BRIDGE DECK DESCRIPTION

2.1 Geometry

The solution adopted is a continuous composite bridge deck carrying three lanes of road traffic, with a constant cross-sectional height of 2,15 m and a total width of 10 m. The deck cross-section comprises an in situ concrete slab 0,25 m deep and two 1,9-m deep welded steel girders, set at a distance of 5,0 m (Figure 1). The bridge has a total length of 103,5 m and three spans: 30,0 +43,5+30,0 m (Figure 2).

0,5 m 0,5 m

0,25 m1,90 m

2,5 m 5,0 m 2,5 m

10,0 m

Figure 1. Composite deck cross-section for a road bridge

30,0 m 43,5 m 30,0 m 103,5 m

Figure 2. Static system

2.2 Material properties

Structural steel:

As per EN 1993-1-1 [3], §3.2:

Steel grade Nominal thickness t [mm]

Yield strength fy [N/mm²]

Modulus of elasticity E_a [kN/mm²]

S355 t ≤ 40 mm 355

S460 40 < t ≤ 80 mm 430 210

Concrete:

As per EN 1992-1-1 [4], §3.1:

Strength class C30

Characteristic cylinder strength fck = 30 N/mm² Secant modulus of elasticity E_cm = 33 kN/mm² Reinforcing steel ¹:

As per EN 1992-1-1 [4], §3.2 and Annex C:

Steel grade B 500

Specified yield strength fsk = 500 N/mm² Modulus of elasticity E_s = 200 kN/mm²

In composite structures, the design value of the modulus of elasticity may be taken to be equal to the value for structural steel: E_s = 210 kN/mm² ([2], §3.2.2).

Stud connectors ²:

Nominal ultimate strength f_u = 450 N/mm²

Diameter φ ^{= 19 mm}

Height h = 125 mm.

1 While in EN 1992-1-1 [4] the yield strength of reinforcing steel is symbolized as fyk,, in EN 1994-1-1 [5] it is shown fsk to distinguish it from structural steel.

2 In the context of the material recommended for stud connectors, reference is made in [2], §3.4.2.1, to EN-13918.

2.3 Steel plate thickness, stiffeners and diaphragms

According to the distribution of stiffeners and diaphragms and the steel plate thickness set out in Figure 3, referred to the bridge deck surface, a total of 100 kg/m² of structural steel is needed.

600x25 600x60 (S460M)

tw = 15 mm

ST: TRANSVERSE STIFFENER; DI: INTERMEDIATE DIAPHRAGM; DB: BEARING DIAPHRAGM; SL: LONGITUDINAL STIFFENER D_I

Figure 3. Distribution of stiffeners and diaphragms

2.4 Construction

For the purpose of structural analysis, bridge construction is assumed to be divided into the following stages:

- Erection of the steel structure.

- Casting of the in situ concrete in a single lift across the entire length of the bridge without temporary supports.

- Simultaneous application of all dead loads, in particular the vehicle restraint system and the asphalt layer, two weeks after the in situ concrete is poured.

3 ACTIONS

3.1 Introduction

Structural reliability is closely related to the recognition of the actions and effects to which the structure may be exposed during construction and use. The goal is to identify all actions and effects likely to arise. Only then can a solution be found that meets the basic requirements laid down in EN 1990 [6], §2.1. In light of the importance of this step, the actions and action effects that might be relevant to the bridge deck in the example are described below. Only persistent and transient design situations are considered for ultimate limit state verification. In other words, the analysis does not address the effects of either accidental or seismic actions. Loads affecting only one half of the bridge deck are considered, however.

3.2 Permanent actions

Self-weight of steel structure

The self-weight of the steel structure is sustained by the steel structure alone without temporary supports:

1, 0 kN/m 5, 0 m2 5, 0 kN/m

gs = ⋅ =

Self-weight of in situ concrete slab

Like the self-weight of the steel structure, the weight of the in situ concrete is borne by the steel structure alone [7]:

0, 25 m 25, 0 kN/m 5, 0 m3 31, 25 kN/m

gc = ⋅ ⋅ =

Dead loads

The dead loads consist primarily of the vehicle restraint system and the asphalt layer and are borne by the composite structure.

1, 6 kN/m 5, 0 m2 8, 0 kN/m

gdl = ⋅ =

3.2 Creep and shrinkage

Shrinkage

Pursuant to EN 1994-2 [2] §3.1(3) and EN 1992-1-1 [4] §3.1.4 and Annex B, total shrinkage strain has two components, drying and autogenous shrinkage strain. Taking ambient relative humidity to be 70 % and assuming that the concrete is manufactured with The basic drying shrinkage strain, εcd,0, is calculated as:

( )

^{6 6}

The notional height is: ₀ 2 2 2,5

0, 244 m

Drying shrinkage strain develops over time as:

6 6 The autogenus shrinkage strain is:

6 6

( ) 1, 0 50 10 50 10 εca ∞ = ⋅ ⋅ ⁻ = ⋅ ⁻ and the total shrinkage strain at t = ∞ is:

6 6

(303 50) 10 353 10 εcs_∞ = + ⋅ ⁻ = ⋅ ⁻ Creep

Given that all dead loads are applied 15 days after the in situ concrete is poured and that the ambient relative humidity is 70 %, it follows that ([2], §2.3.3 and §3.1; [4], §3.1.4 and Annex B):

where t0 is the age of concrete at first loading in days.

The notional creep coefficient ϕ₀ ^is:

0 1, 48 2, 73 0, 55 2, 22

The final creep coefficient is:

(

,t0

)

0

(

,t0

)

2, 22 0,982 2,18 ϕ ∞ = ⋅ϕ β ∞ = ⋅ =

3.3 Variable actions

Traffic loads.

Further to EN 1991-2 [8], §4.3.2, only Load Model 1 is applied. In this model, used for general verification calculations, both concentrated two-axle tandem loading and uniformly distributed loads are considered.

The carriageway width w is assumed to be equal to the distance between the inner limits of the vehicle restraint system, therefore w=9,0 m. As w>6,0 m, the number of conventional lanes, each of which is w_l=3,0 m wide, is afforded by the relation (Figure 4):

int int 9, 0 3

Since the span length is greater than 10 m, each of the three tandem load systems may be replaced by a one-axle load equal to the total load exerted by the two axles constituting the system [8], §4.3.2 (6).

Uniformly distributed loads: Lane1 q1k = 9,0 kN/m²

other notional lanes q_i,k = 2,5 kN/m²

remaining area q_rk = 2,5 kN/m²

Tandem system Lane 1 Q1k = 300 kN (1 axle of 600 kN) Lane2 Q_2k = 200 kN (1 axle of 400 kN) Lane3 Q3k = 1 00 kN (1 axle of 200 kN) other notional lanes Qik = 0.

Figure 4. Traffic loads on the bridge deck

Due to the absence of specific indications related to the expected traffic, the adjustment factors αQ and αq are assumed to be equal to 1,0.

Temperature

Linear temperature variation from the upper to the lower face of the bridge deck (see

§6.1.4.1 of [9] and §4 of chapter 5):

Top surface warmer (heating) ∆T = +15 ºC (7 ºC/m) Bottom surface warmer (cooling) ∆T = −18 ºC (-8,4 ºC/m)

The same linear thermal expansion coefficient is assumed for the steel and the concrete, namely α ^{= 10·10-6 ºC-1} ([2], §3.1(1) and §5.4.2.5(3); [4], §3.1.3(5)).

The value specified in EN 1991-2 [8], section 5, for uniform thermal variation is disregarded because it is irrelevant to the present study.

Construction loads during the casting of concrete

Pursuant to EN 1991-1-6 [10], §4.11.2, the following construction loads are taken into account simultaneously in the calculations to verify steel structure conformity. These loads are intended to be positioned to cause the maximum effects, which may be symmetrical or not.

- Actual area:

Self-weight of the formwork: q_cc,k = 0,5 kN/m²

Q_3k = 100 kN Q_3k = 100 kN 2,0 m

q_1k = 9,0 kN/m²

q_2,3k = 2,5 kN/m² Q1k = 300 kN Q1k = 300 kN

2,0 m

Q_2k = 200 kN Q_2k = 200 kN

2,0 m

Lane 1 Lane 2 Lane 3

w_l = 3,0 m w_l = 3,0 m w_l = 3,0 m

w = 9,0 m

Weight of the fresh concrete (density 26 kN/m³): q_cf,k=0,25 26=6,5 kN/m² - Outside the working area:

Working personnel with small site equipment: qca,k = 0,75 kN/m² - Inside the working area (3 m×3m):

10 % of the self-weight of fresh in situ concrete, but 0,75 ≤ ^qca,3·3≤ ^{1,5 kN/m2:} q_ca,3·3=0,1 6,5= 0,65 kN/m²<0,75 kN/m²

therefore, in the present case qca,3·3 = 0,75 kN/m².

In document Guidebook-2 Design of Bridges (Page 194-200)