Overview
To check that FireSolver results are correct, the calculation engine was compared with numerical examples published in the literature on the fire design of steel structures to EN 1993-1-2.
The analysis uses three reference sources. Each worked example is reproduced independently, with the same input data as in the original publication. The FireSolver results are compared with the published values, and the differences are shown and explained where needed.
The comparison covers:
- the critical temperature for different load cases: tension, compression, bending and combined compression and bending;
- the steel temperature, for both unprotected and protected members;
- the time to reach a given temperature;
- the required thickness of fire protection.
For the examples calculated with the equations of EN 1993-1-2, the FireSolver results are very close to the published ones, and the differences are in general a few degrees Celsius or less. The larger differences come from values read from tables or nomograms, and the note under each table explains them.
Besides the comparisons with the published examples, the calculation engine is checked regularly by a set of more than 10,000 automated tests. The tests cover the sections in the catalogue of the application and the main checks that the application performs.
The reference source
Jean-Marc Franssen, Paulo Vila Real, Fire Design of Steel Structures. Eurocode 1: Actions on structures, Part 1-2. Eurocode 3: Design of steel structures, Part 1-2, 2nd edition, ECCS Eurocode Design Manuals, ECCS and Ernst & Sohn, 2015. ISBN 978-3-433-03143-8 (Ernst & Sohn), ISBN 978-92-9147-128-7 (ECCS).
The reference source is the ECCS (European Convention for Constructional Steelwork) manual for the fire design of steel structures to EN 1991-1-2 and EN 1993-1-2. The examples of chapters 4 and 5 are solved with the formulas of the standards, and some of them are also checked with the Elefir-EN program, described in chapter 8. This page compares the FireSolver results with those of the manual, for every example that the application covers. The example numbers (for example, 5.4) are those of the original manual.
Comparison method
The input data are those of the original examples: the properties of the section and of the steel, the design effects in the fire situation, the buckling lengths and the section factors. For all examples, γM,fi = 1.0, the ISO 834 standard fire curve and the convective heat transfer coefficient αc = 25 W/m²K are used.
In the tables, the "Book" column holds the reference value, that is the result published in the manual, with the same precision and rounding as in the original example. The "Method in the book" column states how this result was obtained: with an equation of the standard, with the Elefir-EN program or by reading a value from a table.
The "FireSolver" column holds the value calculated by the engine of the application, which is also used in the online calculators, in the version of 3 November 2026. An automated test reproduces these examples every week and reports any change in the results.
The "Difference" column holds the FireSolver result minus the reference value of the manual, with the number of decimals published in the original example.
1. Critical temperature
Temperatures in °C. N, M and V are the design effects in the fire situation. κ1 and κ2 are the adaptation factors for non-uniform temperature.
| Example | Failure mode | Book | FireSolver | Difference | Method in the book |
|---|---|---|---|---|---|
| 5.1: HE 200 A tension member, S275, N = 780 kN | cross-section resistance | 576.1 | 576.1 | 0.0 | eq. (4.22) |
| 5.2: IPE 300 beam, S235, laterally restrained, M = 67.6 kNm, unprotected (κ1 = 0.7) | cross-section resistance | 654 | 653.8 | 0 | eq. (4.22) |
| 5.2: same beam, protected (κ1 = 0.85) | cross-section resistance | 624 | 624.1 | 0 | eq. (4.22) |
| 5.4: HE 180 B column, S275, ℓfi = 175 cm, N = 495 kN | flexural buckling | 623 | 623.2 | 0 | eq. (4.22) |
| 5.5: HE 220 B column, S235, ℓfi = 140 cm, N = 980 kN | flexural buckling | 565 | 565.8 | +1 | eq. (4.22) |
| 5.7: IPE 300 beam, S235, L = 5 m, M = 39.0 kNm, laterally restrained | cross-section resistance | 683 | 683.1 | 0 | eq. (4.22) |
| 5.7: same beam, laterally unrestrained, Mcr = 129.4 kNm | lateral-torsional buckling | 519 | 517.6 | −1 | eq. (4.22) |
| 5.8: IPE 450, S235, L = 6 m, N = 136.5 kN, q = 15.89 kN/m (M = 71.5 kNm), laterally restrained | flexural buckling | 595 | 595.2 | 0 | Table 3.1 (a) |
| 5.8: same member, laterally unrestrained, Mcr = 347.2 kNm | lateral-torsional buckling | 515 | 515.4 | 0 | Table 3.1 (a) |
| 5.9: HE 200 B column, S235, ℓfi,y = 150 cm, N = 800 kN, end moments ±50 kNm, buckling about z prevented | flexural buckling | 552 | 552.6 | +1 | Table 3.1 (a) |
| 5.9: same column | cross-section resistance to N and M (governs) | 516.5 | 516.5 | 0.0 | Table 3.1 (a) |
| 5.12: IPE 300 continuous beam, S235, intermediate support, M = 80.64 kNm, V = 80.64 kN, κ1 = 0.7, κ2 = 0.85 | cross-section resistance | 660.5 | 660.5 | 0.0 | Table 3.1 (a) |
| 5.12: same section | shear | 699.4 | 699.4 | 0.0 | Table 3.1 (a) |
| 5.12: same section | bending with shear (governs) | 656 | 655.4 | −1 | Table 3.1 (a) |
| Ch. 8: HE 220 B column, S235, ℓfi,y = 300 cm, ℓfi,z = LLT = 150 cm, N = 130 kN, q = 13 kN/m (M = 14.625 kNm), Mcr = 3457.6 kNm | final value | 752.5 | 752.5 | 0.0 | Elefir-EN (a) |
- (a) The book reads the critical temperature from Table 3.1 of EN 1993-1-2: it looks for the temperature at which ky,θ equals the degree of utilisation μ0, by linear interpolation. Elefir-EN uses the same method. For these rows, FireSolver calculates with the same method (Settings > Appearance and preferences > Critical temperature: Table 3.1), also in the buckling iterations, and the difference from the book is below 1 °C. By default, FireSolver uses eq. (4.22) of EN 1993-1-2 §4.2.4. The two methods give almost the same temperature around 500 °C and above 700 °C and move apart between 550 and 700 °C: in example 5.12, with eq. (4.22), the cross-section resistance gives 651.7 °C, shear 703.0 °C and bending with shear 646.0 °C. In the examples where the book uses eq. (4.22), FireSolver calculates with eq. (4.22), and the difference is below 2 °C.
2. Heating of steel
The calculations use the ISO 834 standard fire curve, with a convective heat transfer coefficient αc = 25 W/m²K.
For unprotected steel members the modified section factor ksh · Am/V is used, and for protected members the section factor Ap/V. Both factors are in m⁻¹.
The protection materials are defined by the thermal conductivity λp (W/mK), the density ρp (kg/m³) and the specific heat cp (J/kgK).
The reference values of the manual do not include the heating delay caused by the moisture of the protection material. The FireSolver calculation model does not take this effect into account either.
Steel temperature at a given time
| Example | Time | Book | FireSolver | Difference | Method in the book |
|---|---|---|---|---|---|
| 4.1: rectangular bar 200 × 50 mm, unprotected, 4 sides, ksh · Am/V = 50 | 30 min | 690 | 691.5 | +2 | Elefir-EN |
| 4.2: circular hollow section Ø220 × 5, unprotected, ksh · Am/V = 200 | 60 min | 942 | 942.0 | 0 | table, Annex A.4 (b) |
| 4.3: HE 200 A, unprotected, 4 sides, ksh · Am/V = 130.5 | 30 min | 802 | 803.2 | +1 | eq. (4.25) |
| 5.4: HE 180 B, unprotected, 4 sides, ksh · Am/V = 99.2 | 30 min | 766 | 767.4 | +1 | table, Annex A.4 (b) |
| 4.6: IPE 300, fibre-cement board encasement 20 mm (0.15 / 800 / 1200), 4 sides, Ap/V = 167.3 | 60 min | 451 | 453.1 | +2 | Elefir-EN |
Time to reach a given temperature
| Example | Steel temperature | Book (min) | FireSolver (min) | Difference | Method in the book |
|---|---|---|---|---|---|
| 4.5: HE 220 B, gypsum board encasement 20 mm (0.20 / 800 / 1700), 4 sides, Ap/V = 96.7 | 559 °C | 98.9 | 95.00 | −3.9 | Elefir-EN (c) |
| 5.1: HE 200 A, unprotected, 4 sides, ksh · Am/V = 130.4 | 576.1 °C | 14.08 | 13.25 | −0.83 | table, Annex A.4 (b) |
| 5.2: IPE 300, unprotected, 3 sides, ksh · Am/V = 125.5 | 654 °C | 18 | 16.75 | −1 | table, Annex A.4 (b) |
| 5.4: HE 180 B, unprotected, 4 sides, ksh · Am/V = 99.2 | 623 °C | 17.4 | 17.33 | −0.1 | table, Annex A.4 (b) |
| 5.5: HE 220 B, gypsum board encasement 20 mm (0.20 / 800 / 1700), 4 sides, Ap/V = 96 | 565 °C | 99 | 96.50 | −3 | table, Annex A.5 (b) |
| Ch. 8: HE 220 B, unprotected, 4 sides, Am/V = 139.6 | 752.5 °C | 30.35 | 30.33 | −0.02 | Elefir-EN |
| Ch. 8: same column, contour mineral fibre 5 mm (0.12 / 300 / 1200), Ap/V = 139.6 | 752.5 °C | 67.67 | 67.00 | −0.67 | Elefir-EN (d) |
- (b) The tables in the annexes of the book give the steel temperature in steps of time and section factor, and the book interpolates in them. For example 4.3 the book gives both values: 786 °C from the table and 802 °C from the equation. FireSolver integrates eq. (4.25) and (4.27) of EN 1993-1-2 in time steps.
- (c) The hand calculation of the book, with the table of Annex A.5, gives 97 min. With 1 s steps instead of 30 s, the FireSolver calculation still gives 95 min, so the difference does not come from the time step. The book gives no other data that would explain the difference from Elefir-EN.
- (d) FireSolver integrates eq. (4.27) in 30 s steps and reports the first step at which the steel reaches the temperature. Elefir-EN uses 1 s steps. With 1 s steps, the same calculation gives 67.68 min.
3. Protection thickness
| Example | Protection, requirement | Book (mm) | FireSolver (mm) | Difference | Method in the book |
|---|---|---|---|---|---|
| 4.4: IPE 300, 3 sides, Ap/V = 139.4, θa,cr = 654 °C | fibre-cement board encasement (0.15 / 800 / 1200), R 90 | 14.3 | 15.5 | +1.2 | table, Annex A.5 (e) |
- (e) The book reads the modified section factor (Ap/V)(λp/dp) from the table of Annex A.5, which gives 17 mm, then reduces the thickness for the heat capacity of the protection, with the factor 1/(1 + φ/2): 14.3 mm. Eq. (4.27) of EN 1993-1-2, which FireSolver integrates, needs 15.2 mm, and the application rounds the thickness up to 0.5 mm. With 14.3 mm, eq. (4.27) gives 654 °C at 85.4 min.
For the column of chapter 8, the book chooses 5 mm of mineral fibre and checks the time (table above). The minimum thickness for R 60 given by FireSolver is 4.5 mm.
4. Other published sources
Worked examples from two other published sources are reproduced, with the input data of the original examples. The section properties and section factors are taken from the FireSolver catalogue, and the values match those published in the reference sources.
- [H] A.F. Hamerlinck, "Fire safety and fire resistant design of steel structures for buildings according to Eurocode 3", Steel Design 2, Bouwen met Staal, 2021, chapter 2, examples 2.2-2.5.
- [J] M. Veljkovic et al., "Eurocodes: Background & Applications. Design of Steel Buildings", JRC report EUR 27346 EN, 2015, chapter 6 (P. Vila Real), examples 1-3.
Critical temperature
Temperatures in °C, γM,fi = 1.0.
| Example | Failure mode | Source | FireSolver | Difference | Note |
|---|---|---|---|---|---|
| [J] ex. 3: IPE 400, S355, Mfi,Ed = 74.3 kNm, unprotected (κ1 = 0.7) | cross-section resistance | 812 | 812.0 | 0 | |
| [J] ex. 3: IPE 400, protected (κ1 = 0.85) | cross-section resistance | 783 | 782.8 | 0 | |
| [J] ex. 3: IPE 400, Vfi,Ed = 49.3 kN | shear | 916.3 | 915.4 | −0.9 | (f) |
| [J] ex. 2: HEB 340 column, S355, ℓfi = 216.75 cm, Nfi,Ed = 2161.9 kN | flexural buckling | 598.5 | 597.7 | −0.8 | (h) |
| [H] 2.2: HEA 550, S235, Mfi,Ed = 351.4 kNm, κ1 = 0.7 | cross-section resistance | 708 | 706.3 | −2 | (f) |
| [H] 2.2: HEB 550, S235, same load | cross-section resistance | 736 | 734.9 | −1 | (f) |
| [H] 2.2: HEA 550, S355, same load | cross-section resistance | 768 | 768.3 | 0 | |
| [H] 2.2: HEA 550, S235, continuous beam, Mfi,Ed = 242.4 kNm, κ2 = 0.85 | cross-section resistance | 789 | 786.6 | −2 | (f) |
| [H] 2.3: HEA 400, S235, Mfi,Ed = 232.8 kNm, κ1 = 0.85 | cross-section resistance | 649 | 649.9 | +1 | |
| [H] 2.5: HEA 400, S235, Mfi,Ed = 233 kNm, λ̄LT = 0.80 | lateral-torsional buckling | 500 | 502.6 | +3 | (g) |
- (f) The source rounds the degree of utilisation before eq. (4.22): 0.32, 0.27, 0.22 and 0.056, against 0.3235, 0.2675, 0.2232 and 0.0563. At a low degree of utilisation, a difference of 0.005 moves the critical temperature by 1-2 °C.
- (g) The book searches for the temperature at which the buckling resistance equals the design effect, with ky,θ and kE,θ from Table 3.1, and reads the result from tables: 500 °C. FireSolver iterates with eq. (4.22), as in EN 1993-1-2 §4.2.4. Report [J] shows the same difference between the two methods for the HEB 340 column: 598.5 °C with eq. (4.22) and 603.6 °C with Table 3.1.
- (h) In the iteration tables of [J], √(ky,θ/kE,θ) is slightly lower than the linear interpolation in Table 3.1 of EN 1993-1-2, for example 1.208 at 605.7 °C, against 1.234.
Heating of unprotected steel
The calculations use the ISO 834 standard fire curve and the convective heat transfer coefficient αc = 25 W/m²K.
The reference source gives the steel temperature at a given time, and FireSolver calculates the time needed to reach that temperature. The modified section factor ksh · Am/V is in m⁻¹.
| Example | Steel temperature | Source | FireSolver | Difference | Note |
|---|---|---|---|---|---|
| [J] ex. 1: HEB 340, 4 sides, ksh · Am/V = 67.4 | 730 °C | 30 min 0 s | 29 min 30 s | −30 s | nomogram |
| [J] ex. 2: HEB 340, 4 sides | 598.5 °C | 20 min 18 s | 20 min 15 s | −3 s | Elefir-EN, 20.3 min |
| [J] ex. 3: IPE 400, 3 sides, ksh · Am/V = 104.4 | 812 °C | 33 min 0 s | 33 min 5 s | +5 s | nomogram |
| [H] 2.2: HEA 550, 3 sides, ksh · Am/V = 59 | 721 °C | 30 min 0 s | 30 min 15 s | +15 s | |
| [H] 2.2: HEB 550, 3 sides, ksh · Am/V = 50 | 693 °C | 30 min 0 s | 30 min 20 s | +20 s |
Protection thickness
Standard fire curve ISO 834, with the critical temperature of the source. Thicknesses in mm.
| Example | Protection, requirement | Source | FireSolver | Difference |
|---|---|---|---|---|
| [J] ex. 1: HEB 340, 4 sides, θa,cr = 598.5 °C | gypsum board encasement 0.20 / 800 / 1700, R 90 | 13.7 | 14.0 | +0.3 |
| [H] 2.3: HEA 400, 3 sides, θa,cr = 649 °C | contour spray 0.12 / 550 / 1100, R 60 | 6.1 | 6.0 | −0.1 |
| [H] 2.5: HEA 400, 3 sides, θa,cr = 500 °C | contour spray 0.12 / 550 / 1100, R 60 | 10.8 | 10.5 | −0.3 |
The sources read the modified section factor (Ap/V)(λp/dp) from a nomogram and calculate the thickness from it. [J] then corrects the thickness for the heat capacity of the protection; in [H] the correction is 3-5% and the book neglects it. FireSolver integrates eq. (4.27) in 30 s steps and rounds the thickness up to 0.5 mm.
5. Automated tests
Besides the published examples, more than 10,000 automated test cases check the calculation engine. They cover every section in the catalogue of the application, several steel grades and several load levels:
- heating of unprotected steel: 3,810 cases (every section, 3 or 4 sides, ISO 834, hydrocarbon and external fire curves);
- heating of protected steel: 1,890 cases (every section with one protection system, plus 6 sections with all 15 systems, contour and box protection, 3 fire curves, 3 thicknesses);
- critical temperature: 5,285 cases in compression, bending about both axes and combined compression and bending, for I and H sections, square, rectangular and circular hollow sections.
Each case compares the engine result with a reference value calculated independently of the application code. The examples on this page are also part of the tests. The full set runs every week, and a subset runs each time the calculation engine is released. A test fails when a result moves outside its tolerance: 5 s for unprotected heating, 30 s for protected heating and 0.01-0.5 °C for critical temperatures.
What the comparison does not cover
- The comparison starts from the same input data: the section properties and the section factor. It does not check the section catalogue of the application.
- The published examples are an independent check of the calculation, not a source of design values. Design values remain those of EN 1993-1-2 and the National Annex.
Information about how the application is checked. It does not replace the text of the standard, the National Annex or verification by a qualified engineer.