TEMPERATURE 1 General

A detailed investigation of the temperature effects is necessary during both the erection and the final stages. Provisions are described in EN1991-1-5 (see Section 6 of the code) [4.3], but additional guidelines may be found in the National Annex. Figure 4.23 demonstrates the division of a “real” temperature profile [∆TREAL] into four independent components. The first component [∆TN] is uniformly distributed along the height of the cross section causing longi- tudinal deformations. Components [∆TMY] and [∆TMZ] result in rotations around the strong and the weak axis, respectively. One can see a fourth component [∆TE], which represents the nonlinear part of the temperature’s profile. This distribution may cause out-of-plane deforma- tions, which may be critical in certain types of bridges such as box girder bridges.

The real distribution is nonlinear and obviously time dependent. Therefore, [∆TREAL] is described by a combination of the previously mentioned temperature components together with the enhancement factors ω(t). The magnitude of these factors is mainly dependent on the

• Geometry of the cross section • Time of the day and the season

• Thermal conductivity and the density of the materials • Orientation of the bridge

• Thickness and color of the surfacing • Variation of air temperature

• Wind speed • Humidity

From the preceding text, it can be concluded that none of the components can be considered as more important than the others. The consideration of [∆TN] and [∆TMY] can be described for the majority of the plate-girder bridges as adequate. The first component leads to lon- gitudinal deformations ∆u, which are associated with forces and shear drifts in bearings

Centroidal axis [ΔTREAL] [ΔTREAL] = ωN(t) [ΔTN] + ωMY(t) [ΔTMY] + ωMZ(t) [ΔTMZ] + ωE(t) [ΔTE] [ΔTN] [ΔTMY] [ΔTMZ] [ΔTE] x, u z, w y, v ωN(t), ωMY(t), ωMZ(t), ωE(t): time-dependent factors

(see Figure 4.24). When the temperature varies linearly over the cross section, additional deflections ∆w and bearings’ rotations ∆φ should be taken into account.

In cases of bridges with flexible deck slabs, for example, footbridges, bending of the bridge due to [∆TMZ] along the weak axis may occur; ∆v ≠ 0. Nonlinear temperature varia- tions produce self-equilibrating stresses, which are also known as eigen- or residual stresses. This is because any fiber, being attached to other fibers, cannot perform free temperature expansion. More information about the consideration of nonlinear temperature effects is given in Section 4.7.5.

Both for global analysis and stress estimations, the coefficient for thermal expansion αT is needed. For the composite sections, a value equal to 10−5_{/°C both for concrete and for steel} can be used. For steel cross sections during the erection stage, an increased thermal expan- sion factor equal to 1.2 × 10−5_{/°C must be applied.}

When the deformations and rotations due to temperature are restrained, additional inter- nal forces are developed (also see Section 4.7.5). This is always the case in indeterminate systems such as continuous, frame, or integral bridges. Stresses that are caused by these forces are also known as continuity stresses.

The main provisions given in EN 1991-1-5 are presented in the following paragraphs. A discussion about the effects of temperature during the erection phase can be found in Section 4.7.6.

4.7.2 Uniform temperature component _∆TN

∆TN expresses a global increase or decrease in temperature of the structure due to the corre- sponding temperature changes in the environment. If the minimum and maximum shade air temperatures are Tmin and Tmax, respectively the corresponding minimum and maximum tem- peratures of the bridge are Te,min and Te,max respectively. The former are nationally determined parameters provided in the National Annex of EN 1991-1-5. For group 2 decks (composite decks), the bridge temperatures are approximately 5°C above the air temperatures. The initial temperature T0 is the temperature at which the structure is finished or when the bearings are placed. If unknown, it may be taken as the mean temperature during the construction period with a recommended value of T0 = 10°C.

The characteristic value of the maximum contraction range is given by

DTN con, = -T T0 e,m in (4.16)

The characteristic value of the maximum expansion range is given by

DTN,exp=Te,m ax-T0 (4.17)

Due to [ΔTN]

Due to [ΔTMZ] Due to [ΔTE] _{Residual stresses}

∫σx dA=0 ∫σx z dA=0 Due to [ΔTMY] Δu Δw Δ Δγ Δv

For the design of bearings and expansion joints, it is recommended to increase the aforemen- tioned values by 20°C in general or by 10°C if the temperatures at which the bearings or joints are set and specified. For example, for values Te,min = −15°C, Te,max = +45°C, and T0 = 10°C, it is

DTN con, =10- -( )15 25= ∞C and DTN,exp= + -45 10 35= ∞C

For bearings and expansion joints with unspecified temperatures at placement, the corre- sponding values are

DTN con, =25 20 45+ = ∞C and DTN,exp= + +35 20 55= ∞C

Unfavorable effects due to the aforementioned temperature differences may obviously arise in cases of longitudinal restraints during both the erection and the final stages. An expansion tem- perature of 35°C may result in excessive compression forces causing buckling phenomena, lat- eral deformations, local failures, etc. Due to creep, the magnitude of these forces is considerably reduced in concrete bridges or filler beam decks. Unfortunately, this relief does not take place in steel and composite bridges. Therefore, greater attention must be paid.

4.7.3 Temperature difference component _∆TM

This expresses the fact that not all parts of the bridge change temperature at the same rate. It includes a linear varying temperature component along the vertical axis, a linear varying temperature component along the horizontal axis, and a nonlinear temperature component that produces self-equilibrating stresses. Out of the three, the first component only, denoted as Approach 1 in EN1991-1-5 [4.3], is usually considered in bridge design. According to Approach 1, ∆TM is a temperature difference between the top and the bottom of the bridge deck. Two values are considered, ∆TM,heat when the top is warmer than the bottom and

∆TM,cool when the bottom is warmer than the top.

The recommended values for composite decks with a surfacing of 50 mm are

DTM heat, = ∞15C and DTM cool, = ∞18 C

For different depths of surfacing, the aforementioned values should be multiplied with the fac- tor ksur of Table 4.14. These values represent upper bound values for surfacing of dark color.

Table 4.14 ksur values according to EN 1991-1-5

Temperature Unsurfaced proofedWater 50 mm 100 mm 150 mm 750 mmBallast Ttop > Tbottom

Tbottom

0.9 1.1 1.0 1.0 1.0 0.8

Tbottom > Ttop

Ttop 1.0 0.9 1.0 1.0 1.0 1.2

Source: EN 1991-1-5: Eurocode 1: Actions on structures—Part 1–5: General actions—Thermal actions, 2003.

4.7.4 Combination between _∆ΤΝ and _∆TM

In some cases (e.g., in integral or frame bridges), the temperature effects ∆TN and ∆TM should be combined and regarded as single actions. The relevant combination rule is

DTM heat, (or TD M cool, )+wN◊DTN,exp(or TD N con, ) (4.18a) or

wM ◊DTM heat, (or TD M cool, )+DTN,exp(or TD N con, ) (4.18b) The aforementioned are considered as a single action, and the most adverse effect should be chosen. The recommended values for the combination factors are ωN = 0.35 and ωM = 0.75.

The temperature combinations (4.18) are highly consistent with the ω(t) factors shown in Figure 4.23. For reasons of simplicity, the code avoids time-dependent factors by offering the earlier combinations. In (4.18a), the linear temperature component [∆TM] is the dominant one. In contrast, (4.18b) covers the case of a dominant uniform distribu- tion [∆TN].

4.7.5 Nonuniform temperature component _∆TE

Nonlinear temperature variations may be in certain cases much more critical than the linear ones. As already mentioned, residual stresses are developed and can accelerate cracking and yielding procedures. In compressed areas, these stresses may also play a negative role and increase the buckling risk. For compact cross sections (classes 1 and 2), nonlinear variations can be neglected. For noncompact cross sections, a more detailed analysis with [∆TE] may be necessary. EN 1991-1-5 suggests that nonlinear temperature variations should be considered without any reference to cross sections, materials, or structural systems.

In Figure 4.25, one can find the temperature differences over composite cross sections with a surfacing of 100 mm. EN 1991-1-5 offers two kinds of procedures: the normal and the simplified one. For different depths of surfacing, recommended values for ∆T1 and ∆T2 are given in Annex B of EN 1991-1-5.

It must be pointed out that [∆T] incorporates [∆TM] and [∆TE] together with a small part of [∆TN]. When designers wish to consider all the temperature components and include nonlinear effects, then in combinations (4.18a) and (4.18b), [∆TM] should be replaced by [∆T].

Generally, the computation of the residual stresses and the corresponding internal forces due to nonlinear effects is laborious. Interesting information on this issue is also given in [4.7] and [4.10].

4.7.6 Temperature effects during erection

Steel cross sections in bridges consist of thin plates, which may easily deform due to thermal effects, thus leading to erection difficulties. Figure 4.26 shows the erection procedure of a composite bridge with an open box steel cross section over a river bank.

The solar radiation on one side of the steel girder leads to lateral deformations v. Usually, segment A is equipped with thicker plates than those of segment B. Therefore, the relative lateral displacements between A and B may cause considerable assembly problems.

Additional difficulties will arise due to different temperatures between the webs (TN1 > TN2). This results in an out-of-plane deformation of the cross section whose unfavorable effects may only be discovered on site.

100 mm

100 mm

Cross sections Temperature distribution Normal procedure

Simplified procedure

(a) Heating (b) Cooling

(a) Heating (b) Cooling h h h h (m) 4 0.2 0.3 1316 4 h h1 h1 h1 = 0.6 h h2 = 0.4 m h2 h2 ΔT2 ΔT2 (°C) ΔT2 ΔT1 ΔT1 −ΔT1 ΔT1 = 10°C ΔT1 (°C) h (m) −8 0.2 0.3 −3.5−5 −8 ΔT2 (°C) ΔT1 (°C) ΔT1 h h 100 mm h

Figure 4.25 Temperature variations for composite bridge decks. (From EN 1991-1-5: Eurocode 1: Actions

on structures—Part 1–5: General actions—Thermal actions, 2003.)

Segment B v A B T1> T2 TN1> TN2 TN2 u1> u2 u2 T2 Segment A

Experienced designers are aware of the “tricky” situations that may emerge due to tem- perature effects. Unfortunately, the codes do not provide the necessary guidelines, and assumptions are unavoidable. Explicit calculations with sophisticated FE-structural models are usually used, and the following parameters are considered:

• Different temperature variations.

• The torsional flexibility of the girders. A 2nd-order theory analysis is recommended. • Additional temperature effects due to welding procedures.

• Changes of the structural system during construction. • Fabrication tolerances according to EN1990 [4.1].

4.8 WIND