Gumbel chart
3 SNOW LOADS
4.1 Temperature changes on bridges
The temperature changes on bridges are given in terms of uniform temperature component, vertical difference component, which includes non linear component also, and, when relevant, a horizontal difference component, which can be assumed linearly varying.
The temperatures in the bridge depend not only by the shade air temperature and solar radiation, but also on the scheme, on the cross section, on the mass and on the material.
Therefore, bridges can be classified in terms of categories and subcategories as follows:
1. Steel bridge: steel box girder
steel truss or plate girder;
2. Composite bridge
3. Concrete bridge: concrete slab concrete beam concrete box girder.
4.1.1 Uniform temperature component
The uniform temperature component depends on the maximum and minimum temperature, Te,max and Te,min, that the bridge can attain during its working life.
Once determined the maximum and minimum shade air temperatures of the site characterized by 50 years return period, Tmax and Tmin, the uniform temperature components Te,max and Te,min can be determined according to the diagrams of figure 6, where Te,max and Te,min, in °C, are expressed in terms of Tmax and Tmin, in °C, for each bridge category recalled before. Values of Te,max values for truss or plated steel bridges (category 1) can be reduced by 3 °C.
-50 -40 -30 -20 -10 0 10 20 30 40 50
-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70
1
2 3
3 2 1
Tmin Tmax
Te,min Te,max
Figure 6. Correlation between shade air temperature (Tmin, Tmax) and uniform components of the bridge temperature (Te,min, Te,max)
If T0 is the initial bridge temperature, i.e. the temperature of the bridge at the time when it is restrained, the variation of the uniform bridge temperature ∆Tu is given by
con N esp N e
e
u T T T T
T = ,max- ,min =∆ , +∆ ,
∆ , (14)
where
∆TN,exp=Te,max-T0 and ∆TN,con=T0-Te,min (15)
are the temperature variations to be considered when the bridge expands or contracts, respectively.
Assessing bearing displacements it can be assumed ∆TN,exp=Te,max-T0+20°C and
∆TN,con=T0-Te,min+20°C.
4.1.2 Vertical temperature varying component
In consequence of the different heating and cooling of the top and bottom surfaces of the bridge, vertical temperature variations can occur. These variations correspond to maximum heating, when the top surface is warmer than bottom surface, and maximum cooling, when the bottom surface is warmer than the top surface.
The vertical temperature profiles can be defined under two different hypothesis, according as non-linear temperature profile ∆TE is disregarded or not: in the former case a simplified equivalent linear profile can be considered, while in the latter one a non linear profile, including ∆TE, is taken into account.
Equivalent linear vertical temperature profile
When equivalent linear vertical temperature profile is adopted, the maximum temperature differences corresponding to maximum heating or maximum cooling, denoted as
∆TM,heat and ∆TM,cool, for the different bridge categories can be deduced by table 3.
The values given in table 3 represent upper bound values of the temperature differences for road and railways bridges carrying a 50 mm surfacing. For different thickness of the surfacing, values of table 3 should be multiplied by the adjustment factors ksur given in table 4.
Table 3. Equivalent linear vertical temperature variations for bridges Type of deck Top warmer than
Table 4. Adjustment factors ksur for road, foot and railway bridges
Surface thickness
Non linear vertical temperature profiles
When more refined analyses are necessary, the vertical temperature profile can be assumed as non linear, considering in the heating and cooling conditions the temperature profiles given in tables 5, 6 and 7 for steel bridges, concrete bridges and composite bridges, respectively.
For composite bridges two alternative profiles, normal and simplified, are given in tables 7.a and 7.b. The simplified profile is generally safe-sided.
The temperature differences ∆T given in tables 5 to 7 include both the vertical temperature component ∆TM and the non linear temperature component ∆TE, together with a little part of uniform component ∆TN, just considered in the uniform temperature component
∆TN, given in §4.1.1.
The temperatures for other surfacing depths of bridge decks of type 1 to 3 are given in Tables B.1 to B.3 of EN 1991-1-5, Annex B.
4.1.3 Horizontal temperature varying component
Horizontal temperature differences in bridges can be generally disregarded, except in special cases, for example when one side of the bridge is much more exposed to the sunlight of the other one.
When horizontal component must be taken into account, a linear variation of 5 °C can be assumed.
Table 5. Non linear vertical temperature differences for steel bridges
Type of construction Temperature difference (∆T)
Heating Cooling
h
Steel deck with 40 mm surfacing
0.1 m0.2 m
0.3 m
24 °C 14 °C 8 °C 4 °C
h
-6 °C
0.5 m h
h
Steel deck on truss or plate girder with 40 mm surfacing
21 °C
0.5 m h
-5 °C
0.1 m h
Table 6. Non linear vertical temperature differences for concrete bridges
Type of construction Temperature difference (∆T)
Heating Cooling
h
100 mm surfacing
Concrete slab 100 mm surfacing
h
Concrete beam
h
100 mm surfacing
Concrete box girder
Table 7.a. Non linear vertical temperature differences for composite bridges, normal profile
Type of construction Temperature difference (∆T)
Heating Cooling
h
100 mm surfacing
Concrete deck on box, truss or plate girder
Table 7.b. Non linear vertical temperature differences for composite bridges, simplified profile
Type of construction Temperature difference (∆T)
Heating Cooling
h
100 mm surfacing
Concrete deck on box, truss or plate girder
On the contrary, special attention should be paid for concrete multicell box girder where temperature of the inner webs can differ significantly (around 15°C) from the temperature of the outer ones.
5. CONCLUSIONS
Effects of variable climatic actions, wind, snow and temperature given in Eurocodes EN 1991-1-x have been illustrated, with special emphasis on their application on bridges, discussing peculiarities, application rules and possible simplification of the relevant load models.
Wind specifications are applicable only to girder bridges spanning up to 200 m with a constant cross section and one or more spans, but they can be extended variable cross sections, to double deck bridges as well as to other bridge types, provided that wind-structure interactions are not relevant.
Bridge types which are sensitive to wind-structure interactions, like lower or intermediate deck arch bridges or suspended and cable stayed bridges, call for specific studies, duly supported by wind tunnel tests.
Simultaneity of snow loads with traffic actions is generally not significant, except in very particular cases, as roofed bridge, and can be disregarded.
Air shade temperature variations and solar radiation result in temperature fields in the bridge, depending on the bridge location and on the structural material. These temperature fields are typically non linear and have been described in detail, but often it is possible to refer to simplified and safe-sided linear distributions.
Seismic actions have been not considered here, as their illustration is beyond the scope of the present Guidebook.
6. REFERENCES
[1] EN1991-1-4, Eurocode 1: Actions on structures - Part 1-4: General actions – Wind actions. Brussels: CEN, 2005
[2] Holicky, M et al., GB1: Basis of design and actions on structures, Leonardo Project number: CZ/08/LLP-LdV/TOI/134020, Prague, CTU, 2010
[3] EN1991-1-3, Eurocode 1: Actions on structures - Part 1-3: General actions – Snow loads. Brussels: CEN, 2004
[4] EN1991-1-5, Eurocode 1: Actions on structures - Part 1-5: General actions – Thermal actions. Brussels: CEN, 2004
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