# Composite column fire design

The use of concrete filled steel tubes (CHS/RHS/SHS) without fireproof coating is a common substitute for steel columns due to the expensive fire protection coating required for design. Eurocode 1994-1-2 offers three design approaches for member analysis of composite columns:

- tabular data,
- simple calculation models
- and advanced computational model.

Unfortunately, none of them cover all the standard (and FEM-design-supported) cross-composite cross-sections, and the standard even lacks guidance on advanced computational model. In order to support all cross-sections for which room temperature planning is available, both tabular data and simplified calculation methods are implemented.

Content

## Concept

The purpose of the calculation methods is to check the cross sections based on their

- normal resistance (simplified calculation models) or
- geometric dimensions (tabular methods).

For this reason, fire resistance verification is integrated into the regular checking process of composite columns, and all the data required for fire design are located in the *Fire *tab of Composite column *Calculation parameters.*

## Calculation methods

The standard distinguishes three types of cross-sections and suggests completely different calculation methods for them.

In all three cases, the fire check is ultimately a cross-sectional utilization calculation, so the other utilizations of the column (e.g., steel section check, flexural buckling check, etc.) are not affected by the fire combinations.

**Restrictions**

Regardless of the method used, the standard imposes certain restrictions on a member to be examined:

- the strength class of the concrete must not be lower than C20/25,
- the steel grade must be between S235 and S460,
- cross-section is exposed to fire from all sides, and
- only nominal temperature-time curves are supported.

##### Concrete encased profiles

The tabular method for this cross-section type is independent of the load level and specifies minimum / maximum geometrical dimensions for the section and reinforcement arrangement. FEM-Design also checks the criteria *[1.1, 1.2, 1.3] *and *[2.1, 2.2, 2.3]* of *Table 4.4*.

A cross-section is considered to be appropriate if it can be verified against at least one of the two sets of conditions. Linear interpolation is used to determine the limits for the duration of the internal fire.

**Additional restrictions**

- the length of the column must be less than or equal to 30 times the minimum external dimension of the cross-section,
- the minimum reinforcement is 4xφ12, and
- the duration of the fire must be less than or equal to 240 minutes.

##### Partially encased profiles

This method calculates the buckling resistance for bending around the z’ axis (weak axis) using the balanced summation model: it sums the individual contributions of the webs, flange, concrete and rebar. To calculate the resistance, only the fire duration and the buckling length multiplier for the fire situation around the weak axis is required (these can be set at *Calculation parameter*).

For eccentric loads, the buckling resistance should be multiplied by the ratio of the buckling load for eccentric and centrifugal loads calculated according to EN 1994-1-1 for normal temperature design:

**Note:** As this summation method is calculating the resistance around the weak axis, only the *M _{2}*-caused eccentricity is considered.

For the centric buckling resistance (*N _{Rd}*) of the flexural buckling check

*EN 1994-1-1 6.7.3.5*is applied.

For the eccentric buckling resistance (N_{Rd,δ}):

- First, the interaction curve of the cross-section is calculated from the combined compressive and uniaxial bending (
*EN 1994-1-1 6.7.3.6*), taking into account the coefficient*α*and the upper limit of the bending resistance._{M} - Then the eccentric buckling resistance is given by the intersection point (its normal force value) of the interaction curve and the half ray drawn from the origin though the internal force point acting in the section.

**Additional restrictions**

- in the event of a fire, the buckling length must less than or equal to 13.5*b (in some special cases 10.0*b),
- the minimum height and width of the section must be at least 230 mm if fire duration is less than 90 minutes, otherwise 300 mm,
- the maximum height of the section is 1100 mm, the maximum width of the section is 500 mm,
- the reinforcement ratio must be between 1% and 6%, and
- the fire duration must be less than or equal to 120 minutes.

##### Concrete filled profiles

This method consists of two main steps:

- calculation of the temperature distribution within the cross section, and
- calculation the design axial buckling resistance based on the temperature field.

To determine the correct temperature distribution in the cross-section, FEM-Design performs a nonlinear, transient finite element heat transfer analysis with an explicit time integration scheme. The thermal effects required for temperature analysis are given by the third section of *EN 1991-1-2*, which describes the net heat flux through convection and radiation to the fire-exposed surfaces of the member (based on standard fire curves). The temperature-dependent thermal properties of structural steel and concrete are taken according to *EN 1992-1-2* and *1994-1-2*.

The input parameters for the calculation of the temperature distribution are the highlighted settings of *Calculation parameters*:

According to *EN 1994-1-2 H.2 (2)*, the thermal resistance between the steel wall and the concrete is disregarded.

For hollow sections filled with concrete, the design axial buckling load results from the following equation:

*Nfi,Rd=Nfi,cr=Nfi,pl,Rd*

Both the Euler buckling load () and the plastic axial resistance (*Nfi,pl,Rd*) are temperature dependent, which means that each node in the cross-sectional mesh has an individual material model, depending on the actual temperature value in it. The stress-strain relationships corresponding to the elevated temperatures specified in section *3.2.1.* and *3.2.2*. apply to structural/reinforcement steel and concrete, respectively. For both materials, the descending branch is also taken into account to calculate the normal stress and the tangential modulus.

**Note:** The Euler buckling load in the fire situation depends on the buckling length, which can of course be different in the two principal directions. Because the standard does not instruct in this case, the program calculates both and chooses the lower one for safety.

To solve this nonlinear problem, i.e. to find an ε that satisfies the equality, FEM-Design uses an iterative method (the variation of the Euler and plastic resistance in the function of axial strain can be seen in column detailed result).

In the case of an eccentric load, the design value of the axial load (*Nfi*,*Sd*) must be reduced by the multiplication of two correction coefficients:

where ϕ_{S} depends on the reinforcement percentage of the cross-section, and ϕ_{δ} is the function of eccentricity (δ), buckling length in fire situation (*l _{0}*) and cross-sectional dimensions (

*b/d*). To calculate this coefficient, two ratios must be determined in advance:

- the
*l*_{0/b}_{ }or*l*_{0/d}_{ }ratio is calculated in both the first and second principal directions, and the smaller one is chosen; - the
*δ/b*or*δ/d*ratio is calculated in both directions (substituting the resultant eccentricity in both cases), and the bigger one is chosen.

By selecting these ratios, the calculation of the eccentric design load is on the safe side. Both *Figure H.1* and *Figure H.2* are digitized for interpolation.

**Hint:** The standard restricts the applicability of this method to the CHS and SHS sections. In FEM-Design, with the constraints and considerations mentioned above, this design procedure also covers the RHS sections.

**Additional restrictions**

- in the event of a fire, the buckling length must be less than or equal to 4.5 m,
- the cross-sectional dimensions must be between 140 mm and 400 mm,
- the strength class of the concrete must be between C20/25 and C40/50,
- the reinforcement ratio must be between 0% and 5%, and
- the fire duration must be less than or equal to 120 minutes.

## Design

Check for fire is available for both *Load combinations* and *Load groups*. In the case of *Load combinations*, the check applies to accidental combinations that include a *“+ Fire”*-type *Load case*. In the case of *Load groups*, like for steel and timber bars, an accidental *Load group* is required with a *“+ Fire”*-type *Load case*.

## Results

The detailed result of the composite columns contains *Fire design data* and *Section utilization* for fire combinations and maximum results where fire combinations are relevant. Depending on the calculation model, the content of these sections changes dynamically.

**Concrete encased profiles**

For the tabular method, the only fire-specific input is fire duration (*t*). The minimum values for the cross-sectional size, concrete cover and axis distance of the rebars are determined for each section. Utilization is given by the maximum of the three criteria.

**Partially encased profiles**

The contribution of each component (flanges, web, concrete, rebar) to each section is listed in tabular form. In the case of an eccentric load, the design buckling load is modified according to *Equation G.22*. The interaction curve is displayed for those cross-sections that appear in the table. If multiple sections have the same interaction curve, the tooltip for the curve shows the corresponding sections.

**Concrete filled profiles**

For the CHS, SHS, and RHS cross-sections, the detailed result consists of two main parts:

*Temperature distribution*: contains all the input data needed to calculate the heat transfer, as well as the temperature distribution within the composite section.*Section utilization*(according to*Annex H*): for eccentric loading, ϕ_{S}and ϕ_{δ}are interpolated on*Figure H.1*and*Figure H.2*, and increase the axial design load. In the case of a central load, they are marked with a*"-"*in the table. The graph of*Nfi,cr*and*Nfi,pl,Rd*are displayed to show their characteristics and the intersection of the buckling load and the plastic resistance.