Eurocode 3 Heat Transfer to External Steelwork

Warning

Work in progress

Calculation documented herein follows annex B in BS EN 1993-1-2:2005 “Eurocode 3: Design of steel structures — Part 1-2: General rules — Structural fire design”. This method allows the determination of the average temperature of an external steel member.

Units, symbols and abbreviations are consistent with BS EN 1991-1-3 unless explicitly stated. Reference texts in italic refers to BS EN 1993-1-2:2005 unless explicitly stated.

Important

1. In this method, the fire compartment is assumed to be confined to one storey only. All windows or other similar openings in the fire compartment are assumed to be rectangular.

2. The determination of the temperature of the compartment fire, the dimensions and temperatures of the flames projecting from the openings, and the radiation and convection parameters should be performed according to annex B of BS EN 1991-1-2:2002.

3. A distinction should be made between members not engulfed in flame and members engulfed in flame, depending on their locations relative to the openings in the walls of the fire compartment.

4. A member that is not engulfed in flame should be assumed to receive radiative heat transfer from all the openings in that side of the fire compartment and from the flames projecting from all these openings.

5. A member that is engulfed in flame should be assumed to receive convective heat transfer from the engulfing flame, plus radiative heat transfer from the engulfing flame and from the fire compartment opening from which it projects. The radiative heat transfer from other flames and from other openings may be neglected.

Column Engulfed in Flame (Forced Draught)

The convention for geometrical data may be taken from the figure below.

The following parameters should be given prior the assessment:

\(\lambda_1\) [\(m\)] is the distance between side of the column and the window opening edge.

\(\lambda_3\) [\(m\)] is the separation between the column and the window opening.

\(d_1\) [\(m\)] is the column dimension transverse to the wall.

\(d_2\) [\(m\)] is the column dimension longitudinal to the wall.

\(C_i\) [\(1\)] is the coefficient associated with protection.

\(L_L\) [\(m\)] is the external flame height.

\(L_H\) [\(m\)] is the external flame projection transverse to the wall.

\(w_t\) [\(m\)] is the window opening width.

\(h_{eq}\) [\(m\)] is the window opening height.

\(T_f\) [\(K\)] is the flame temperature at the window opening.

Column location parameter \(\lambda_2\)

\(\lambda_2\) is given by:

\[\lambda_2=w_t-\lambda_1-d_2\]

Column location parameter \(\lambda_4\)

\(\lambda_4\) is given by:

\[\begin{split}\lambda_4=\max \begin{Bmatrix} 0\\ \min \begin{Bmatrix} \frac{1}{2}h_{eq}\cdot \frac{L_H}{L_L}\\ h_{eq}\frac{L_H}{L_L}-(\lambda_3+d_1)\\ \end{Bmatrix} \end{Bmatrix}\end{split}\]

Distance from the window to column along flame axis

The distance from the window to column along flame axis \(l\) is given by:

\[\begin{split}l=L_x=\min \begin{Bmatrix} \left(\lambda_3+0.5d_1\right)\frac{L_L}{L_H}\\ 0.5h_{eq}\frac{L_L}{L_H} \end{Bmatrix}\end{split}\]

Equation B19.a and B.19b, Clause B.4(5)

Note

This is the same as \(L_x\) in BS EN 1991-1-2:2002

Flame temperature column

The flame temperature along the flame axis at the the column is given by:

\[T_z=\left(T_w-T_0\right)\left(1-0.4725\frac{L_x\cdot w_t}{Q}\right)+T_0\]

Equation B.15, Clause B.4.1(10)

The emissivity of the flames

The emissivity of the flames for each of the faces 1, 2, 3 and 4 of the column are:

\[\varepsilon_{z,i}=1-e^{-0.3\lambda_i}\]

Equation XX, Clause B.4(2)

The radiative heat flux from flames

The radiative heat flux from the flames for each of the faces 1, 2, 3 and 4 of the column are:

\[I_{z,i}=C_i\cdot \varepsilon_{z,i}\sigma \cdot T^4\]

Equation XX, Clause B.4 (1)

The radiative heat flux from an opening

The radiative heat flux from an opening for each of the faces 1, 2, 3, and 4 of the column are:

\[I_{f,i}=\phi_f\cdot\varepsilon_f\left(1-\varepsilon_{z,i}\right)\sigma\cdot T_f^4\]

Equation XX, Clause B.1.3 (5)

The convective heat transfer coefficient

The convective heat transfer coefficient \(\alpha\) is given by:

\[\alpha_c=4.67\left(\frac{1}{d_{eq}}\right)^{0.4}\left(\frac{Q}{A_v}\right)^{0.6}\]

Clause B.4.1 (12) in BS EN 1991-1-2:2002

Note

This is the same as \(α_c\) in BS EN 1991-1-2 with unit \(\frac{W}{m^2\cdot K}\). This is converted to \(\frac{kW}{m^2\cdot K}\) for this assessment.

Steel temperature at its four sides

The temperature of the steel member for each of its faces 1, 2, 3, and 4 can be calculated by solving the heat balancing equation:

\[\sigma T_{m,i}^4+\alpha T_{m,i}=I_{z,i}+I_{f,i}+293\alpha\]

Equation B.2 in Clause B.1.3(3)

Radiative heat flux from flames

The radiative heat flux \(I_z\) from the flames should be determined from:

\[I_z=\frac{(I_{z,1}+I_{z,2})\cdot d_1+(I_{z,3}+I_{z,4})\cdot d_2}{(C_1+C_2)\cdot d_1+(C_3+C_4)\cdot d_2}\]

Equation B.18, Clause B.4(1)

Radiative heat flux from an opening

The radiative heat flux \(I_f\) from an opening should be determined from:

\[I_f = \phi_f \cdot \varepsilon_f \left(1-a_z\right)\cdot \sigma \cdot T_f^4\]

Equation B.3, Clause B.1.3(5)

Average steel temperature

The average temperature of the steel member \(T_m\) [\(K\)] should be determined from the solution of the following heat balance:

\[\sigma \cdot T_m^4 + \alpha \cdot T_m = I_z + I_f + \alpha \cdot T_z\]

Equation B.2, B.1.3(3)

Column not Engulfed in Flame (Forced Draught)

The B.1.2(1), Equation B.1

\[\sigma T_m^4+\alpha T_m=\sum_{i=1}^4I_{z,i}+\sum_{i=1}^4I_{f,i}+293\alpha\]

Column Engulfed in Flame (No forced Draught)

Column not Engulfed in Flame (No forced Draught)