adopted with flat section angles (L sections) or T sections.

Closed section stringers, are of a trapezoidal shape made by cold forming a plate with a thickness of 6–10 mm. Stringer dimensions (Figure 4.50) should not exceed 42ε t_s, where t_s is the stringer thickness. Nowadays, the trend of adopting stringers with large cross sections and slender plates may require the need to consider local buckling effects in the stringer. Minimum bending stiffness of stringers needs to be respected to avoid large deflections between the cross beams or diaphragms. The minimum stringer stiffness can be found in Ref. [19] as a function of cross beam spacing.

Finally, a main aspect in designing steel orthotropic plate decks is fatigue resistance. As a rule, the welding connection details of Figure 4.51 should be respected for open and closed shape stringers. The lower flange of the stringer is not welded to the web of the cross girder, which is done by copes holes as shown in Figure 4.51.

4.5.4.1 Superstructure Components

A plate girder bridge superstructure (Figure 4.52) integrates the following components:

• the slab deck, usually a concrete slab in reinforced or PC;
• two or more (four at the most nowadays) steel plate girders – the main girders;
• a vertical bracing system between the main girders composed by cross girders or steel trusses with a diaphragm function;
• an horizontal bracing system nearby the lower flange level, composed by an horizontal truss between main girders and cross girders or diaphragms.

The last component, the horizontal bracing system, is usually adopted only for rail bridges and curved road bridges. The overall system works as an equivalent box girder, the lower flange being an equivalent thin plate to the truss. The torsional stiffness is increased and consequently it reduces torsion deformability under eccentric loads and torsion vibration frequencies. This aspect is quite relevant in High Speed Railway bridges.

The slab deck has a variable transverse thickness, varying between a minimum of 17 cm at the tip of the overhangs and a maximum of 40 cm over the girders; at transverse mid‐span between main girders, the slab thickness is generally 20–25 cm. For rail bridges, the minimum allowable slab thickness is generally 30 cm (better 35 cm).

The plate girders may have only transverse stiffeners with different shapes (Figure 4.53), or transverse and one or two longitudinal stiffeners, as shown in Figure 4.54. At support sections, the vertical transverse stiffeners are placed symmetrically at the girder cross section (Figure 4.53). Hence, a symmetrical horizontal deck cross section, composed by the vertical stiffeners and parts of the web, is obtained to resist the vertical reaction from the bearings. At span sections, the vertical stiffeners are placed at one side only of the webs of the main girders. In case one or two longitudinal stiffeners are adopted, they may be placed at the outside of the cross section (Figure 4.54). If they are placed at the inside, they cross the vertical stiffeners and should adopt a fatigue detail of Figure 4.51.

The vertical bracing is made of hot rolled or welded composed sections, as is usually the case for road bridges. In the case of straight road bridges, the vertical bracing is generally reduced to a cross beam (Figure 4.55). Trusses are, also adopted for the vertical bracing system or plate diaphragms (Figure 4.56), with a manhole at the mid‐depth to allow an inspection walkway in many railway bridges (Figure 4.52).

4.5.4.2 Preliminary Design of the Main Girders

Taking into consideration resistance at ULS and elastic behaviour at SLS, the following geometrical characteristics (Figure 4.57) for main plate girders are adopted.

4.5.4.2.2 Slenderness of Flanges and Webs

Flanges are generally designed for being totally effective at ULS (see Annex A) allowing its full plastic resistance N_f,pl to be mobilized. For a preliminary design of the cross section, one assumes the bending moment is taken by flanges and the shear force is taken by the web.

A plate girder bridge section (Figure 4.57) is considered, with unequal flanges of areas A_fs and A_fi, respectively, for the upper and lower flanges and a section depth, h. If the depth h is assumed, for the time being, to be approximately equal to the distance between centroids of the flanges, the resistant bending moment of the cross section is reached when the stress at the most loaded flange (the upper flange in the figure) reaches the yield stress:

(4.9)

where f_y is the flange yield stress of width b_s and thickness t_s. To reach N_fs,pl = A_fs f_y local plate buckling in the compressed flange (upper flange in the figure) should be avoided (Figure 4.58).

As shown in Annex A, the flange is fully effective if it has a non‐dimensional slenderness . For flanges, this yields:

(4.10)

If this limit value is exceeded the flange should be considered reduced to its effective width (Annex A), as shown in Figure 4.59.

By taking E = 210 GPa, one has a fully effective flange if approximately c/t < 14 for S235, c/t < 13 for S275 and c/t < 11 for S355. For pre‐design of a plate girder in a bridge composite deck, one may take the following plate dimensions:

• upper flanges 500 mm < b_s = 2c_s < 800 mm with 30 mm < t_s < 80 mm
• lower flanges 600 mm < b_i = 2c_i < 1200 mm with 40 mm < t_i < 120 mm

The plate thicknesses vary along the span length to accommodate the tensile or compressive stresses due to bending moment variation.

In Figure 4.60, one shows the post‐buckling behaviour of web panels under normal stresses due to bending and under shear stresses. The elastic critical stress of a plate girder web, under in‐plane bending only, is determined as a function of the stress ratio ψ = σ₂/σ₁ at top and bottom longitudinal edges, with compressive stresses taken as positive. For an equal flange girder (quite unusual in plate girder bridges) one has ψ = σ₂/σ₁ = −1. Slender webs do not allow for taking the full depth as effective under the bending moment. As shown in Figure 4.60, the compressed zone of a web under bending goes into the postbuckling range and its effective width is taken as shown in Figure 4.61. Thus, the resistance of the section under bending is taken for the effective section composed by the flanges and the effective parts of the web.

Assuming the flanges are fully effective, the ultimate moment in Eq. (4.9) is always smaller than the resistant bending moment of the reduced section in Figure 4.61.

For the webs (Figure 4.60a), assuming they are going to predominantly resist shear force, they reach the elastic shear critical stress (Annex A) determined as a function of the geometry of the web panels between transverse stiffeners, a/d.

Slender webs have a considerable post‐buckling resistance under shear forces. They reach the ultimate shear force resistance at values much higher than the elastic critical value for the shear force V_cr = τ_cr d t_w. Nowadays, steel bridge design takes advantage of the post‐buckling strength of web panels, designing webs with a slenderness d/t_w such that, in general, for webs with only transverse stiffeners one has,

(4.11)

The usual web thicknesses in plate girder bridges are as follows:

• At span sections – t_w = 14–18 mm
• At support sections t_w = 16–25 mm

For pre‐design, webs may be taken with a thickness allowing a maximum shear stress for the characteristic load combination (permanent + live loads) less than 100 N mm⁻² for steel grade S355.

If one restricts the bending resistance to flange action, as previously referred, the webs are assumed in the post‐buckling range under shear and a diagonal tension field is developed at ULS, as shown Figure 4.60a.

Reducing the distance a between transverse stiffeners, taking in general as 0.5d < a < 1.5d), increases τ_cr and consequently reduces its slenderness, , thus increasing its post‐buckling strength. The reader is referred to Chapter 6 for the detailed evaluation of ultimate strength of webs working in the post‐buckling range and to specific literature [19, 20]. Adding one or two longitudinal stiffeners to the web may be justified in deep plate girders, say d > 3.0 m. The elastic critical stress, τ_cr, is still obtained in the same way, but is now applied to each sub‐panel. The diagonal tension field for post‐buckling shear resistance is not significantly increased by adding longitudinal stiffeners. However, they may help, if located nearby the flanges (say approximately d/3 from the flanges) in bending resistance and for resistance under concentrate loads as it occurs during launching operations (‘patch loading’ – Figure 4.62).

The slenderness of the web panels cannot be increased above a certain limit due to flange induced buckling. This instability problem is associated to buckling of the flanges in the plane of the web as shown in Figure 4.63. The web is subjected to compressive stresses along the longitudinal edges, coming from the deviation forces induced by flanges, due to overall bending of the cross section. Taking the web as a long plate simply supported and loaded along the longitudinal edges, its critical load should always be higher than the deviation force coming from the flanges when the ultimate resistance is reached. Flange induced buckling does not occur (see Chapter 6) if the slenderness of the web of height h_w, thickness t_w and area A_w = h_w t_w, is limited to:

(4.12)

where f_yf is the yield stress of the flange of area A_fc (first reaching yielding) and k a factor, taken as 0.55 or 0.40, respectively, for an elastic or plastic design. For different steel grades and web and flange area ratios, the expression 4.12 yields the limits for web slenderness of Table 4.4.

	Aw/Afc
Steel grade	0.2	0.4	0.6	0.8	1.0
S235	219	310	380	439	491
S355	145	205	252	291	325

Execution method	Concrete bridges cast in place	Concrete bridges Precasted girders or segmental construction	Steel or composite bridges
Scaffolding supported from the ground	30–60 m	–	–
Erection with cranes supported from the ground	–	30–50 m	30–80 m
Formwork launching girders	30–60 m	–	–
Launching girders	–	30–45 m – girders 40–80 m – segments	(rare)
Incremental launching	–	30–60 m	30–70 m1
Cantilever construction	60–250 m	60–150 m2	70–300 m

Notes

¹ Spans well above 70 m, for steel and composite girders, may be erected by incremental launching if temporary piers or stays are adopted;

² Cantilever construction of concrete bridges with precasted segments.

The nominal stresses in the section at SLS also need to be controlled when designing a plate girder bridge, and the web slenderness should be restricted by web breathing phenomena. This is a problem at SLS inducing of transverse vibrations of the web under traffic loading, which may yield cracks at the welding between the web and the flanges (Figure 4.64). The limits to avoid checking web breathing are given in [21], for road and railway bridges. Designating the depth of the web as d and its thickness as t_w, one has

where l is the span length.

4.5.4.3 Vertical Bracing System

The main function of the vertical bracing system is to limit distortion of the superstructure cross section in its plane (Figure 4.65) under eccentric loading due to traffic and lateral horizontal loads due to wind or earthquakes. It is composed of cross girders or diaphragm trusses as solid plates, as previously referred to. The vertical bracing system benefits transverse load distribution between main girders under torsion loads.

An open section superstructure, composed by two main girders and a vertical bracing system, under eccentric loading due to traffic or (and) lateral transverse horizontal loads, is subjected to warping stresses σ_ω that should be added to the normal stresses σ_b due to global bending of the cross section (Figure 4.66). An asymmetric vertical loading may always be decomposed into a symmetric component, inducing overall bending only, and a skew symmetric load case, inducing torsion only. The last component induces a differential bending between main girders.

To reduce distortion and warping effects, cross girders are introduced at approximately mid‐height of the main girders, or even at the upper flange level as shown in Figure 4.67. In this last case – cross girders at upper flange level – one may benefit from them to support the slab deck. Since the distance of cross girders is always less than 5–8 m in road bridges with a maximum of 4h, h being the height of the main girders, the deck slab has bi‐directional bending reducing the transverse bending moments. In this case, it is usual to locate the cross girders at approximately 4 m maximum for main girders at 7–8 m distance apart. The cross girders are usually connected to the deck slab by shear head studs and may be extended to the transverse cantilevers of the deck slab (the overhangs) allowing wide decks with two girders only. Wide decks (Figure 4.68) with only two girders may be adopted with the mentioned cross girders, with distances reduced to 2–3 m only. Precasted slabs, supported by the cross girders, allow to cast the in situ slab deck. The precasted slabs may work just as a lost formwork or may work together with the cast in situ slab deck.

The height of the cross girders is usually 1/15–1/10 of the height of the main girders. The cross girders and diaphragms also have a function of avoiding lateral torsional buckling of the compressed flange. This global buckling mode, discussed in Chapter 6, is particularly relevant in continuous girders nearby the support sections, where important negative moments induce a high compressive stress in the lower flange. During the erection stages, flanges may need to be braced against lateral buckling. After casting the deck slab, lateral buckling of the upper flange cannot occur due to the connection with the slab. A temporary bracing of the upper flange in composite bridge decks, where the width of the upper flange is usually smaller than the lower flange, may be necessary for stability.

Lateral buckling effects in the lower flange, may be reduced by limiting the longitudinal distance between the vertical bracing elements (l_b) to values of approximately 9b_f for S355 steel, where b_f is the flange width. In fact, if l_b < 9b_f one can show [20] the non‐dimensional slenderness of the compressed flange for lateral torsional buckling [19, 20, 23] does not exceed 0.4, which allows a reduction, due to flange lateral buckling effects, of not more than 10% of f_y on maximum compressive stresses. Hence, the preliminary design of the cross section of the main girders may be performed by allowing a compressive stress at ULS in the order of 0.9 f_y at the compressive flange.

4.5.4.4 Horizontal Bracing System

As previously referred to in Section 4.5.4.1, in rail bridges and curved road bridges open section decks need certain torsion stiffness, which may be achieved by adopting a horizontal bracing system at the level of the lower flange of the main girders (Figure 4.69). The horizontal cross bracing may be made by hot rolled sections (e.g. Type 1/2 HEA 400) with a cross (X) configuration, a diamond configuration and a K configuration, as shown in Figure 4.70. The horizontal bracing may participate in the resistance to global longitudinal bending moments at the overall cross sections. However, its main function is to yield an equivalent horizontal plate, closing the section and working as a horizontal girder with a depth approximately equal to the distance between webs of the main girders. The in‐plane forces from the lower flanges are transferred to this horizontal girder and then to the bearings at support sections.

The thickness of the equivalent plate to the horizontal cross bracing is evaluated by strain energy consideration of a segment between two diaphragms under torsion. For different horizontal bracing configurations, a different value of the equivalent thickness is obtained as presented in [19, 24].

One relevant design aspect of the horizontal bracing configuration is the effect on the thermal locking stresses induced by the bracing. These stresses in the flanges are induced because thermal deformations are not free to occur. The configuration in X induces higher lock‐in stresses, while the K configuration is the less rigid one, inducing very light lock‐in stresses. This may be easily understood by comparing the deformation of the X configuration with the K configuration (Figure 4.70) under an axial force, N, at the flanges.

4.5.5.1 General

Box girder decks, as referred to in Section 4.5.1, are adopted for long span bridges, curved bridges (Figure 4.71) and bridges with specific requirements for increased slenderness (span/depth ratio) like urban bridges (Figures 4.32 and 4.36). Box sections are also adopted for axially suspended decks [25] due to requirements of torsional stiffness for static and aerodynamic stability. Examples of these cases are presented in Figures 4.33 and 4.34.

Box girder cross sections may have vertical (Figures 4.32 and 4.71) or inclined webs (Figure 4.33) and may be single cell or multicell box girders (Figures 4.34 and 4.72).

In cable‐stayed bridges and suspension bridges, steel box girders with an aerofoil cross sectional shape (Figures 4.33, 4.48b and 4.72) are adopted for aerodynamic stability reasons. One of the first suspension bridges built with this type of aerodynamic shape and with inclined hangers was the Humber Bridge in the UK (Figure 4.48b), with a main span of 1410 m: this was the record in Europe for some years before the Storebelt Bridge in Denmark. The recently built third Crossing of Bosporus, Turkey, is a more recent example (Figure 4.72). The deck of this modern steel suspension / cable‐stayed bridge has a main span of 1408 m with 1360 m being a steel deck and the remainder a PC box girder as the side spans with the same external configuration. The total deck width is 50 m and accommodates eight road traffic lanes and two rail tracks at the axis. Some stay cables complementing the main suspension cables stiffen the deck.

In the following sections, the main design concepts for the pre‐design of box girder decks are discussed. The analysis and design of box girders are discussed in Chapter 6.

4.5.5.2 Superstructure Components

Box girder decks integrate the following structural elements:

• A deck slab made of a steel orthotropic plate (steel box girders) or by a reinforced or PC slab (composite box girders), as happens in plate girder bridges.
• A complete steel box section or a U‐shaped steel girder, respectively, in steel decks or composite decks: in both cases the webs being vertical or perpendicular to the lower flange, or inclined as in trapezoidal boxes. The flanges and webs of box girders are steel plates with longitudinal and transverse stiffeners.
• Vertical transverse cross frames or (and) diaphragms, with or without web and flange transverse stiffeners between them.

Figure 4.73 shows the basic typologies for single cell box girder decks with vertical or inclined webs. In composite bridges, if the deck is large, the slab in RC or PC may be supported by cross beams extending to the overhangs. Another option is to adopt a longitudinal central beam supported the top flange and transferring its load to the diaphragms as shown in Figure 4.74. The lower flange in box composite girder decks is usually made of a steel reinforced panel (Figures 4.32 and 4.72) transferring its load to the diaphragms or cross frames. However, to save steel, one may adopt a double composite action (as shown in Figures 4.36 and 4.74), nearby support sections where high negative bending moments induce high compressive stresses in the lower flange.

The deck slab may also be cast on top of a steel plate (Figure 4.71). In this case, the top steel plate should have sufficient rigidity to avoid transverse deformations of the slab. It may have shear connectors transferring the longitudinal and transverse shear flows due to transverse bending and torsion. The steel box girder may be erected as a complete steel box (Figure 4.75) and the slab is cast after closing the superstructure. In negative bending sections, nearby supports, the steel plate is in tension but at the span sections the longitudinal compressive stresses due to bending requires a stiffened plate as in the lower flange section near the supports.

One of the main differences between plate girder bridges and box girder bridges is the existence of a stiffened plate at the bottom flange. The longitudinal high compressive stresses at this panel requires longitudinal stiffeners, which may be open or closed section stiffeners as shown in Figure 4.76.

4.5.5.3 Pre‐Design of Composite Box Girder Sections

A composite box girder section, with vertical or inclined webs, is generally a U or trapezoidal shape. Two top flanges, welded to the webs, are adopted and the bottom flange is made a stiffened plate (Figure 4.76). Since it is an open section during erection and before casting the slab deck, a top horizontal bracing is required for stability and torsion stiffness at the construction stages.

4.5.5.3.1 Deck Slenderness

Box sections generally have an increased slenderness with respect to plate girder superstructures for the same span length. Designating l as the internal span length of a continuous girder and h the depth of the box girder, values in the order of 1/25–1/30 are typical ones in practice. Of course, the width, B, of the deck influences the slenderness to be adopted. Empirical expressions have been proposed in Ref. [4.26] for pre‐design, like

(4.13)

For example, for a wide deck with B = 18 m, one has h/l = 27 for a continuous span.

4.5.5.3.2 Flange and Web Slenderness

The upper flanges may be pre‐designed as follows (Figure 4.77):

• b_s = 600–1000 mm
• t_s = 30–120 mm

With c_s/t_s < 10, in general, (c_s ≈ b_s/2) for the same reasons as plate girder bridges.

The webs are pre‐designed in a similar way to the webs of plate girder bridges. One generally has 12 < t_w < 16 mm at span sections and 15 < t_w < 25 mm at support sections. To take into account the width of the deck, some empirical expressions, taken from practice may be adopted (at least for support sections), such as the following [26]:

(4.14)

For example, for B = 18 m and l = 50 m, one has t_w = 20 mm at support sections; at span sections thinner webs (min. t_w = 12 mm) may be adopted.

The lower flange is pre‐designed taking the three main buckling modes of the compressive steel panel into consideration (Figure 4.78)

• The local plate buckling mode between longitudinal stiffeners;
• The global plate buckling mode where the stiffened panel buckles as an orthotropic plate supported at the longitudinal edges by the webs and at end sections by the transverse cross frames or diaphragms;
• A column buckling mode, typical for a wide panel with stiffeners deflecting with the plating between transverse cross frames or diaphragms.

The interaction between the plate mode and the column mode may exist, as discussed in Chapter 6. The plate thickness is generally 12 ≤ t_i ≤ 60 mm. At span sections, one generally has 12 ≤ t_i ≤ 30 mm and at support sections, 22 ≤ t_i ≤ 50 mm.

The slenderness of the plate between longitudinal stiffeners should be pre‐designed following: b/t_i < 60 in compressed regions and b/t_i < 120 in tension regions.

The longitudinal and transverse stiffeners should satisfy conditions of strength and minimum rigidity. The transverse stiffeners, cross frames or diaphragms supporting the end sections of the longitudinal stiffeners, should constitute rigid supports for the longitudinal stiffeners. Its slenderness (l_s/h_s), measured for the free length, l_s, between webs, for a transverse stiffener of height, h_s (Figure 4.49), should be limited to l_s/h_s ≤ 15.

If the longitudinal stiffeners are very rigid, local buckling modes control the design. However this condition is difficult to fulfil in design practice and the longitudinal stiffeners, characterized by area A_s and inertia I_s, will deflect between transverse stiffeners with the plate (Figure 4.79). Even assuming the longitudinal stiffeners are designed as flexible, slenderness should be limited to a/h_s ≤ 25, where a is the distance between transverse cross beams and h_s is the depth of the longitudinal stiffener.

The behaviour of a stiffened panel under compressive stresses, like at the bottom flange of a box girder, is considered in Chapter 6. However, it is anticipated the simplest model is the so‐called strut approach. The ultimate load of the panel is evaluated as a series of independent columns (struts) under compression, which is always a conservative assumption for pre‐design. The ultimate load is evaluated from the buckling loads of the individual columns composed by a stiffener and its associated effective plate widths to each side of the stiffener, as shown in Figure 4.80. The struts are assumed to be simply supported at the diaphragms (Figure 4.81) because the bottom flange is considered continuous over multiple supports.

4.5.5.4 Pre‐Design of Diaphragms or Cross Frames

Box girders need to have diaphragms or cross frames of two types: (i) at support sections and (ii) at intermediate sections.

The aim of diaphragms, made by solid plates with manholes for inspection and maintenance, cross frames or truss systems (Figure 4.82), is to reduce distortional effects leading to increased normal stresses. Slightly different schemes, such as the one shown in Figure 4.83, may be adopted. Distortional effects are associated with the one of the components of torsional loading as shown in Figure 4.84. Distortional effects lead to folded plate action in box sections [6, 24, 28] inducing axial normal stresses that should be added to the primary bending normal stresses. To avoid this effect, the maximum distance between intermediate diaphragms, generally between 5 and 8 m, should not exceed four times the web girder depth (l_d ≤ 4d).

Besides, the stiffness of the diaphragms shall be sufficient to reduce distortional effects. During erection of ‘open box sections’ (U shape) of composite girder decks, a horizontal top bracing is necessary to ‘close’ the section (Figure 4.36) because otherwise there is no sufficient resistance to torsion under wind loading and eccentric construction loading.

Diaphragms at support sections (piers or abutments) are generally made of solid plates (Figure 4.85) since, apart from avoiding distortional effects, they have to transfer vertical and horizontal bearing reactions to the webs of the box girder. In case of Figure 4.85a, a double bearing exists at pier sections and torsion moment reactions are taken by a couple of vertical forces in the bearings. In Figure 4.85b there is no resistance to torsion moments at support pier sections. The plate diaphragms, generally 18–22 mm thick, have vertical and horizontal transverse stiffeners; the slenderness of each sub‐panel should avoid plate‐buckling effects as a basic criterion. For maintenance requirements, these diaphragms are designed to accommodate, at the bottom flange of the box girder, concentrated forces due to hydraulic jacks required to replace bridge bearings. That requires clearances and specific stiffeners in the diaphragm.

4.6.2.1 General

Concrete decks are executed by one of the following methods:

• Scaffolding or stationary formwork
• Formwork launching girders
• Incremental launching
• Cantilever construction

As already mentioned in the previous section, concrete decks may be cast in place or precasted. In this latter case, one adopts precast girders (Section 4.4.6) or a precast segmental scheme, where entire cross section deck elements, 2–3 m long in general, are assembled in place as will be discussed in 4.6.2.6.

The range of span lengths for the main execution methods for concrete decks is represented in Figure 4.87, showing optimum typical spans and exceptional span lengths for each method. The reader is referred to specific literature [4, 30, 31] for a general discussion on execution methods for concrete bridges.

4.6.2.2 Scaffoldings and Falseworks

For cast in place decks, one has two options – classical scaffolding or stationary falsework. The first is a ‘continuous’ falsework (Figure 4.88) made with multiple small posts, adequately braced and supported from the ground. The stationary falsework is a ‘discrete’ scheme (Figure 4.89) where temporary piers are adopted at certain sections to support temporary girders, generally trusses. Classical scaffolding or stationary falsework are generally adopted for small or medium spans between 30 and 50 m and usually for shorter bridges. Classical scaffolding is not convenient when the height of the deck to the ground is greater than approximately 20 m. The same happens when the bridge is located in a valley or when the ground has relevant slopes making foundations of the scaffolding difficult. Standardized steel posts or towers (Figure 4.90) are adopted in both schemes, with hot rolled profiles as supporting beams to the formwork panels. The posts and towers, as well as truss girders adopted in these systems, are very often made of modular elements reutilized in a sequence of construction stages of the deck.

The main aspects for safety of scaffoldings or stationary falsework are adequate bracing and adequate foundations. Settlements of foundations should be considered. The foundation of the posts on the ground is generally through wood or steel plates. Accidents during construction associated with inadequate stability of scaffoldings have generally occurred during casting stages of the deck.

For classical scaffolding, a main issue is to understand the concept for the bracing system. The posts are small diameter tubes, with approximately 50 mm, braced between them to resist buckling effects. The connections between bracing elements and posts are through standardized node devices. The scaffolding, as a global structure, should have an overall bracing system to withstand lateral loads due to wind, construction loads and instability effects of the vertical members. When the height of the deck to the ground exceeds approximately 20 m, the stationary falsework is easier to control than a “continuous” falsework, with respect to overall stability. Tall towers, composed of multiple standardized elements braced between them, support main truss girders at its top. These girders, composed by modular elements connected by special devices, support the secondary elements of the formwork. The truss girders may generally reach spans of approximately 15–20 m, exceptionally spans up to 30 m.

Classical scaffolding or stationary falsework, except for very small bridges, are not economic for adoption without a sequence of construction phases allowing the reutilization of the construction equipment. In Figure 4.91, one represents the most adopted scheme for these bridges: a span by span construction with construction joints approximately one‐fifth of the internal span lengths. At theses sections, the bending moments for the final static scheme (a continuous girder) are very small for the permanent loads. The prestressing stages are also span‐by‐span allowing the scaffolding or the falsework to be moved to the next span at each stage. A set of prestressing cables at each stage are tensioned. The remaining cables of the span may be stressed at the next construction joint. At each construction joint, it is necessary to adopt continuity anchorages (couplers) for the cables stressed at that section.

4.6.2.3 Formwork Launching Girders

Formwork launching girders are construction equipments consisting of a moving formwork supported by launching girders usually made by plate, box or truss girders. These girders may work from below (Figure 4.92) or from above (Figure 4.93) with respect to the deck level. In the latter case, they may designated by launching gantries.

Launching girders are adequate for long bridges (viaducts) with straight or curved in‐plane geometries and with multiple spans between 30 and 60 m. The deck cross section may be a ribbed slab, a slab girder or a box girder. The launching girders generally have a length corresponding to two spans of the deck or have a support at the part of the deck already built, as shown in Figure 4.92. They are equipped with one or two launching noses (one at the front and one at the back) to reach the next pier during launching operations (Figure 4.92). They are equipped with hydraulic devices to move the equipment forward and to install and re‐install the formwork as exemplified in Figure 4.92 and 4.93. The most convenient sections to be built with formwork launching girders are slab twin girder decks, with span lengths up to 45 m, allowing building of one span per week. For box girders, with spans between 45 and 60 m, the progress of construction is generally lower and approximately equal to one span every 10–12 days. Formwork launching girders working from below are usually more costly than formwork launching girders working from above, because the available space for the structural depth for launching girders working from above may be larger allowing a lightest girder. Truss girders may be adopted in this case. The steelwork required for launching girders is controlled by maximum deformability requirements. A maximum deflection of the launching girders in the order of 1/600 of the span length is usually required in design specifications. The main inconvenience of launching girders working from above is the constraints resulting from the hangers suspending the formwork (Figure 4.93) not allowing prefabrication of the reinforcing cages. Moving forward operations are usually more difficult than with formwork launching girders working from below. But, supporting the launching girders in the pier shafts (Figure 4.93) is usually more difficult for formwork launching girders working from below. Launching girders may also be adopted for precasted segmental construction (section 4.6.2.6) as shown in Figure 4.94.

The cost of formwork launching girders is an investment that cannot be recovered without reutilization of this equipment. The adaptation to a new bridge cross section is usually possible but the span lengths cannot be much larger than that adopted for the original design of the launching girder.

4.6.2.4 Incremental Launching

Incremental launching is one of the most recent methods for the execution of concrete decks. It was initially developed last century in the 1960s [30, 32] and has been one of the most adopted methods in Europe in last decades.

The method consists of producing deck segments, usually between one‐third and half of the bridge span length, to the back of an abutment. After a certain bridge deck segment is completed, this is pushed or pulled forwards by hydraulic devices as shown in Figure 4.95. The reaction forces to move the deck forwards are induced at the abutment.

The method is usually applicable for long bridges with an in‐plane straight or constant curvature alignment (circular – R = const.) and with medium span lengths between 30 and 60 m. To reach one pier when pushing the deck forward at the rear section, a constant radius of the in‐plane alignment is necessary. Otherwise, a longitudinal movement induces a transverse deviation from the in‐plane alignment at the front section and the new pier support cannot be reached. However, the in‐plane alignment may be composed, for example, by straight and a circular alignments, but the deck should be pushed or pulled from both sides by executing one platform at the back of each one of the abutments. Intermediate launching platforms can be adopted to overcome the problem of in‐plane alignments made of more than two constant curvature bridge segments.

A front nose made of a plate or truss steel structure is necessary to reduce the bending moments at the front pier section as shown in Figure 4.95. The length of the nose is usually in the order of 50–60% of the span length. The same segment passes during the movement over support sections (negative bending moments) and at mid‐span locations (positive bending moments). The evolution of the static scheme during launching phases induces an envelope of bending moments as shown in Figure 4.96. The critical section for negative bending moments is of course at the last pier section before the nose landing at the pier. The nose may be equipped with a curved ‘landing device’ to facilitate support at the front piers.

In order to avoid tensile stresses in the concrete sections, the prestressing for the execution phase is likely to be centred and the cross section should have similar lower and upper section modulus. The ideal cross section deck is a single cell box girder. Span lengths of 30–60 m are the most adopted ones although longer spans are possible with intermediate piers or with a temporary staying scheme (Figure 4.97).

Temporary prestressing is required for the construction phases that may be done by external cables, some of them dismantled at the end before additional cables are added to support positive and negative deck bending moments at final stage.

Long bridges (more than 200 m length), or bridges with main spans crossing a river where no support from the ground is possible, may be executed by incremental launching at a construction progress of at least one segment per week. For segment lengths of half the span, one has at least one span made every two weeks.

For pre‐design, one may take the following guidelines:

• spans – 20–70 m, usual 35–55 m
• slenderness of box girder cross sections are l/h = 14–17 for road bridges and l/h = 12–15 for railway decks
• steel reinforcement quantity – 130 to 150 kg m⁻³
• prestressing quantities – 40–70 kg m⁻³

The length of the launching plant is at least one or two span lengths. The segments are cast in a formwork supported from the launching platform (Figure 4.98). Hydraulic jacks lower the formwork before the deck is moved forwards. Sliding supports under the webs are adopted as shown in Figure 4.98. The capacity of the launching equipment to move the deck is calculated on the basis of a friction coefficient (μ) of at least 5% and if the longitudinal profile has a positive slope i (%), which has to be taken into consideration when evaluating the required capacity of the hydraulic jacks, that is, μ > 5% + i. When the slope is negative, retaining cables have to be added to guarantee stability during launching operations. The most common jacking system to push the deck forwards is as shown in the scheme of Figure 4.99. Two jacks are adopted – a lifting jack reacting by friction at the deck underneath and a horizontal jack reacting against the abutment to induce the movement. The total dead load of the deck to be launched may reach some thousand tonnes (65 000 tons for the ship‐canal Bridge in Belgium [4]). Temporary sliding guided‐bearings are adopted at each pier for launching operations and made of PTFE plates with neoprene pads to accommodate rotations.

4.6.2.5 Cantilever Construction

4.6.2.5.1 Basic Aspects

Historically, the cantilever construction method, developed initially for wood bridges, has taken its place in bridge engineering with cantilever construction of steel bridges. With the development of RC bridges, the method has attracted attention from bridge builders after the Herval Bridge over River Peixe in Brazil was built in 1930 by a construction technique similar to that adopted nowadays. Although Freyssinet had previously (1945–1950) adopted the cantilever method to some extent, it was only with Finsterwalder in Germany (1950–1951) that the cantilever method for PC bridges was similar to modern technology.

Cantilever construction is a segmental construction method where small segments, generally in the order of approximately 2.5–5.0 m length, are built and assembled from the end section of an already‐built deck cantilever. The segments may be cast in place or precasted. In the former case, a moving scaffolding and formwork (Figure 4.100a), attached to the last segment already built is needed. In the last case (Figure 4.100b), precasted segmental cantilever construction, the segments are positioned at the end section of the cantilever. For precasted segmental cantilever construction, the segments are positioned with a launching girder, lifted from a barge or from the ground with a derrick. The cantilever construction scheme may be executed:

• Symmetrically to each side of a pier – balanced cantilever scheme
• Asymmetrically, from a span already built
• Asymmetrically, from an abutment

Usually, at the end span, a mixed technique is adopted as shown in Figure 4.3. The cantilever construction scheme (Figures 4.3 and 4.4) is adopted from the end pier for part of the end span and the remaining area is made with scaffolding supported from the ground.

In the cantilever construction method, cast in place or precasted segments are prestressed at each phase after casting or assembling a new segment (as shown later in Figure 4.101).

The connection between the end sections of each one of the cantilevers coming from two piers of one span is made through a closing segment with a general length between 2 and 3 m. Continuity prestressing cables (Figure 4.101) are applied after casting of the closure segment to face the induced bending moments at mid‐span sections, developing in the continuous structure as explained in Section 4.3. Part of this prestressing may be made by external cables.

The dead weight of each cantilever and the weight of the moving equipment (scaffolding and formwork) is supported in bending by the already completed part of the cantilever. Figures 4.102 and 4.103 show moving scaffoldings for cantilever construction. The moving scaffoldings are usually designed for capacities between 250 and 750 kN and standard maximum segment lengths of 5.0 m.

Large negative bending moments exist during the cantilever scheme. The most adequate section to resist these bending moments is, of course, a box girder section due to its large lower flange. The box girder is in most cases a single cell box girder with vertical or inclined webs. For very large width sections, a double cell box girder may be adopted, or a single box with inclined struts or with transverse ribs.

The depth of single cell box girder at pier sections for cantilever construction is between 1/20 and 1/17 of the span length. A maximum slenderness of 1/22 at the support sections may be adopted for aesthetics (Figure 5.14 – Alcacer do Sal Bridge at IP1 over the River Sado, Portugal) when the vertical alignment is at a low level.

In balanced cantilever schemes, the piers (Figure 4.104) resist the differences between the moments coming from each cantilever. These differences result from deviations in weight of the segments, and possible asymmetry in concreting the segments, construction loads and wind loading. The quantification of these loadings is addressed in Chapter 6.

The connection between the piers and the deck to resist these moments during construction may be monolithic in frame bridges, connected through anchorages by prestressing cables or supported by temporary piers (Figure 4.105) in the case of continuous girder decks supported on bearings.

4.6.2.5.2 Span Arrangement for Balanced Cantilever

In continuous multiple span decks, the easiest solution for span arrangement is to make, as far as possible, multiple internal span lengths (l) and two end spans with lengths in the order of 0.6l to 0.8l. Some examples are shown in Figure 4.106a. In the Porto Novo Viaduct (1988), 80 m typical internal spans with a constant depth (4 m) and two side spans of 60 m with a reducing depth towards the abutments were adopted. For the internal spans, the balanced cantilever was executed from each pier and a sequence of closure segments from the side spans to the centre was executed. At the end piers, 38 m deck lengths to each side of the pier were executed and the remainder 20 m of the side spans (20 m) between the abutment and end cantilever were executed on a scaffolding from the ground. Then closure segments were executed in the first and last spans, followed by the closure segments at the second and fourth span and, finally, the centre closure segment. The evolution of the static scheme is similar to that already discussed in Section 4.3. In the bridge over the Zambezi River in Caia, Mozambique, with 137.5 m internal typical spans, the end spans are 80 m and a sequence of closure segments was executed from the side spans to the centre, see Figure 4.106b. Details on this long bridge (2376 km) and sequence of construction may be seen in [33]. When different internal spans are adopted as in the Rosso Bridge over the River Senegal (Figure 4.106c), with a main span of 120 m over the main channel, the balanced cantilever scheme can also be adopted but the span distribution should be established taking into consideration the sequence of closure segments. In a sequence of internal spans, l₁, l₂, l₃,…, for a general symmetrical arrangement as shown in Figure 4.106c, a balanced cantilever scheme from piers P1, P2 and P3 requires, for example, l₂ = (l₁ + l₃)/2.

4.6.2.5.3 Asymmetric Cantilever Construction

Site data, like topography, geotechnical conditions or a main span over a river, may justify adopting an asymmetric (unbalanced) cantilever scheme. An example of a design case [34] of two parallel bridge decks is shown in Figure 4.107 The topography and geotechnical conditions of the valley have shown the best option to be a deck for each of the bridges built from a single pier in a balanced cantilever scheme and the remaining part of the deck from the tunnel as a single cantilever in an unbalanced scheme. The closing segment was then executed at the centre of the main span of 104 m. Site conditions showed the location of the single pier for each of the decks to be skew symmetric, as shown in Figure 4.107. The bridge is curved in‐plan and the pier is made of two thin RC walls. The deck is made monolithic with the pier, which allows the imposed deformations (thermal, shrinkage and creep) by flexibility of the two shafts of the deck, rigidly connected at the tunnel and having unidirectional bearings at the abutment. The bridge, with two spans for each of the decks, from the front view looks like a classical three‐span bridge. The reader is referred to Ref. [34] for details.

4.6.2.5.4 Frame Bridges with Inclined Piers and Arches

For frame bridges with inclined piers, usually hydraulic jacks are inserted between the deck and the temporary piers (Figure 4.108) for removing the temporary supports after closing the deck at the mid‐span section. The cantilever method may be also adopted for the construction of arch bridges. The reader is referred to [35] for developments on the cantilever construction method.

4.6.2.6 Precasted Segmental Cantilever Construction

It has been already mentioned that precasted concrete segments can be adopted with launching girders and cantilever construction. This is a very convenient alternative for multiple span long bridges, because segments are being executed and at same time others are being assembled. The rate of construction may reach an average of 10 m of deck per day. If one compares it, for example, with a cast in situ cantilever scheme, with two pairs of movable false work where it is possible to build 20 m week⁻¹ (2 × 2 segments of 5.0 m length), the speed of construction with precasted segments is at least twice the one achieved with a cast in‐place cantilever scheme.

The length of segments is up to 3.5 m in general, limited by transport, lifting and assembling capacities of the equipment and the amount of prestressing required at each assembling stage. They are precasted on site or in a specific facility and transported to the bridge site. The most adopted method for precasting is ‘match cast’ segmental construction, where the segments are cast one against the other in order to achieve a coupled joint (Figure 4.109). The segments are then assembled on the alignment of the bridge deck, by cranes (if the height of the bridge deck allows), via a launching girder or the cantilever method.

An important issue in precasted segmental bridges concerns the joints between segments. The three possible options are cast in situ joints (requiring approximately 200 mm for the joint and a formwork), mortar joints allowing a reduction in the gap between segments to approximately 5 cm and, finally, coupled match cast joints with ‘epoxy’ glue. The last procedure is nowadays the most adopted one due to the quality usually achieved and the rate of construction allowed. In coupled match cast joints, the ‘epoxy’ allows lubrication of the contact surfaces of the segments facilitating the assembling and, most important, seals the joint allowing waterproofing, thus avoiding the water ingress into the ducts of the prestressing cables crossing the joint. The joints are designed to be permanently compressed even under live loads and thermal gradients. The shear resistance is achieved nowadays by a multiple ‘shear key’ detail, as shown in Figure 4.109, improved by the presence of the ‘epoxy’. The reader is referred to Refs. [4, 26, 35, 36] for details and specifications on precasted segmental construction.

4.6.2.7 Other Methods

A brief reference is here made to other possible options for execution of concrete bridge decks. Three additional methods are:

• Deck erection by transverse displacement
• Deck erection by rotation
• Deck erection by heavy lifting equipment

One is the possibility of executing the bridge deck on a site parallel and adjacent to the in‐plane bridge alignment and moving the deck laterally after completion, previously erected on sliding bearings, by hydraulic equipment. The transverse sliding method is adopted for small bridges and usually when replacing an existing deck where severe traffic disruption is a main constraint.

Rotation of the deck built on site is, perhaps, the most spectacular bridge erection method. The deck may be executed, for example, along a river bank on scaffolding supported from the ground and then rotated to the final bridge alignment. It is adopted for the same span range spans of the cantilever method since during rotation the static system is similar. Yet, this method has been already adopted for cable‐stayed bridges like Ben‐Ahin bridge, Belgium [4].

Heavy lifting erection methods have been developed in the last few decades for long bridges offshore or crossing long estuaries like the Great Belt Bridge in Denmark, Vasco da Gama Bridge in Portugal, and the Prince Edward Island Bridge in Canada. Precasted entire spans may be transported on barges to the site and lifted with special equipment: gantry cranes, reaching capacities of several thousand tonnes. In the Vasco da Gama Bridge, entire 80 m box girder spans were transported and lifted and for the Prince Edward Bridge, with multiple spans of 250 m, segments reaching 7800 tons were erected. The construction rate with heavy lifting is the largest, generally reaching 250 m per week for the Prince Edward Bridge [31].

4.6.3.1 Erection Methods, Transport and Erection Joints

The most adopted methods for the erection of the superstructure of steel and composite bridges are:

• Erection from the ground with cranes
• Incremental launching of the steelwork
• Cantilever construction

The last method, cantilever construction, is adopted for long spans as for concrete bridges, namely for box girder bridges and cable‐stayed bridges. Specific methods, such as the ones referred to for concrete bridges in Section 4.6.2.6, like transverse displacement and rotation, are also adopted in a more limited range of applications. The fundamentals of the methods are similar to the ones already mentioned for concrete bridges. One of the specific aspects of steel and composite bridges is transport to the site of the steelwork. After fabrication, a main issue is how the steelwork should be transported to the bridge site. This aspect has been already mentioned in the introductory section on steel bridges (Section 4.5) but is also related to the erection procedures. The most common transportation is by trucks, but without special permissions a segment limit in the order of 30 m length and 3 m width by 4 m height is imposed in most countries. The weight of the segment is usually limited to approximately 50 tons. Rail and ship or barge transport is a possible option in some cases, with segment lengths limited to approximately to 12 m for railway transport and container limitation for ship transport.

Plate girder steelwork decks are generally transported in independent girders, the number of segments being limited to a maximum total weight of approximately 40 tons for the truck. Box girders are transported in two halves (Figure 4.35) requiring a longitudinal site joint as previously referred to.

The segments after transport to the site may be assembled in longer segments by execution of full penetration welding joints at flanges and web sections that are subjected to Non Destructive Testing (NDT) on site. The quality welding control on site is currently done by ultrasonic or magnetoscopic tests and less frequently by RX tests. Of course, basic geometric quality control, visual inspection of the welding and dye penetrant tests are always done.

The segments are then erected and positioned at the deck alignment and bolted or welded at erection joints. The tendency nowadays is to prefer welding erection joints for the benefit of durability of the structure but, of course, this requires the appropriate means for site execution and inspection. The number of NTDs to be carried out on‐site inspection depends on the Execution Class (EXE) of the structure according to EN 1090 [37]. For bridges, EXE 4 is required in most cases and for site welding:

• Transverse butt weld subjected to tensile stresses 100%
• Transverse fillet welds, in general 10%
• Longitudinal welds and welds to stiffeners 10%

In a span‐by‐span erection, it is possible to have erection joints at intermediate span sections, for example, at one‐fifth span sections, and to execute complete penetration site welding on webs and flanges. For most cases, bolted temporary erection joints are needed, which could be done according to the scheme of Figure 4.110. After final adjustment of the new segment position the definitive site welding is executed.

4.6.3.2 Erection with Cranes Supported from the Ground

If the height of the deck with respect to the ground is relatively low (order of less than 15 m) and access to bridge site allows, it is possible to erect the steelwork with cranes from the ground. The crane capacity is dependent on the lever arm required and on the weight of the segments of the steelwork. A reference value of 100 tons at maximum distances of 10–20 m may be considered for standard crane erection of the steelwork. The deck may be erected by a span‐by‐span scheme with erection joints as discussed in Section 4.6.3.1.

For a main span on a river, it is possible to erect the central part of the steelwork by cranes on barges, or even with two cranes located on each river bank as in the example of Figure 4.111.

4.6.3.3 Incremental Launching

The incremental launching method for the erection of the steelwork is, concerning its basic aspects, constraints, advantages and disadvantages, quite similar to the incremental launching method for concrete bridge decks discussed in Section 4.6.2.4. The erection scheme is as represented in Figure 4.95 for concrete decks. The segments of the steel deck coming from the manufacturer are positioned along a launching platform, welded at the end section of the previously launched segment and moved forward, by pushing or pulling, by hydraulic devices.

Long straight alignments or curved with constant curvature steelwork decks, with spans up to 150 m, may be incrementally launched. Longer spans are possible with intermediate temporary piers or staying schemes during launching (Figure 4.96). The span length is one of the main differences with respect to the incremental launching of concrete bridge decks, where spans above 60 or 70 m are very difficult to launch due to the deck dead weight inducing too large internal forces during erection. The incremental launching method of steel and composite decks (Figure 4.112) requires:

• a launching platform with a minimum of two span lengths
• an hydraulic device system for pulling or pushing the steelwork
• temporary bearings at all piers and guiding devices
• a launching nose equipped at the front with a ‘landing device’ or with the possibility for lifting the end section from the pier

The capacity of the hydraulic devices system is usually between 3 and 10% of the weight of the steelwork. Temporary sliding bearings at piers are shown schematically in Figure 4.113. The friction coefficient is for design purposes at least 5%. If the geometric slope of the longitudinal profile is, for example, 2% as in case of Figure 4.112a, an equivalent friction to 7% is considered. Launching stages in the order of 2 h for 20 m segments are typical, as in the case of Figure 4.112a.

When the deck approaches a new pier, the vertical deflections at the front section of the launching nose requires either a special type of device – a landing device – or the possibility of lifting the end section of the nose upwards. Introducing upward movements in the order of 200–300 mm is usual. All these deflections induce internal forces and the final precamber to adopt for the deck should be determined at design stages. Patch loading in the webs (Figure 4.63) under combined shear and bending moments should be checked at all erection stages and critical sections.

The deck is usually launched at its final level or at level of the lower flange and then moved downwards to its final position. In a twin girder deck, both girders are launched simultaneously, in general and if needed, with a temporary transverse horizontal bracing, usually at level of the upper flanges. The transverse stability of both flanges should be checked at the erection stages taking the distance between diaphragms restraining horizontal transverse buckling of the compressed flanges into consideration.

4.6.3.4 Erection by the Cantilever Method

The cantilever method, already discussed for concrete bridges, is the most adaptable method for erection of steel decks of large spans (more than 100 m) and with or without a variable curved in‐plane alignment. The segments are erected by derrick devices at the end section of the cantilever, from the ground or from a barge in a river. The length of the segments may be much longer than in concrete bridges, reaching 15–20 m in length. The method is adopted based on a balanced cantilever scheme or by an asymmetric scheme as shown in Figure 4.114a. At closure of the segment section (Figure 4.3), the bending moment due to dead loads is zero when the erection joint is done by site butt welding of flanges and webs, and it remains zero contrary to what happens to concrete bridges, as explained previously in Section 4.3.

For very long spans, intermediate temporary piers or staying schemes are adopted. Cable‐stayed bridges with steel, concrete or steel‐concrete composite decks can also be erected by the cantilever method (Figure 4.114b).

4.6.3.5 Other Methods

Other methods, like the ones referred to for concrete bridges, are possible. In particular, transverse sliding [19] is very much adopted for replacement of an existing steel deck when, in railway bridges (in particular), traffic interruption is a main constraint. Another option is erection of a central part of a long main span (Figure 4.115) from a barge with heavy lifting equipment or of a bowstring arch in three segments, as in Figure 4.116.

4.7.2.1 Structural Materials and Pier Typology

Piers may be made in masonry, wood, concrete or steel. Masonry piers have been adopted for a long time, since bridges were first made. The lack of tension resistance is one of their main limitations. Even in the middle of last century, beautiful bridges (Figure 4.117) were made with masonry piers and engineers should be aware of masonry as structural material. Effectively, retrofitting of old bridges very often requires replacement of the deck keeping the existing piers for economy but, most importantly, for respecting historical heritage. It should be borne in mind the resistance of a hard stone may reach 50–100 MPa, while standard masonry due to the influence of the mortar may be limited to values 5–10 MPa. However, this depends very much on the case, and values for compressive stress resistance from tests of prismatic specimens of masonry for the piers of the bridge in Figure 4.117, with joints of 3–4 cm, can reach minimum values as high as 70 MPa [40].

Wood piers are adopted in wood and temporary bridges. It is also adopted as a structural material for scaffoldings in bridge construction. However, the majority of bridge piers nowadays are made in RC. Some prestressing is adopted in some cases but currently compressive stresses due to permanent loads are enough to balance any tensile stresses due to variable actions. In any case, if tensile stresses are induced due to live loads or imposed displacements, the problem is overcome, in most cases, with just ordinary reinforcement. RC is an excellent structural material for piers, since the main actions induce compressive stresses, and reinforcement steel is required to limit crack widths and for ULS resistance due to induced tensile stresses under the combination of compression and bending due to permanent and variable actions.

A pier shaft with its foundation is shown in Figure 4.118. If the pier has a double shaft, or more than two shafts, a transverse cross beam, capping beam, between pier shafts may be needed for transverse stability (Figure 4.119). Although not very aesthetically pleasant, the cross beam yields a transverse frame action to the pier.

The geometry of cross section of bridge piers may be quite diverse and it is possible to define the following typologies:

• solid section piers or tubular piers – column piers (Figure 4.120)
• wall piers – leaf piers (Figure 4.121)

In column piers, cross sectional dimensions a and b (Figure 4.120) are of the same order of magnitude, usually in the order of 0.5–1.0 m. For pre‐design of the cross section, an average medium compressive stress at SLS in the order of 4–5 MPa may be adopted. In leaf piers, the width a is much larger than the thickness b, usually at least four times. In this case, b is generally between 0.4 and 1.0 m and the width a is very often reduced towards the base section for aesthetics and sometimes to increase horizontal clearances at the ground level, namely in urban viaducts. An average compressive stress at SLS in the order of 2–3 MPa may be adopted. At the top section, cross sectional dimension a is dependent on bearing location requirements in most cases. For piers with a single shaft, and heights up to 15–20 m in general, column piers (Figure 4.120a) are usually preferred. For medium piers, say between 20 and 30 m, solid or tubular box sections may be adopted. Above 30 m and sometimes reaching 200 m height or even more (Figure 4.33 – Viaduct the Millau), tubular piers (Figure 4.120b) are the preferred option. The wall thickness is in general at least 30 cm for easiness of formwork and placement of reinforcement.

4.7.2.2 Piers Pre‐Design

Designing pier shaft cross sections should take into consideration:

• resistance
• stability
• aesthetics

Stability should be considered at the final static model of the bridge and also at construction stages. Its overall cross section dimensions are kept constant for short and medium piers, say up to 30–40 m. In tubular tall piers, at least one of the cross sectional dimensions, usually the transverse dimension, is variable (see Figure 5.17).

The slenderness of a pier for aesthetics is usually defined as l/b or l/a, l being the pier height of its shaft and b or a the overall cross section dimensions (Figure 4.120). For stability, slenderness is defined by:

(4.15)

where l_e is the buckling length and i is the relevant radius of gyration of the pier cross section. The radius of gyration , where I is the relevant moment of inertia and A the cross sectional area. For a rectangular section, or . This means the slenderness for aesthetics is approximately 28% of slenderness for stability. Assuming b is the smaller dimension of a constant rectangular cross section, a pier with l/b = 20 has λ = 70 if l_e = l. At the final static model of the bridge, one may have from l_e = 0.5 l if the pier is monolithic to the deck, up to l_e = 2 l if a sliding bearing is adopted between the deck and the top of the pier shaft. At the construction stage, one very often has l_e = 2 l, or even more if rotation at connection with foundations is considered, as discussed in Chapter 7.

A basic pre‐design criterion for selecting the cross sectional dimension of a pier section is to limit its slenderness to 70 for the final static scheme and 100 during construction. A limit of 70 at the final static scheme is adopted to avoid relevant creep effects of the concrete on the ultimate buckling resistance of the pier. For tubular piers, if one compares its cross section with a solid section pier with same cross section area, one has a larger radius of gyration i. That is why tubular sections are preferred for high piers. In tubular piers one has, compared to a solid section pier with the same cross sectional area, A, a more stable shaft (smaller λ) and the same compressive stresses due to axial loads, which is relevant to reducing tensile stresses coming from imposed permanent actions due to creep and shrinkage and variable actions.

The slenderness of a concrete pier is generally smaller than in a steel pier, and second order effects due to instability effects govern this. RC piers are always adopted in concrete bridges and are the main option for steel and composite bridges. In piers in rivers, it is usual to adopt wall piers, with hydrodynamic details as shown in Figure 4.121. If the risk of ship impact exists, the cross sectional dimension b of a wall pier may be larger than 3 m. In those cases, ship impact defences (‘fencers’) may be adopted. A similar case occurs in viaducts over railways where wall piers are usually required and minimum distance to tracks should be respected [41]. In short, whenever an accidental impact event in pier shafts due to traffic needs to be considered, possible options for design are:

• to locate the pier at a sufficient distance to minimize risk of impact
• to adopt pier protections (fences in rivers, walls nearby tracks, metal fences near road traffic lanes)
• to design the pier shaft for impact loading

The risk of ship impact in piers depends on the dimensions, tonnage and speed allowed of the vessels in the navigation channel. Ship impact, reaching thousands of kN, tends to be the critical action for the design of piers in rivers.

Design of pier shaft cross sections should take into consideration resistance, stability and aesthetics. Overall cross sectional dimensions in piers are kept constant for short piers, say l < 10–15 m, and medium piers, say 15 m < l < 40 m. In tubular tall piers, at least one of the cross section dimensions, usually the transverse dimension, is variable.

One important aspect when designing pier cross sections is the dimension required for the bearings as indicated, for example, in a leaf pier in Figure 4.121. Besides, the space required for hydraulic jacks for replacement of bearings is another aspect to be taken into consideration.

4.7.2.3 Execution Method of the Deck and Pier Concept Design

The execution method of the deck may influence the shape of the pier shaft. In incremental launching girders working from below, the upper part of the pier shaft should be designed to accommodate the fixation devices of the launching girders as shown in Figure 4.92. In the incremental launching method, the pier top cross section requires sufficient clearance to accommodate temporary bearings and transverse guiding devices to avoid deviations of the in‐plane alignment during launching operations. Besides, the pier shaft should be designed to withstand the horizontal forces due to bearing friction during launching or even due to the longitudinal slope of the bridge deck. However, from all execution methods for the bridge deck, the cantilever method for deck execution generally has the largest impact on the concept design of piers. By this reason, it is dealt with specifically in the following.

4.7.2.3.1 Piers for Bridges Built by Cantilever Construction

Actions induced in bridge piers built by balanced cantilever during construction are due to a multiplicity of actions (Figure 4.122), namely:

• dead loads (pier and deck)
• unbalanced segments during construction
• dead loads of moving travellers (scaffoldings)
• construction live loads
• wind loads

All these loads induce large axial loads and bending moments (in two directions) and are easy to resist with tubular column piers. In tall piers, second order effects due to instability come into play and may be relevant, as will be discussed in Chapter 7.

The connection between the pier and the deck may be rigid (frame bridges) or through bearings (continuous girder bridges), as shown in Figure 4.123. Bending moment resistant of the piers is usually adopted for tall piers to avoid bearings, and temporary devices for stability during construction and to benefit from frame action at the final static scheme.

Short piers are usually connected to the deck through one single row of bearings. Temporary anchorage, stay cables or temporary piers (Figure 4.124) are needed to guarantee a stable system during the erection stages.

Medium height piers are usually provided with one or two rows of bearings reducing the stiffness of the pier for imposed deformation (creep, shrinkage and temperature) of the deck; in long continuous bridges, the central piers are usually rigidly connected to the deck, while the remainder have fixed pot bearings or unidirectional movable pot bearings. In some cases, a pier made of two flexible concrete shafts (Figure 4.107 and 4.125) is adopted, which are stabilized during the erection stage by a temporary steel structure, as will be discussed in the following.

In short, there are three main possible options for typology and schemes of pier‐deck connections:

• tubular monolithic piers with the deck
• tubular or solid section piers (depending on height) supporting the deck by bearings
• piers made by two independent solid section shafts monolithically connected to the deck or eventually hinged at the deck

Stability in the first case – monolithic tubular piers – adopted for tall piers, may guarantee stability during construction phases by resistance of the tubular section shaft. The second case, a deck being articulated to the pier shaft, requires specific devices of course, as said before, guaranteeing overall stability of the deck. There are the following options:

• adopt temporary high strength prestressing bars or cables connecting deck and pier sections
• adopt one or two temporary piers adjacent to the definitive pier shaft
• adopt temporary stability cables (stays) anchored to the deck and to pier foundation

Finally, the option of adopting a pier with two slender pier shafts (Figure 4.125) is a possibility when the imposed displacements by the deck tend to induce large forces. In a pier made of two flexible shafts, any unbalanced moment M during construction is taken by a couple effect; no tensile stresses are usually accepted in the section at any construction stage, except for accidental load combinations. The shafts shall be sufficiently braced between them in such way that the full section works as a global section during construction stages. After closing the deck, the bracing system is removed and the shafts can deform as independent piers towards the centre of stiffness, as shown in Figure 4.125. The buckling length of the shafts at the built structure tends to be half the free length. During construction, the two pier shafts work together and the buckling length is taken for the pier with the overall cross section inertia.

The temporary stability systems referred to here – anchorages, temporary piers and stay cables – should be designed to guarantee the necessary overall stability of the deck and to have sufficient stiffness for good control of deflections during construction. Any rotation of the deck at support section has a large impact on deflections of the cantilevers, and precamber control becomes difficult to achieve. Sometimes, the three schemes (as before – anchorages, temporary piers or stay cables) are combined (Figure 4.124). It is usual to adopt anchorages and temporary piers or anchorages and stay cables due to lack of space at the top section of the pier in order to introduce a sufficient number of anchorages to guarantee overturning stability of the deck until the casting of the closure segment. Stay cables are very often sufficient for stability of the deck during execution but are not very efficient concerning deflection control (camber) because the deformability of the stays is usually too large. The use of temporary supports, if possible, is usually simpler and more efficient. The anchor bars for temporary connections between segment 0 and the end section of the pier are always required.

All these stability devices are designed for forces coming from overturning moments of the deck. Temporary bearings or wood shims are usually adopted in the anchorage scheme system between the underneath of the deck and top of pier section. At the end, after the closure segments are executed and stability of the deck is guaranteed, the anchorages and any temporary devices are removed.

4.7.2.3.2 Design Safety Checks of Piers During Deck Cantilever Construction

Actions during construction stages, referred to in Section 3.19, have been mentioned in the present chapter. For designing bridge piers built by the cantilever method, or the stability devices previously referred to, some specific construction loads and load combinations need to be specified. The basic system is represented in Figure 4.122, where G_i and G_i′ denote the weights of segments i and i^′. The weights of each cantilever are G = ∑ G_i and G′ = ∑ G_i′. For G_max and G_min, one usually takes a ±2% deviation on the nominal weight, G, of one of the cantilevers; that is, G_max = 1.02 G and G_min = 0.98 G. Construction loads (equipment, formwork travellers, construction live loads etc.), are denoted by Q_c1, Q_c2 and Q_c3, in Figure 4.122. Load Q_c1 denotes a live load during construction, applied anywhere, Q_c2 is associated with a construction load at the end segment due to weight of prestressing equipment (cables, anchorages, etc.) and Q_c3 denotes the weight of the form traveller (500–800 kN in general). W_c designates an uplift differential wind action between the cantilevers.

Safety should be checked involving stability systems, for a load combination:

(4.16)

where G are permanent loads, Q_ci construction loads and W_c unbalanced wind loading. Partial safety coefficients γ_g = 1.1 or 0.9 as most unfavourable and γ_q = 1.25 have been proposed in [26, 42, 43].

An accidental load combination should also be checked replacing Eq. (4.16) by

(4.17)

where F_a represents the action induced by the falling of a form traveller during a manoeuvring or the falling of a precasted segment during erection, with a dynamic coefficient of 2.

In cast in‐place balanced cantilever bridges, sometimes in Eqs. (4.16) or (4.17) one considers a construction load Q_ci associated with a difference in weight between the end segment n and n′ due to a differential time between castings. To take Q_ci = 0.5 G_n where G_n is the dead weight of segment n is, in general, enough, provided the concreting of the slab deck in one side is not initiated before the bottom flanges and webs at both sides are concluded. This control, to be made by the Engineer, is sufficient because in box girder bridges the deck slab weighs about 50% of the full weight of the segment. Even with Q_c = 0.5 G_n applied at the end section of only one of the cantilevers, the associated load combination tends to be the most critical for the pier, at least for long span balanced cantilever bridges.

During the balanced cantilever scheme of a curved box girder bridge (Figure 4.126), the dead load of the deck induces transverse bending moments in the piers, unless some provisional prestressing, internal or external, is adopted. It is possible to balance the total applied transverse bending moments during construction by external prestressing tendons applied with an effective force P and eccentricity e (Figure 4.126).

Balanced cantilever bridges, with tall piers, present low natural frequencies in bending and torsional modes of the piers during construction. It is usual to have longitudinal and transverse bending frequencies and torsional frequencies f_x, f_y and f_t, respectively for tall piers (say between 60 and 100 m) and spans between 100 and 180 m in the range 0.1–0.4 Hz. An example was shown in Figure 4.4 where f_x = 0.17 Hz and f_t = 0.29 Hz.

Under random excitation and due to wind gusts, bending and torsional effects due to unbalanced wind buffeting should be considered in designs when checking the structural safety during the construction stages. For torsional effects, the historical Sir Benjamin Baker's rule‐of‐thumb, as considered in the design of the Firth of Forth Bridge, assumes a ‘full mean wind’ with a wind velocity v_m on one overhang and ‘no wind’ on the other [43] as wind pressure W_c2 shown in Figure 4.122. This load needs not to be combined simultaneously with normal construction loads, since it is unlikely construction is being done at a strong wind event. The pioneering work of Davenport [44] in 1967 evaluates the torsional effects induced by wind gusts on a cantilever bridge due to the resonant component of the torque only. Dyrbye and Hansen in 1996 [45] presented an approach suitable for design practice to consider the problem of torsional effects of balanced cantilever bridges of constant height decks. The approach was generalized by Mendes and Branco [46] for variable depth box girder bridges, as well as for the joint analysis or bending and torsion effects. Codes and design recommendations, like ASCE 1982, ECCS 1989 and NBCC 1990, refer to the need to investigate the wind torsional effects in balanced cantilever bridges during construction.

The characteristic average wind speeds (U_k,50) are usually defined for time intervals of 10 minutes with a reference period of 50 years. For checking the structure during construction, one adopts a shorter reference period T, say T = 10 years for a construction time not greater than 1 year according to EN 1991‐1‐4. The associated characteristic averages wind speed yields for T = 10 years U_k,T = 0.88 U_k,50, that is, a 12% reduction in wind velocity representing in the wind pressures (depending on U²) a 23% reduction. The reader is referred to specific literature [45] on this subject for further information.

For the design of temporary stability devices, one should take into consideration the uplift condition at a temporary pier or the minimum prestressing force required for temporary stays. The reader is referred to references [35, 45] for additional information.

4.7.2.4 Construction Methods for Piers

Piers are usually built by griping formwork. The formwork for the shaft with 3–4 m length, is moved upwards in steps discontinuously, after concreting the previously segment of the shaft. It is fixed to the part of the pier shaft already built and moved upwards by hydraulic devices. Then, after erection of the steel reinforcement of next segment the formwork is moved upwards and the new segment is casted.

The example of the Guadiana bridge in Figure 4.127, shows a griping formwork for casting a tubular shaft of a box girder bridge built by the cantilever method.

Tall piers may be executed with sliding forms, where forms are moved continuously. The method requires specific measures to guarantee the required position of the reinforcement, namely the required concrete cover. Sliding forms have encountered some restrictions by technical specifications and tender documents in some countries, due to the sensitivity of the method in achieving a good concrete quality control and control of geometry of the reinforcement steel. Sub‐contractors specialize in sliding forms, as was the case of the tall piers of the João Gomes Bridge (Figure 5.1); with a variable pier cross section, it reached a construction progress with sliding forms of approximately 5 m per day for piers of about 100 m.

4.7.3.1 Functions of the Abutments

The abutments, establishing the transition between superstructure and access roads or railways, have the following main functions:

• supporting vertical and horizontal loads from the superstructure at the end spans
• supporting soil actions transmitted by the backfill and to avoid erosion of the soil contained in the abutment
• accommodating movements of the deck, in particular at the expansion joints between deck and abutment
• accommodating small foundation settlements without inducing risks to the superstructure
• allowing the positioning of the end section bearings of the superstructure

4.7.3.2 Abutment Concepts and Typology

Options for abutment types are very much dependent on topographic and geotechnical conditions at the bridge end sections, type of bridge superstructure and aesthetical conditions. Transition of the bridge to the ground should be as smooth as possible but abutments should be at the scale of the bridge. A large bridge should not have a very small abutment, even if that is possible by extending the superstructure towards the slopes of the valley. On the other hand, a pedestrian bridge should not have a large and tall abutment since it is out of the bridge scale. The height of an abutment should be established leaving a minimum space of at least 1–2 m between the underneath of the superstructure and the ground. This clearance is required to avoid accumulation of debris, to allow an easy access for abutment bearing inspection and replacement and to allow a clear visual separation between the superstructure and the ground. There are two main types of abutments (Figure 4.128):

• Closed/solid abutments
• Open or skeletal/spill‐through abutments

Additional abutment types can be considered, namely:

• Bankseats
• Reinforced earth abutments
• Integral abutments

Closed abutments have a fully visible superstructure in such a way the complete structure of the abutment, apart its foundation, is apparent. They integrate a front wall, wing walls and a seating beam for bridge deck bearings.

If the topography allows, or if the end spans of the superstructure are sufficiently extended against the slopes, it is possible to avoid the front wall (at least one part of it) and reduce the wing walls to small lateral retaining walls connected to the seating beam. This yields an open abutment, also called a skeletal or spill‐through abutment. These are cheaper than closed abutments but an additional cost is involved in extending the deck to allow the adoption of an open abutment. Open abutments have aesthetical advantages and do not induce, in cases of overpasses over highways, the visual impression of having front walls too close to the road platform. Viewed from a certain distance, closed abutments near the road platform induce a tunnel visual impression, which is avoided with open abutments (as shown in Figure 4.132 later). Natural slopes of the soil are retained in open abutment cases.

Wing walls in closed abutments can be parallel or inclined with respect to the bridge axis, as shown in Figure 4.129. Inclined wing walls have generally a better appearance but their geometry is very much dependent on topographic and geotechnical conditions, since they need to retain the soil at the backfill. The longitudinal horizontal free length of the wing wall (Figure 4.129) is generally limited to 5 m. The lateral soil pressure at rest conditions should be considered when designing this lateral cantilever wall.

Front and wing walls may have counterforts if needed, depending on the height of the abutment. If the height of the abutment is higher than approximately 7 m it may be economic to adopt counterforts at 3–5 m distances (Figure 4.130) in such a way to take the soil pressure by wall resistance as a slab working mainly in the transverse direction, as will be discussed in Chapter 7. If the counterforts are in the front wall, they are the main resistant elements to longitudinal horizontal forces at the abutment, namely soil pressures and seismic longitudinal forces in the case of a deck fixed at the abutment.

A transition slab as shown in Figure 4.130 makes the transition between the abutment and the earthfill. It reduces effects of differential settlements between soil at the backfill and the rigid superstructure of the abutment. Transition slabs have thicknesses usually of 0.25 or 0.30 m and should have sufficient steel reinforcement (min Ф12 every 0.10–0.20 m) in two layers (upper and lower faces) avoiding excessive crack widths due to differential settlements of the soil under impact of traffic loading. The transition slab should be articulated to the abutment in order to accommodate rotations due to settlement of the soil at the backfill (Figure 4.130).

Abutments should integrate the drainage system at the backfill, which is presently made in most cases by a scheme as shown in Figure 4.131, including a lateral discharge as indicated.

The earthfill at the abutment shall respect the minimum distances shown in Figure 4.132. In some cases, it may be justified to reduce the abutment to a simple bankseat. The superstructure of the abutment is reduced to the seating beam supported directly by a footing or by pile foundation as in Figure 4.133.

Reinforced earth abutments integrate reinforcement earth walls, replacing RC wing walls or (and) front walls. Earth walls are made of precasted concrete panels and steel reinforcement bars inside the earthfill. A back seat is adopted integrated with the reinforcement earth abutment.

Integral abutments are a possible option for shorter bridges, say in the order of 60 m at a maximum, avoiding any expansion joint and bearings between the superstructure and the abutments. The superstructure is monolithic with the abutment, reducing problems of maintenance of expansion joints. In an integral abutment, the structure moves against or away from the backfill depending on induced movements due to temperature. Reference is made here to specific literature [39] on bridges with integral abutments, a subject of many investigations in recent years.

4.7.4.1 Foundation Typology

Bridge foundations follow typologies and design rules of structural foundations in most cases. For this reason, the reader is referred to references on foundation engineering [47]. Only specific aspects are dealt with in the present chapter. The main bridge foundation types are:

• Direct foundations by footings
• Indirect foundations by piles
• Special foundations

The last case includes foundations by digging shafts, pile walls, micropiles, jet grouting and caissons. Another aspect specific to bridge foundations is how to execute foundations in rivers, a subject discussed here.

A direct foundation is a shallow foundation where load is transferred at a depth h_f by direct soil pressures at the underneath of a footing with a base dimension characterized by a typical dimension, b. What differs from an indirect foundation made by piles, with a cross section dimension b (diameter in a circular pile), is the ratio, h_f/b. One has, in general, h_f/b < 5 for shallow foundations and h_f/b > 10 for deep foundations. Sometimes, one has direct foundations quite deep as represented in Figure 2.2. In pile foundations, the load is transferred at bearing pressures at the base, but also to some extent by friction along the length of the pile.

4.7.4.2 Direct Foundations

Direct foundations of bridge piers are made by footings at a depth h_f at least 1.5–2 m in order to avoid any erosion effects of the soil above the footing due to expansion effects of soil or erosion due to superficial waters. After execution of the footing, refilling, as shown in scheme of Figure 4.134, is done. The inclination i of excavation is a function of soil type and excavation method. Distance a may be reduced to zero if lateral formwork is avoided, mainly for hard/compact soils. The best choice, if possible, is always to cast the footing against the soil.

The height h of bridge footings is at least 0.70 m and may reach more than 3.0 m in very large footings. Minimum footing height h is established as a function of the horizontal length c of the free cantilever measured from the pier shaft. A rigid footing (say, h > 0.4c) is usually the best choice allowing assumption of a linear distribution of bearing pressures on soil. The upper surface of the footing may be tapered, in large footings, as shown in Figure 4.134, but care should be taken to avoid the need for an upper formwork for concreting the footing. In general, slopes up to 10% are acceptable without upper formwork.

Design of bridge footings are made for soil resistance at ULS and deformability at SLS. Differential settlements between pier bridge footings needed to be evaluated and considered in design of the superstructure.

4.7.4.3 Pile Foundations

Bridge piles are the most current type of deep foundations, made by driven piles in steel (I, H, circular tubular sections) or precasted concrete small diameter piles and cast in situ concrete piles. The latter have diameters in the range 0.6–3.0 m.

Risk of corrosion in driven steel piles in rivers, for example, is ruled out, apart from the pile length above the water table. Thickness of tubular piles is established taking into consideration long‐term corrosion effects, which is done by adopting an over thickness of some millimetres. The upper part of the steel tube above the water level needs to have adequate corrosion protection.

Cast in place piles may be executed with a recovered or lost steel tube. In piers in rivers, the steel tube is generally left in the pile to guarantee quality of execution. If soil permits, cast in place piles are executed with bentonite if that is allowed by environmental protection and bridge site constraints. Piles should penetrate the bed‐rock between 0.5–2 diameters, in general, for load diffusion at the end sections. If required, a trepan is adopted to excavate the bed‐rock. An execution scheme for concrete cast in situ piles is shown in Figure 4.135.

Distance between pile axis is at least 2.5 diameters to avoid pile interaction effects at the foundation. This distance is generally what defines the in‐plan dimensions of the pile cap, as shown in the example of Figure 4.136 for piles of 2 m diameter. The height of the pile cap (between 1.0 and 3.0 m in general) should be in the order of 1.5–2Ф, where Ф is the pile diameter. In large diameter piles, with 2–3 m diameter, the pile cap depth can be reduced to a minimum of 1.0–1.5 pile diameter. A rigid pile cap allows designing based on a linear distribution of pile forces due to axial load and longitudinal and transverse bending moments at the base of the pier shaft.

4.7.4.4 Special Bridge Foundations

Special foundations in bridges with caisson shafts are not so common nowadays. They are similar to large diameter cast in place piers, executed by excavation and adopting an external and internal formwork to make a RC tube that is filled up with concrete. The depth reached is moderate but allows to reach a soil layer with sufficient load capacity.

Pile walls are rectangular foundation elements in cast in place RC, executed by a similar technology of cast in place piles made with bentonite. They may be associated to yield T or U sections presenting a high bearing capacity.

Micropiles have been adopted in some cases, sometimes when standard pile diameters are not easily available at the bridge site or adopted as a technique for improvement of existing bridge foundations. Micropiles have been adopted as standard equipment for bore holes in soil site investigations, for perforating small diameter holes. Steel tubes in the order of 150 or 200 mm, with a 5–10 mm thickness, are adopted as structural elements for the foundations. Steel reinforcement bars are installed at the inside of the tubes and afterwards the tubes are injected with cement grout. Micropiles reach load capacities in the order of 500–1000 kN, depending on the tube diameter and thickness as well as the soil proprieties. One of the advantages of micropiles is the capacity to resist to tensile forces, which for some accidental load cases may be considered.

Jet grouting is a soil improvement reinforcement technique done by adopting high pressure water to disaggregate the soil, then cement grout injections are made. A bridge foundation example using this technique is shown in Figure 4.137.

Finally, in the case of caissons, a foundation type adopted only for large foundations in water, usually of long span bridges like cable‐stayed and suspension bridges. A caisson is a RC prefabricated structure that is driven to a certain depth according to the scheme shown in Figure 4.138. Caissons are driven by a technique called ‘havage’: progressively excavating the soil at the inside. Soil may be excavated in the open air or by using pressurized air allowing excavation below the water level. Working health requirements limit this technique usually to depths of 25 m, which, even so, requires air pressures of 2.5 atm (0.25 MPa). The reader is referred to specific literature for further information [48] on this type of foundation.

4.7.4.5 Bridge Pier Foundations in Rivers

The main issues for pier foundations in rivers are:

• Foundation levels and scour effects
• Cofferdams for pile foundations in rivers
• Protection against scour effects

The level of a direct foundation of a pier in a river can only be established after a hydraulic study is performed determining the design level against scour effects (Figure 2.4), discussed in Chapter 2. The main approaches to determine the referred maximum scour level are discussed in specialized bridge hydraulic manuals [49, 50]. In Figure 4.139, a scheme is shown for the direct foundation in a river after the maximum scour level has been determined.

Execution of pier foundation in rivers generally requires a cofferdam execution, by driving sheet piles to allow to work inside and below water levels. A cofferdam is shown in Figure 4.140, where the bracing system to withstand water pressures may be observed. At the bottom of the cofferdam, a solid RC sealing slab to resist water pressures from the underneath is required. Self‐weight of this slab should be sufficient, with a certain safety factor, to withstand upwards water pressures to the underside. Conditions for erecting the steel reinforcement of the pile cap at the inside of the cofferdam do exist. Hence, the pile cap is cast at the end.

For executing piles in rivers, if distance to the riverside is not too large, the simplest scheme is to make a land reclamation, an artificial peninsula, usually using sand, and to do the piles from the top of it. If this possibility does not exist, the cofferdam should be driven directly to the riverbed.

After execution of the pile caps, riverbed protection is very often required to avoid local scour around the foundations. Rock materials with a variety of diameters, the upper ones with sufficient weight to resist water flow hydrodynamic forces, are adopted. This is again a bridge hydraulics problem and reference is made to particular literature. In Figure 4.141, an example is shown of the geometry and specification of a foundation protection of a bridge pier in a river.