Available in: 3D Structure, 3D Frame


Eurocode offers three design methods of RC beam/column member calculation for fire: "tabulated data", "simple calculation models" and "advanced calculation models".

Due to the facts that the applicability of "tabulated data" is very limited in terms of cross-sections and exposure conditions, and the guidance for the "advanced calculation models" is completely missing from the standard, FEM-Design uses the "simple calculation models" methods - namely the "500°C isotherm" and "Zone" methods - that allows us to run fire design for any cross-sectional shape.

Contents


Concept

Despite the identical thermal actions on different bars, the concept of implementation is quite different from steel and timber bars. In case of the latter ones, the aim of the design process is to find such an insulation for the fire exposed sides, which ensures that the structure fulfills the load-bearing requirements for the necessary duration of fire. For concrete bars, the approach of the standard is to verify at the end of the fire duration that the damaged bar still has enough load-bearing capacity, considering the reduction in the cross-section dimensions and material parameters. Consequently, in contrary with steel and timber bars, where the design element is the insulation, for concrete bars it still remains the reinforcement. 

In order to conform with these considerations, the calculation parameters of bar reinforcement is extended with fire design parameters.  

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Temperature distribution

The core of the design for both steel and concrete bars is to determine the temperature (distribution) in the cross-section and obtain the reduced cross-section and/or material properties based on that. Upon this preliminary process, a “normal” design check can be performed to verify the bar for fire conditions. The thermal actions for temperature analysis are given by the third section of EC 1991-1-2, which describes the net heat flux through convection and radiation on the fire exposed surface(s) of the member (based on the standard fire curves). For steel bars, due to the thinness of the typical sections, constant temperature distribution can be assumed. For the calculation of this (constant) member temperature, EC3 provides an analytical solution. However, this assumption becomes totally false when it comes to the concrete sections. In order to determine the correct temperature distribution in the section, FEM-Design performs a non-linear, transient finite element heat transfer analysis by using explicit time integration scheme.  

The input parameters of the temperature distribution calculation are the highlighted settings parts of Design calculation parameters (RC Design > Bar reinforcement):

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As an explicit solver is used for the numerical calculation, the proper selection of Time step parameter is essential. It affects both the numerical stability of the solver and the accuracy of the solution. Before the solution procedure, FEM-Design calculates the critical time step of the problem (considering the initial room temperature) and chooses the smaller from the critical and requested one to ensure the numerical stability. As the critical time step may change with time, but its calculation would be extremely time consuming before every time step, FEM-Design calculates it at the beginning only. Thus, the divergence of the solution still might happen, in this case the calculation restarts itself with a smaller time step until a limit value is reached (warning message). For the calculation, the program generates the finite element mesh of the cross-section. According to our experience, from engineering point of view a middle density provides adequate accuracy in most of the cases. 

Usually, higher mesh density leads to lower critical Time step, thus the necessary computational time increases exponentially by using denser mesh. 

We can check the applied finite element mesh (and so its density) by displaying it with the Show mesh on section exposure option.

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At the section exposure, three types of boundary condition can be defined on all edges of the arbitrary shaped cross-section: fire, ambient and insulation. 

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For circle cross-sections, instead of defining only one condition, the contour of the section is divided into eight equal parts to define the exposure conditions on them. 

In case of those cross-sections containing holes, the holes are also meshed, and the thermo-mechanical properties of the air assigned to them. The calculation time of the temperature distribution can vary on a wide range, depending on the mesh density, time step and duration of fire. To follow up the process, a breakable progress bar indicates the current status.

Calculation models

For the verification of fire resistance, the member analysis approach of the Eurocode 1992-1-2 is used, combined with the simplified calculation methods: "Zone" and "500°C isotherm" methods.

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  • Both methods are based on temperature distribution. A transient heat transfer module should calculate the actual temperature distribution within the cross section, according to the selected fire duration. It should take into account the temperature dependence of specific heat, density and thermal conductivity.
  • Both methods reduce the cross-section and change the material properties of concrete (and bar steel), and do a "normal" design based on these reduced inputs.
  • For rectangular sections, the more precise and reliable method is the "Zone" method. And, as "Zone" method uses empirical formulas, it can be applied only to rectangular cross-sections.
  • The "500°C isotherm" method can be applied to all cross-sectional shapes.

The "Zone" method, according to the standard is more accurate, especially for columns, although it can be applied only on rectangle shaped cross-sections. In reality, as the temperature can be different in every point of the section, the concrete material model can be also different point by point. This method suggests that to take the coldest point in the section (reference temperature), and to reduce the dimensions of the original section in such a way that this reduced section with a constant concrete material (based on the reference temperature) be equivalent with original section with the variable concrete material. For the calculation of this damaged part, the section is divided into 20 "zones" by using the B.12 formula for beams and B.13 formula for columns (annex B). Based on temperature distribution, the reduced concrete and steel material models are used. The reference temperature for the concrete is the coldest point in the cross-section, used to evaluate the reduction factor(s) for the room temperature properties. The modified version of the standard’s proposed material model is applied, the descending branch is not considered (being on the safe side) in order to avoid numerical instabilities during the nonlinear stress distribution calculation within the cross-section. 

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For the steel bars the reduced material model of the standard is applied (based on the temperature distribution, steel classes and manufacture type) with same modification as for concrete, namely with neglecting of the descending branch.

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In case of concrete, the safety factors for fire are considered in fire design:

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The "500°C isotherm" method is applicable for cross-sections of any shape, its basic idea is to remove those (damaged) parts of the cross-section, which are higher than 500°C, and the rest (so-called reduced section) can be modeled with the original (room temperature) concrete properties (except the design values, which are calculated also with safety factor for fire). Thus, it is very important that the concrete material model is not temperature dependent. For modelling reinforcement bars both methods use the same reduced material model of the standard. 

Upon obtaining the reduced section and reduced material properties with any of these calculation models, the standard recommends applying the same design process as for the original RC bars (according to EN 1992-1-1). In annex B of EN 1992-1-2 the principles of the simplified calculation models are introduced together with a basic example, although it focuses only on section utilization calculation, does not deal with shear and torsional checks. Annex D (informative) covers these missing parts, according to it these kinds of failures are very uncommon for fire situations, also the calculation methods in this Annex are not fully verified. Considering these notes of the standard, shear and torsional checks are optional, depending on the Check/design fire resistance against shear and torsion calculation parameter. In case of the "Zone" method, the modification of concrete properties leads to different anchorage length during the design, which is also not verified, thus this consideration is also controlled by the option Design anchorage length with reduced material properties

According to the standard, the effects of thermal deformations resulting from thermal gradients across the cross-section need to be considered. These indirect actions can be added manually to the “+Fire” type load case, if they are relevant (not all sides are exposed to fire). Unfortunately, the automatic calculation of these effects in a realistic and adequate way is extremely complicated. The equivalent linear kinematic loads calculated from the thermal actions highly overestimate the real value of these indirect actions. The correct solution of this problem requires an advanced thermo-mechanical simulation, where the material model of the concrete follows the rising of temperature and the cracking process.

Design

Checking and auto design for fire are both available for Load combinations and Load groups. In case of Load combinations, the checking/design is applied for such accidental combinations, which contain a “+Fire” type load case. In case of Load groups, an accidental Load group with this type of load case is required, similarly to the steel and timber bars. In the calculation parameter, the Design reinforcement for fire resistance option controls that these kind of fire combinations should be also considered in the design process, or only after the calculation of required reinforcement, in the checking process.

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Results

In the model space, the utilization result for fire combinations are available at Results > RC bar > Utilization (RC design tab).

The detailed result of RC bars is extended with a new "Temperature distribution" section in case of fire combinations and maximum results, where fire combinations are relevant. 

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Other sections of the detailed result are changing/containing additional information depending on the fire relevancy of the currently display result. In the "Cross-section" part, the dimensions and sectional data of the reduced section are also displayed. 

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At "Concrete materials" both the original (room temperature) and reduced calculation/strength parameters are listed together with their graphical representation. 

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Reinforcement steel materials are more complicated, because of the arbitrary temperature distribution of every reinforcement bar might have different material properties, despite they are from the same steel material. In addition, the reference temperature for stirrups is a bit ambiguous to determine according to the annex D, thus they are separated into two different tables. The reduced properties of the longitudinal steel materials are listed with their "Position", reference temperature (T) and number (No.) in the "Reinforcement" section figures. 

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In case of stirrups the reference temperature is based on the effective tension area, thus it is combination dependent (can be different section by section), also the segments of a stirrup might have different reference temperatures, based on the ‘a-a’ line of Figure D.2 (if there is no intersection point of line ‘a-a’ and the stirrup segment exists, the middle point of the stirrup segment is used for it).  

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In the other sections of the detailed result, the relevant values ("original" or "fire") of the variables are used and listed in tables, depending on Load combination type. 


Parent topic: RC Design

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