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Flying over Germany's highest mountain

At 2962 metres, Zugspitze is Germany's highest mountain and highest ski resort. There, you can enjoy powdery ski slopes in the winter and hiking trails in the summer. To transport visitors to the summit, a new cable car was installed. Its construction involved HD profiles supplied by ArcelorMittal Europe – Long Products and ArcelorMittal Downstream Solutions in Neckarsulm.

The world's highest structural support for aerial tramways

After three years of planning and construction, Zugspitze’s new cable car started its ascent last winter. For this unique project, our colleagues at ArcelorMittal Europe – Long Products, together with ArcelorMittal Downstream Solutions, delivered HD profiles in steel grade S355 J2, which were used to build the structure of the cable car. The beams were produced in ArcelorMittal’s Differdange mill in Luxembourg, where they were cut to length, and the team at ArcelorMittal Downstream Solutions in Neckarsulm sold the final products to the customer.

Zugspitze's cable car holds three world records:

1. First, the particularity of this cable car is that instead of using two supports, it only has one support measuring 127 metres high making it the tallest tramway support in the world.
2. Then, the distance between the support and the mountain summit station is 3213 metres.
3. Finally, another unique feature is the height difference of 1945 metres between the valley station and the mountain summit station.

A new era

The modern cable car is a strong investment marking the beginning of a new era for the Zugspitze mountain.The 50-million-euro project has been providing visitors with maximum comfort and giving tourism a boost throughout the region.

So far, around half a million visitors are transported annually, but the historic Eibsee cable car from 1963 reached the limits of its transport capacity on peak days. The new cable car should attract about 10 percent more passengers, which means an increase for the entire, predominantly touristy, region.

The two new cabins with a sparkling new and elegant design can carry up to 120 passengers each with the floor-to-ceiling glazed open-plan cabins offering grandiose panoramic views of Germany's highest peak. They now guides alpinists, summer hikers, winter sports enthusiasts, and tourists from all over the world to the mountain top.

Text: ArcelorMittal Europe Communications
    
Photos: ©Victor Maschek / Shutterstock.com  ©Trey Waggener / Shutterstock.com

In this technical article, Gian Carlo Giuliani, structural engineer at Redesco, presents the main theory on the fire resistance calculations for structures through the presentation of a case study: the steel structure of a commercial center in Cyprus.

1. Fire Safety Assessment of Structures: General Approach

A structure subjected to fire must be safe for the time necessary for the escape of the people and for the safe operation of the rescue and fire brigade; the verification is based on the fulfilment of the following conditions for the evacuation time and the safe operation of the fire brigade:

• R structural resistance
• E structure and pavement smoke tightness
• I isolation or limit of the temperature of the floor above the fire

These conditions are verified taking into account the temperature versus time evolution by means of:

-  for the R condition: a step by step analysis of the temperature in the ambient and in the structural elements, followed by the verification of the load bearing capacity resulting from the reduction of the material mechanical parameters.
- a verification of the existence of a structure capable of satisfying the E and I conditions
 
The assessing of the structure is related to the actual use of the building and to the relevant amount of possibly combustible materials; therefore the calculations are based on the temperature development induced by a real fire in a closed space, which is bound by the floor, the ceiling and the edge partitions and connected to the open air through the side openings.

The standard fires, recommended by codes for the structural design or by the national laws, show a continuous increase of temperature which, because of the correspondent reduction of the strength of the materials, limits the time of the load bearing capacity of the structure.

On the contrary, the real fires can evolve from the amount of possibly burning material and from the oxygen available in the space or drawn in through the side openings and therefore always have a decay phase.

2. Shopping Malls & Fire Safety: Special Requirements

In many cases, recent shopping malls are based on large column grid lines and are developed over two or three stories; a steel-concrete composite structure is a very efficient solution for the floors.

Because of the appealing contrast between the elegant exhibited goods and the high technical aspect of the in sight structure, the application of any passive fire protection spoils the architectural results and only sprinkler system are accepted.

Therefore the “naked” structure fire resistance has to be assessed for the real operating conditions.

In the annexe A of the Eurocode 1, the temperature evolution developed by the natural fire is defined as depending on the fuel amount and on the ventilation conditions given by the compartment geometry, the boundary thermal characteristics and the openings...

Other parameters, defined in the annex E of the Eurocode 1, are related to the danger of fire activation as per the table E1 and to the function of active fire fighting measures, as per the table E2.

3. A Case Study

The fire resistance assessment is developed for the composite steel-concrete floor of a building which is composed of main beams continuous over 8.00 m spans and of secondary ones also continuous over 16.00 m spans.

The design value of the fire load qf,d is defined as: qf,d = qf,k m δq1  δq2 δn (MJ/m2)

where m = 0.80 is the combustion factor of the material

δq1 = is a factor taking into account the fire activation risk due to the size of the compartment
δq2 = is a factor taking into account the fire activation risk due to the type of occupancy
δn = Πδni = 0.237 is a factor taking into account the different active fire fighting measures (sprinkler, detection, automatic alarm transmission, firemen). These active measures are generally imposed for life safety reason.

qf,k  (MJ/m2) is the characteristic fire load density per unit floor area

The temperature raising depends on the kind of the fire which can occur:

- the general fire which is controlled by the ventilation
- the local fire which is controlled by the fuel amount

each one of the above said conditions yields a completely different result.

The temperature evaluation was performed for two basic fire conditions:

• local fire in a department store bounded by wood shelves; this condition yields a fire development governed by the fuel and is more stringent than the following one;
• general fire in the total floor surface bounded by masonry walls with few openings; this condition occurs as a consequence of the local fire and yields a fire development governed by the ventilation.

For the examined case history, according to the site and the building features, the following parameters were used for the calculations taken from tables E1 and E2 of EC1.

δq1 = 1,60 is a factor taking into account the fire activation risk due to the size of the compartment
δq2 = 1,00 is a factor taking into account the fire activation risk due to the type of occupancy
δn1 = 0,61 automatic water extinguishing system
δn2 = 0,87 independent water supplies
δn3 = 1,00 automatic fire detection & alarm – by heat
δn4 = 0,73 automatic fire detection & alarm – by smoke
δn5 = 0,87 automatic alarm transmission to fire brigade
δn6 = 1,00 on site fire brigade
δn7 = 0,78 off site fire brigade
δn8 = 0,90 safe access routes
δn9 = 1,00 fire fighting devices
δn10 =1,00 smoke exhaust system

Because of the above said parameters the fire can be by fuel or by ventilation controlled; the growth rate of the fire was selected as fast (tlim=15 minutes) in all the calculations.

The strategy adopted for the fire resistance assessment was based on the calculation of the maximum amount of possibly burning material which can be stored in the compartment having the internal height h=4.50 m ; the goods on show are mainly composed of cellulosic clothes and tissues having a specific calorific value Hu=20.00 MJ/kg (the same parameter for the wood is 17.5) and a combustion factor m=0.80.

Two different scenarios were used for the fires controlled by the fuel amount or by the ventilation; the growing rate of the fire was selected as fast with the corresponding limit time tlim=0.25 hours.

The relevant parameters are indicated in the following table:


(*) qtd (MJ/m2)=qfdAf/At
(**) tmax=max(0.0002qtd; tlim)

In general the fire governed by the ventilation lasts for hours but with temperatures below the steel critical ones.

An interesting remark is given for the above said condition:

- the amount of air necessary for burning one kg of cellulosic material with the relevant calorific value of Hu=20MJ/kg is Aa=0,312Hu+0.65=6.89 kg/kg
- being ρ =1.225 kg/m3 the specific mass of the air, the specific air volume which is necessary for burning the material is Va=5.62 m3/kg
- given the compartment volume V=23040 m3, the total mass M of the material which can burn by using the inside air is therefore given by M=V/Va=4100 kg, which corresponds to an average distribution of M/AF=0.8 kg/m2 <f.

The evolution of the temperatures developed by the natural fire is defined by the following function as per the annex A of the Euro code 1; a decay branch of the temperature curve is taken into account because the temperature increasing of the steel is shifted in time and the maximum value appears during the ambient cooling phase.

The gas temperature versus time is therefore given by the function:

with t expressed in hours.

4. Loading condition and material mechanical properties concurrent to the fire

• the fire was considered as an exceptional loading condition.
• the fire, originated in the floors, was considered as a local hazard.
• the material resistance safety factors were reduced accordingly to the temperature (figure 6)
• the loading safety factors were reduced also gg =1.0, gq=1.0 and the design live load q was reduced by a participation factor ψq =0.7 related to the use of the area.
  
  Figure 6: Scheme of the moment redistribution for an edge bay of the continuous beam
  

5. Structural Analysis Procedure

A step by step versus time procedure for both the cases was used for calculating the temperatures of the fire and of the materials, for determining the correspondent resistance.

- set time to 0s
- increment time 5s
- calculate the temperature of the standard fire versus time
- calculate the correspondent temperature of the steel according to the mass / exposed surface ratio of the beams and of the material and fire parameters
- calculate the resistance of the steel and of the concrete correspondent to the temperature
- for the mid span and the support sections calculate the ultimate resistance according to the schemes here under:

 - perform an elastic-plastic structural analysis taking into account the action redistribution between the most exposed sections towards the ones subjected to a lower temperature according to the scheme of figure 6: at the ultimate state, the mid span moment capacity is given by Mus=M1R+M2R/2 and the maximum resisted load is qu=8Mus/L2
- verify the resistance to the vertical shear at supports and the studs subjected to the horizontal shear
- compare the structure resistance R with the action A of the supported load
- if R>A start a new iteration ; if not, the time resistance is determined, because, due to the exhaustion of its redistribution capability, a part of or the whole structure is transformed into a mechanism.

In the examined case history, because of the limited stiffness of the columns and of the sliding supports at the relevant bases, the axial forces introduced in the beams by the constrai t of the thermal strains were not crucial for the ultimate bending resistance.

6. Calculation of the Steel Temperatures

The calculation of the temperatures takes into account the geometry of the structure:

- the bottom flange of a beam is directly hit by the fire
- the web and the upper flange are in shadow from the flame radiating effect and therefore are subjected to a lower temperature
- the top of the reinforced concrete slab and the relevant reinforcement are subjected to a much lower temperature

The following relations, taken from Eurocode 4, were used for the calculation of the temperature of the structural steel.


where :

kshadow  is a correction factor for the shadow effect
ca         is the specific heat of steel (J/kgK)
ρa         is the density of steel (kg/m3)
Ai         is the exposed surface area of the part i of the steel cross-section per unit length (m2/m)
Ai/Vi    is the section factor (m-1) of the part « i » of the steel cross-section
Θa,t     is the steel temperature at time t (°C) supposed to be uniform in each part of the steel cross-section
Δt         is the time interval (sec)

The shadow effect was determined from:


With e1, b1, ew, hw, e2, b2 and cross sectional dimensions

Because of the different section sizes and of the continuity conditions (see figure 4), the verifications were effected for any single element of the structure; the results for the edge bay of a secondary beam over the 16.00 m span are illustrated in the figures 7 and 8.