This document summarizes the fire resistance design of a steel member according to EN1993-1-2:2005. The design checks the member for shear, bending moment, temperature, and time to critical temperature under fire conditions. The summary shows the member passes all criteria with utilization levels below 1.0. Key details of the member, loading, fire protection, and temperature analysis are provided.

1. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
STEEL MEMBER FIRE RESISTANCE DESIGN (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda December 2005,
September 2006 and March 2009 and the recommended values
Design summary
Description Unit Applied Allowable Utilisation Result
Shear in fire condition kN 102.6 480.3 0.214 PASS
Bending in fire condition kNm 165.3 176.1 0.939 PASS
Steel member temperature C 409.8 436.9 0.938 PASS
Time to crit. temperature min 30.0 33.0 0.909 PASS

2. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
Partial factors - Section 6.1
Resistance of cross-sections; M0 = 1.00
Resistance of cross-sections in fire situation; M,fi = 1.00
Section details
Section type; IPN 280 (Arcelor)
Steel grade - EN 10025-2:2004; S275
Nominal thickness of element; tnom= 15.2 mm
Nominal yield strength; fy = 275 N/mm2
Nominal ultimate tensile strength; fu = 410 N/mm2
Modulus of elasticity; E = 210000 N/mm2
Fire protection details
Beam exposure; Under a concrete slab
Beam fire protection; Insulated - Hollow encasement
Required fire resistance; R30
Analysis results
Design vertical shear VEd = 180.00 kN
Design bending moment MEd,y = 290.00 kNm
Classification of cross sections - Section 5.5 - Ambient temperature
 = [235 N/mm2 / fy]= 0.92
Internal compression parts subject to bending - Table 5.2 (sheet 1 of 3)
Width of section; c = d = 224.4 mm
c / tw = 22.2 = 24   <= 72  ; Class 1
Outstand flanges - Table 5.2 (sheet 2 of 3)
Width of section; c = (b - tw - 2  r1) / 2 = 44.4 mm
c / tf = 2.9 = 3.2   <= 9  ; Class 1
Section is class 1
Shear resistance – Section 6.2.6
Height of web; hw= h - 2  tf = 250 mm
 = 1.2
Shear area - cl. 6.2.6(3); Av = max(A - 2  b  tf + (tw + 2  r1)  tf,   hw  tw) = 3025 mm2
Design shear resistance; Vc,Rd = Vpl,Rd = Av  (fy / (3)) / M0 = 480.31 kN
Shear reduction factor - cl. 6.2.8(2); Shear,red = 0 = 0.00
Bending moment resistance – Section 6.2.5 & 6.2.8
Design bending resistance - exp. 6.13 MRd,y = Mpl,Rd,y = Wpl.y  fy / M0
MRd,y = 176.07 kNm

3. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
Effects of actions in fire situation – Section 2.4.2
Reduction factor - cl. 2.4.2(3); fi = 0.57
Design bending moment; Mfi,Ed,y = fi  MEd,y = 165.30 kNm
Design vertical shear; Vfi,Ed = fi  VEd = 102.60 kN
Classification of cross sections - Section 5.5 - Fire situation
 = 0.85  [235 N/mm2
/ fy]= 0.79
Internal compression parts subject to bending - Table 5.2 (sheet 1 of 3)
Width of section; c = d = 224.4 mm
c / tw = 22.2 = 28.3   <= 72  ; Class 1
Outstand flanges - Table 5.2 (sheet 2 of 3)
Width of section; c = (b - tw - 2  r1) / 2 = 44.4 mm
c / tf = 2.9 = 3.7   <= 9  ; Class 1
Section is class 1
Shear resistance – Fire situation
Strength reduction factor for steel - Table 3.1; ky,,web = 1.0
Design shear resistance - cl. 4.2.3.3(6); Vfi,t,Rd = ky,,web  Vc,Rd  M0 / M,fi = 480.31 kN
Degree of utilisation - cl. 4.2.4(3); 0,Shear = max(Vfi,Ed / Vfi,t,Rd, 0.013) = 0.214
Vfi,Ed / Vfi,t,Rd = 0.214
PASS - Shear resistance exceeds design shear in fire condition
Bending moment resistance
Strength reduction factor for steel -Table 3.1; ky, = 1.0
Adaptation factor - cl 4.2.3.3(7); k1 = 0.85
Adaptation factor - cl 4.2.3.3(8); k2 = 1.00
Design bending resistance - ; Mfi,Rd,y = min(ky,  MRd,y  M0 / M,fi /(k1  k2), MRd,y) =176.07 kNm
Degree of utilisation - cl. 4.2.4(3); 0,Bending = max(Mfi,Ed,y / Mfi,Rd,y, 0.013) = 0.939
Mfi,Ed,y / Mfi,Rd,y = 0.939
PASS - Bending resistance exceeds design bending in fire condition
Degree of Utilisation
Degree of utilisation - cl. 4.2.4(3); 0 = max(0,Shear,0,Bending) = 0.939
Critical temperature - Section 4.2.4
Critical temperature - exp. 4.22; a,crit = 39.19  Ln(1/(0.9674  0
3.833
) - 1) + 482 = 437
Protected beam - Section 4.2.5.2
Density of steel; s = 7850 kg/m3
Appropriate area of fire material per length; Am = b + 2  h = 679.0 mm
Volume of protected beam per length; V = A = 6178399.5 mm3
/m
Section factor - Table 4.3; SF = Am / V = 109.90 m-1
Time interval; t = 30 s

4. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
Fire protection
Fire protection material thickness; dp = 10 mm
Fire protection material density; p = 800 kg/m3
Fire protection material thermal conductivity; p = 0.2 W/m
Fire protection material specific heat; Cp = 1700 J/kg
Temperature development
Initial time; t0 = 0 min
Initial temperature of steel (C); m.0 = 20
Iteration 1
Time; t1 = t0+t = 0.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.1 = 20 + 345  log(8 t1/(1 min) + 1) = 261.14
Gas temperature increment; .g.1 = g.1 - g.0 = 241.14
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.1 = 425 (Jkg-1) + 7.7310-1 (Jkg-1)  m.0 - 1.6910-3 (Jkg-1)  m.0
2+ 2.2210-6 (Jkg-1)  m.0
3
ca.1 = 439.8 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.1 = Cp  p / (ca.1  s)  dp  SF = 0.43
Increase of temeperature (3-1-2, exp. 4.27)
.m.1 = max(p  SF/(dp  ca.1  s)  (g.1 - m.0) / ( 1 + storage.1 / 3)  t - (exp(storage.1/10) -1)  .g.1, 0)
.m.1 = 0.00
Member temperature; m.1 = m.0+.m.1 = 20.00
Iteration 2
Time; t2 = t1+t = 1.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.2 = 20 + 345  log(8 t2/(1 min) + 1) = 349.21
Gas temperature increment; .g.2 = g.2 - g.1 = 88.07
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.2 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.1 - 1.6910-3
(Jkg-1
)  m.1
2
+ 2.2210-6
(Jkg-1
)  m.1
3
ca.2 = 439.8 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.2 = Cp  p / (ca.2  s)  dp  SF = 0.43
Increase of temeperature (3-1-2, exp. 4.27)
.m.2 = max(p  SF/(dp  ca.2  s)  (g.2 - m.1) / ( 1 + storage.2 / 3)  t - (exp(storage.2/10) -1)  .g.2, 0)
.m.2 = 1.60
Member temperature; m.2 = m.1+.m.2 = 21.60
Iteration 3
Time; t3 = t2+t = 1.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.3 = 20 + 345  log(8 t3/(1 min) + 1) = 404.31
Gas temperature increment; .g.3 = g.3 - g.2 = 55.10
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.3 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.2 - 1.6910-3
(Jkg-1
)  m.2
2
+ 2.2210-6
(Jkg-1
)  m.2
3

5. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
ca.3 = 440.9 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.3 = Cp  p / (ca.3  s)  dp  SF = 0.43
Increase of temeperature (3-1-2, exp. 4.27)
.m.3 = max(p  SF/(dp  ca.3  s)  (g.3 - m.2) / ( 1 + storage.3 / 3)  t - (exp(storage.3/10) -1)  .g.3, 0)
.m.3 = 3.94
Member temperature; m.3 = m.2+.m.3 = 25.54
Iteration 4
Time; t4 = t3+t = 2.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.4 = 20 + 345  log(8 t4/(1 min) + 1) = 444.50
Gas temperature increment; .g.4 = g.4 - g.3 = 40.19
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.4 = 425 (Jkg-1) + 7.7310-1 (Jkg-1)  m.3 - 1.6910-3 (Jkg-1)  m.3
2+ 2.2210-6 (Jkg-1)  m.3
3
ca.4 = 443.7 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.4 = Cp  p / (ca.4  s)  dp  SF = 0.43
Increase of temeperature (3-1-2, exp. 4.27)
.m.4 = max(p  SF/(dp  ca.4  s)  (g.4 - m.3) / ( 1 + storage.4 / 3)  t - (exp(storage.4/10) -1)  .g.4, 0)
.m.4 = 5.18
Member temperature; m.4 = m.3+.m.4 = 30.72
Iteration 5
Time; t5 = t4+t = 2.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.5 = 20 + 345  log(8 t5/(1 min) + 1) = 476.17
Gas temperature increment; .g.5 = g.5 - g.4 = 31.66
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.5 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.4 - 1.6910-3
(Jkg-1
)  m.4
2
+ 2.2210-6
(Jkg-1
)  m.4
3
ca.5 = 447.2 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.5 = Cp  p / (ca.5  s)  dp  SF = 0.43
Increase of temeperature (3-1-2, exp. 4.27)
.m.5 = max(p  SF/(dp  ca.5  s)  (g.5 - m.4) / ( 1 + storage.5 / 3)  t - (exp(storage.5/10) -1)  .g.5, 0)
.m.5 = 5.95
Member temperature; m.5 = m.4+.m.5 = 36.67
Iteration 6
Time; t6 = t5+t = 3.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.6 = 20 + 345  log(8 t6/(1 min) + 1) = 502.29
Gas temperature increment; .g.6 = g.6 - g.5 = 26.12
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.6 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.5 - 1.6910-3
(Jkg-1
)  m.5
2
+ 2.2210-6
(Jkg-1
)  m.5
3
ca.6 = 451.2 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.6 = Cp  p / (ca.6  s)  dp  SF = 0.42

6. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
Increase of temeperature (3-1-2, exp. 4.27)
.m.6 = max(p  SF/(dp  ca.6  s)  (g.6 - m.5) / ( 1 + storage.6 / 3)  t - (exp(storage.6/10) -1)  .g.6, 0)
.m.6 = 6.47
Member temperature; m.6 = m.5+.m.6 = 43.14
Iteration 7
Time; t7 = t6+t = 3.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.7 = 20 + 345  log(8 t7/(1 min) + 1) = 524.53
Gas temperature increment; .g.7 = g.7 - g.6 = 22.24
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.7 = 425 (Jkg-1) + 7.7310-1 (Jkg-1)  m.6 - 1.6910-3 (Jkg-1)  m.6
2+ 2.2210-6 (Jkg-1)  m.6
3
ca.7 = 455.4 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.7 = Cp  p / (ca.7  s)  dp  SF = 0.42
Increase of temeperature (3-1-2, exp. 4.27)
.m.7 = max(p  SF/(dp  ca.7  s)  (g.7 - m.6) / ( 1 + storage.7 / 3)  t - (exp(storage.7/10) -1)  .g.7, 0)
.m.7 = 6.84
Member temperature; m.7 = m.6+.m.7 = 49.99
Iteration 8
Time; t8 = t7+t = 4.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.8 = 20 + 345  log(8 t8/(1 min) + 1) = 543.89
Gas temperature increment; .g.8 = g.8 - g.7 = 19.36
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.8 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.7 - 1.6910-3
(Jkg-1
)  m.7
2
+ 2.2210-6
(Jkg-1
)  m.7
3
ca.8 = 459.7 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.8 = Cp  p / (ca.8  s)  dp  SF = 0.41
Increase of temeperature (3-1-2, exp. 4.27)
.m.8 = max(p  SF/(dp  ca.8  s)  (g.8 - m.7) / ( 1 + storage.8 / 3)  t - (exp(storage.8/10) -1)  .g.8, 0)
.m.8 = 7.11
Member temperature; m.8 = m.7+.m.8 = 57.10
Iteration 9
Time; t9 = t8+t = 4.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.9 = 20 + 345  log(8 t9/(1 min) + 1) = 561.03
Gas temperature increment; .g.9 = g.9 - g.8 = 17.14
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.9 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.8 - 1.6910-3
(Jkg-1
)  m.8
2
+ 2.2210-6
(Jkg-1
)  m.8
3
ca.9 = 464.0 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.9 = Cp  p / (ca.9  s)  dp  SF = 0.41
Increase of temeperature (3-1-2, exp. 4.27)
.m.9 = max(p  SF/(dp  ca.9  s)  (g.9 - m.8) / ( 1 + storage.9 / 3)  t - (exp(storage.9/10) -1)  .g.9, 0)

7. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
.m.9 = 7.31
Member temperature; m.9 = m.8+.m.9 = 64.40
Iteration 10
Time; t10 = t9+t = 5.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.10 = 20 + 345  log(8 t10/(1 min) + 1) = 576.41
Gas temperature increment; .g.10 = g.10 - g.9 = 15.38
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.10 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.9 - 1.6910-3
(Jkg-1
)  m.9
2
+ 2.2210-6
(Jkg-1
)  m.9
3
ca.10 = 468.4 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.10 = Cp  p / (ca.10  s)  dp  SF = 0.41
Increase of temeperature (3-1-2, exp. 4.27)
.m.10 = max(p  SF/(dp  ca.10  s)  (g.10 - m.9) / ( 1 + storage.10 / 3)  t - (exp(storage.10/10) -1)  .g.10, 0)
.m.10 = 7.45
Member temperature; m.10 = m.9+.m.10 = 71.85
Iteration 11
Time; t11 = t10+t = 5.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.11 = 20 + 345  log(8 t11/(1 min) + 1) = 590.36
Gas temperature increment; .g.11 = g.11 - g.10 = 13.95
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.11 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.10 - 1.6910-3
(Jkg-1
)  m.10
2
+ 2.2210-6
(Jkg-1
)  m.10
3
ca.11 = 472.6 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.11 = Cp  p / (ca.11  s)  dp  SF = 0.40
Increase of temeperature (3-1-2, exp. 4.27)
.m.11 = max(p  SF/(dp  ca.11  s)  (g.11 - m.10) / ( 1 + storage.11 / 3)  t - (exp(storage.11/10) -1)  .g.11, 0)
.m.11 = 7.55
Member temperature; m.11 = m.10+.m.11 = 79.40
Iteration 12
Time; t12 = t11+t = 6.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.12 = 20 + 345  log(8 t12/(1 min) + 1) = 603.12
Gas temperature increment; .g.12 = g.12 - g.11 = 12.76
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.12 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.11 - 1.6910-3
(Jkg-1
)  m.11
2
+ 2.2210-6
(Jkg-1
)  m.11
3
ca.12 = 476.8 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.12 = Cp  p / (ca.12  s)  dp  SF = 0.40
Increase of temeperature (3-1-2, exp. 4.27)
.m.12 = max(p  SF/(dp  ca.12  s)  (g.12 - m.11) / ( 1 + storage.12 / 3)  t - (exp(storage.12/10) -1)  .g.12, 0)
.m.12 = 7.62
Member temperature; m.12 = m.11+.m.12 = 87.02

8. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
Iteration 13
Time; t13 = t12+t = 6.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.13 = 20 + 345  log(8 t13/(1 min) + 1) = 614.88
Gas temperature increment; .g.13 = g.13 - g.12 = 11.76
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.13 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.12 - 1.6910-3
(Jkg-1
)  m.12
2
+ 2.2210-6
(Jkg-1
)  m.12
3
ca.13 = 480.9 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.13 = Cp  p / (ca.13  s)  dp  SF = 0.40
Increase of temeperature (3-1-2, exp. 4.27)
.m.13 = max(p  SF/(dp  ca.13  s)  (g.13 - m.12) / ( 1 + storage.13 / 3)  t - (exp(storage.13/10) -1)  .g.13, 0)
.m.13 = 7.67
Member temperature; m.13 = m.12+.m.13 = 94.69
Iteration 14
Time; t14 = t13+t = 7.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.14 = 20 + 345  log(8 t14/(1 min) + 1) = 625.78
Gas temperature increment; .g.14 = g.14 - g.13 = 10.90
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.14 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.13 - 1.6910-3
(Jkg-1
)  m.13
2
+ 2.2210-6
(Jkg-1
)  m.13
3
ca.14 = 484.9 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.14 = Cp  p / (ca.14  s)  dp  SF = 0.39
Increase of temeperature (3-1-2, exp. 4.27)
.m.14 = max(p  SF/(dp  ca.14  s)  (g.14 - m.13) / ( 1 + storage.14 / 3)  t - (exp(storage.14/10) -1)  .g.14, 0)
.m.14 = 7.70
Member temperature; m.14 = m.13+.m.14 = 102.39
Iteration 15
Time; t15 = t14+t = 7.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.15 = 20 + 345  log(8 t15/(1 min) + 1) = 635.94
Gas temperature increment; .g.15 = g.15 - g.14 = 10.16
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.15 = 425 (Jkg-1) + 7.7310-1 (Jkg-1)  m.14 - 1.6910-3 (Jkg-1)  m.14
2+ 2.2210-6 (Jkg-1)  m.14
3
ca.15 = 488.8 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.15 = Cp  p / (ca.15  s)  dp  SF = 0.39
Increase of temeperature (3-1-2, exp. 4.27)
.m.15 = max(p  SF/(dp  ca.15  s)  (g.15 - m.14) / ( 1 + storage.15 / 3)  t - (exp(storage.15/10) -1)  .g.15, 0)
.m.15 = 7.71
Member temperature; m.15 = m.14+.m.15 = 110.10
Iteration 16
Time; t16 = t15+t = 8.000 min

9. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.16 = 20 + 345  log(8 t16/(1 min) + 1) = 645.46
Gas temperature increment; .g.16 = g.16 - g.15 = 9.52
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.16 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.15 - 1.6910-3
(Jkg-1
)  m.15
2
+ 2.2210-6
(Jkg-1
)  m.15
3
ca.16 = 492.6 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.16 = Cp  p / (ca.16  s)  dp  SF = 0.39
Increase of temeperature (3-1-2, exp. 4.27)
.m.16 = max(p  SF/(dp  ca.16  s)  (g.16 - m.15) / ( 1 + storage.16 / 3)  t - (exp(storage.16/10) -1)  .g.16, 0)
.m.16 = 7.71
Member temperature; m.16 = m.15+.m.16 = 117.82
Iteration 17
Time; t17 = t16+t = 8.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.17 = 20 + 345  log(8 t17/(1 min) + 1) = 654.40
Gas temperature increment; .g.17 = g.17 - g.16 = 8.95
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.17 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.16 - 1.6910-3
(Jkg-1
)  m.16
2
+ 2.2210-6
(Jkg-1
)  m.16
3
ca.17 = 496.2 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.17 = Cp  p / (ca.17  s)  dp  SF = 0.38
Increase of temeperature (3-1-2, exp. 4.27)
.m.17 = max(p  SF/(dp  ca.17  s)  (g.17 - m.16) / ( 1 + storage.17 / 3)  t - (exp(storage.17/10) -1)  .g.17, 0)
.m.17 = 7.70
Member temperature; m.17 = m.16+.m.17 = 125.52
Iteration 18
Time; t18 = t17+t = 9.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.18 = 20 + 345  log(8 t18/(1 min) + 1) = 662.85
Gas temperature increment; .g.18 = g.18 - g.17 = 8.44
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.18 = 425 (Jkg-1) + 7.7310-1 (Jkg-1)  m.17 - 1.6910-3 (Jkg-1)  m.17
2+ 2.2210-6 (Jkg-1)  m.17
3
ca.18 = 499.8 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.18 = Cp  p / (ca.18  s)  dp  SF = 0.38
Increase of temeperature (3-1-2, exp. 4.27)
.m.18 = max(p  SF/(dp  ca.18  s)  (g.18 - m.17) / ( 1 + storage.18 / 3)  t - (exp(storage.18/10) -1)  .g.18, 0)
.m.18 = 7.69
Member temperature; m.18 = m.17+.m.18 = 133.20
Iteration 19
Time; t19 = t18+t = 9.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.19 = 20 + 345  log(8 t19/(1 min) + 1) = 670.84
Gas temperature increment; .g.19 = g.19 - g.18 = 7.99

10. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.19 = 425 (Jkg-1) + 7.7310-1 (Jkg-1)  m.18 - 1.6910-3 (Jkg-1)  m.18
2+ 2.2210-6 (Jkg-1)  m.18
3
ca.19 = 503.2 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.19 = Cp  p / (ca.19  s)  dp  SF = 0.38
Increase of temeperature (3-1-2, exp. 4.27)
.m.19 = max(p  SF/(dp  ca.19  s)  (g.19 - m.18) / ( 1 + storage.19 / 3)  t - (exp(storage.19/10) -1)  .g.19, 0)
.m.19 = 7.66
Member temperature; m.19 = m.18+.m.19 = 140.87
Iteration 20
Time; t20 = t19+t = 10.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.20 = 20 + 345  log(8 t20/(1 min) + 1) = 678.43
Gas temperature increment; .g.20 = g.20 - g.19 = 7.59
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.20 = 425 (Jkg-1) + 7.7310-1 (Jkg-1)  m.19 - 1.6910-3 (Jkg-1)  m.19
2+ 2.2210-6 (Jkg-1)  m.19
3
ca.20 = 506.6 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.20 = Cp  p / (ca.20  s)  dp  SF = 0.38
Increase of temeperature (3-1-2, exp. 4.27)
.m.20 = max(p  SF/(dp  ca.20  s)  (g.20 - m.19) / ( 1 + storage.20 / 3)  t - (exp(storage.20/10) -1)  .g.20, 0)
.m.20 = 7.63
Member temperature; m.20 = m.19+.m.20 = 148.50
Iteration 21
Time; t21 = t20+t = 10.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.21 = 20 + 345  log(8 t21/(1 min) + 1) = 685.65
Gas temperature increment; .g.21 = g.21 - g.20 = 7.22
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.21 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.20 - 1.6910-3
(Jkg-1
)  m.20
2
+ 2.2210-6
(Jkg-1
)  m.20
3
ca.21 = 509.8 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.21 = Cp  p / (ca.21  s)  dp  SF = 0.37
Increase of temeperature (3-1-2, exp. 4.27)
.m.21 = max(p  SF/(dp  ca.21  s)  (g.21 - m.20) / ( 1 + storage.21 / 3)  t - (exp(storage.21/10) -1)  .g.21, 0)
.m.21 = 7.60
Member temperature; m.21 = m.20+.m.21 = 156.09
Iteration 22
Time; t22 = t21+t = 11.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.22 = 20 + 345  log(8 t22/(1 min) + 1) = 692.54
Gas temperature increment; .g.22 = g.22 - g.21 = 6.89
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.22 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.21 - 1.6910-3
(Jkg-1
)  m.21
2
+ 2.2210-6
(Jkg-1
)  m.21
3

11. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
ca.22 = 512.9 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.22 = Cp  p / (ca.22  s)  dp  SF = 0.37
Increase of temeperature (3-1-2, exp. 4.27)
.m.22 = max(p  SF/(dp  ca.22  s)  (g.22 - m.21) / ( 1 + storage.22 / 3)  t - (exp(storage.22/10) -1)  .g.22, 0)
.m.22 = 7.56
Member temperature; m.22 = m.21+.m.22 = 163.65
Iteration 23
Time; t23 = t22+t = 11.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.23 = 20 + 345  log(8 t23/(1 min) + 1) = 699.13
Gas temperature increment; .g.23 = g.23 - g.22 = 6.59
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.23 = 425 (Jkg-1) + 7.7310-1 (Jkg-1)  m.22 - 1.6910-3 (Jkg-1)  m.22
2+ 2.2210-6 (Jkg-1)  m.22
3
ca.23 = 516.0 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.23 = Cp  p / (ca.23  s)  dp  SF = 0.37
Increase of temeperature (3-1-2, exp. 4.27)
.m.23 = max(p  SF/(dp  ca.23  s)  (g.23 - m.22) / ( 1 + storage.23 / 3)  t - (exp(storage.23/10) -1)  .g.23, 0)
.m.23 = 7.52
Member temperature; m.23 = m.22+.m.23 = 171.16
Iteration 24
Time; t24 = t23+t = 12.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.24 = 20 + 345  log(8 t24/(1 min) + 1) = 705.44
Gas temperature increment; .g.24 = g.24 - g.23 = 6.31
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.24 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.23 - 1.6910-3
(Jkg-1
)  m.23
2
+ 2.2210-6
(Jkg-1
)  m.23
3
ca.24 = 518.9 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.24 = Cp  p / (ca.24  s)  dp  SF = 0.37
Increase of temeperature (3-1-2, exp. 4.27)
.m.24 = max(p  SF/(dp  ca.24  s)  (g.24 - m.23) / ( 1 + storage.24 / 3)  t - (exp(storage.24/10) -1)  .g.24, 0)
.m.24 = 7.47
Member temperature; m.24 = m.23+.m.24 = 178.63
Iteration 25
Time; t25 = t24+t = 12.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.25 = 20 + 345  log(8 t25/(1 min) + 1) = 711.49
Gas temperature increment; .g.25 = g.25 - g.24 = 6.05
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.25 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.24 - 1.6910-3
(Jkg-1
)  m.24
2
+ 2.2210-6
(Jkg-1
)  m.24
3
ca.25 = 521.8 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.25 = Cp  p / (ca.25  s)  dp  SF = 0.36

12. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
Increase of temeperature (3-1-2, exp. 4.27)
.m.25 = max(p  SF/(dp  ca.25  s)  (g.25 - m.24) / ( 1 + storage.25 / 3)  t - (exp(storage.25/10) -1)  .g.25, 0)
.m.25 = 7.42
Member temperature; m.25 = m.24+.m.25 = 186.06
Iteration 26
Time; t26 = t25+t = 13.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.26 = 20 + 345  log(8 t26/(1 min) + 1) = 717.31
Gas temperature increment; .g.26 = g.26 - g.25 = 5.82
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.26 = 425 (Jkg-1) + 7.7310-1 (Jkg-1)  m.25 - 1.6910-3 (Jkg-1)  m.25
2+ 2.2210-6 (Jkg-1)  m.25
3
ca.26 = 524.6 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.26 = Cp  p / (ca.26  s)  dp  SF = 0.36
Increase of temeperature (3-1-2, exp. 4.27)
.m.26 = max(p  SF/(dp  ca.26  s)  (g.26 - m.25) / ( 1 + storage.26 / 3)  t - (exp(storage.26/10) -1)  .g.26, 0)
.m.26 = 7.37
Member temperature; m.26 = m.25+.m.26 = 193.43
Iteration 27
Time; t27 = t26+t = 13.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.27 = 20 + 345  log(8 t27/(1 min) + 1) = 722.91
Gas temperature increment; .g.27 = g.27 - g.26 = 5.60
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.27 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.26 - 1.6910-3
(Jkg-1
)  m.26
2
+ 2.2210-6
(Jkg-1
)  m.26
3
ca.27 = 527.4 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.27 = Cp  p / (ca.27  s)  dp  SF = 0.36
Increase of temeperature (3-1-2, exp. 4.27)
.m.27 = max(p  SF/(dp  ca.27  s)  (g.27 - m.26) / ( 1 + storage.27 / 3)  t - (exp(storage.27/10) -1)  .g.27, 0)
.m.27 = 7.32
Member temperature; m.27 = m.26+.m.27 = 200.75
Iteration 28
Time; t28 = t27+t = 14.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.28 = 20 + 345  log(8 t28/(1 min) + 1) = 728.31
Gas temperature increment; .g.28 = g.28 - g.27 = 5.40
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.28 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.27 - 1.6910-3
(Jkg-1
)  m.27
2
+ 2.2210-6
(Jkg-1
)  m.27
3
ca.28 = 530.0 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.28 = Cp  p / (ca.28  s)  dp  SF = 0.36
Increase of temeperature (3-1-2, exp. 4.27)
.m.28 = max(p  SF/(dp  ca.28  s)  (g.28 - m.27) / ( 1 + storage.28 / 3)  t - (exp(storage.28/10) -1)  .g.28, 0)

13. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
.m.28 = 7.27
Member temperature; m.28 = m.27+.m.28 = 208.02
Iteration 29
Time; t29 = t28+t = 14.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.29 = 20 + 345  log(8 t29/(1 min) + 1) = 733.52
Gas temperature increment; .g.29 = g.29 - g.28 = 5.21
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.29 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.28 - 1.6910-3
(Jkg-1
)  m.28
2
+ 2.2210-6
(Jkg-1
)  m.28
3
ca.29 = 532.7 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.29 = Cp  p / (ca.29  s)  dp  SF = 0.36
Increase of temeperature (3-1-2, exp. 4.27)
.m.29 = max(p  SF/(dp  ca.29  s)  (g.29 - m.28) / ( 1 + storage.29 / 3)  t - (exp(storage.29/10) -1)  .g.29, 0)
.m.29 = 7.22
Member temperature; m.29 = m.28+.m.29 = 215.24
Iteration 30
Time; t30 = t29+t = 15.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.30 = 20 + 345  log(8 t30/(1 min) + 1) = 738.56
Gas temperature increment; .g.30 = g.30 - g.29 = 5.04
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.30 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.29 - 1.6910-3
(Jkg-1
)  m.29
2
+ 2.2210-6
(Jkg-1
)  m.29
3
ca.30 = 535.2 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.30 = Cp  p / (ca.30  s)  dp  SF = 0.36
Increase of temeperature (3-1-2, exp. 4.27)
.m.30 = max(p  SF/(dp  ca.30  s)  (g.30 - m.29) / ( 1 + storage.30 / 3)  t - (exp(storage.30/10) -1)  .g.30, 0)
.m.30 = 7.16
Member temperature; m.30 = m.29+.m.30 = 222.40
Iteration 31
Time; t31 = t30+t = 15.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.31 = 20 + 345  log(8 t31/(1 min) + 1) = 743.43
Gas temperature increment; .g.31 = g.31 - g.30 = 4.87
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.31 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.30 - 1.6910-3
(Jkg-1
)  m.30
2
+ 2.2210-6
(Jkg-1
)  m.30
3
ca.31 = 537.7 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.31 = Cp  p / (ca.31  s)  dp  SF = 0.35
Increase of temeperature (3-1-2, exp. 4.27)
.m.31 = max(p  SF/(dp  ca.31  s)  (g.31 - m.30) / ( 1 + storage.31 / 3)  t - (exp(storage.31/10) -1)  .g.31, 0)
.m.31 = 7.10
Member temperature; m.31 = m.30+.m.31 = 229.50

14. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
Iteration 32
Time; t32 = t31+t = 16.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.32 = 20 + 345  log(8 t32/(1 min) + 1) = 748.15
Gas temperature increment; .g.32 = g.32 - g.31 = 4.72
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.32 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.31 - 1.6910-3
(Jkg-1
)  m.31
2
+ 2.2210-6
(Jkg-1
)  m.31
3
ca.32 = 540.2 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.32 = Cp  p / (ca.32  s)  dp  SF = 0.35
Increase of temeperature (3-1-2, exp. 4.27)
.m.32 = max(p  SF/(dp  ca.32  s)  (g.32 - m.31) / ( 1 + storage.32 / 3)  t - (exp(storage.32/10) -1)  .g.32, 0)
.m.32 = 7.05
Member temperature; m.32 = m.31+.m.32 = 236.55
Iteration 33
Time; t33 = t32+t = 16.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.33 = 20 + 345  log(8 t33/(1 min) + 1) = 752.73
Gas temperature increment; .g.33 = g.33 - g.32 = 4.58
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.33 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.32 - 1.6910-3
(Jkg-1
)  m.32
2
+ 2.2210-6
(Jkg-1
)  m.32
3
ca.33 = 542.7 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.33 = Cp  p / (ca.33  s)  dp  SF = 0.35
Increase of temeperature (3-1-2, exp. 4.27)
.m.33 = max(p  SF/(dp  ca.33  s)  (g.33 - m.32) / ( 1 + storage.33 / 3)  t - (exp(storage.33/10) -1)  .g.33, 0)
.m.33 = 6.99
Member temperature; m.33 = m.32+.m.33 = 243.54
Iteration 34
Time; t34 = t33+t = 17.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.34 = 20 + 345  log(8 t34/(1 min) + 1) = 757.17
Gas temperature increment; .g.34 = g.34 - g.33 = 4.44
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.34 = 425 (Jkg-1) + 7.7310-1 (Jkg-1)  m.33 - 1.6910-3 (Jkg-1)  m.33
2+ 2.2210-6 (Jkg-1)  m.33
3
ca.34 = 545.1 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.34 = Cp  p / (ca.34  s)  dp  SF = 0.35
Increase of temeperature (3-1-2, exp. 4.27)
.m.34 = max(p  SF/(dp  ca.34  s)  (g.34 - m.33) / ( 1 + storage.34 / 3)  t - (exp(storage.34/10) -1)  .g.34, 0)
.m.34 = 6.93
Member temperature; m.34 = m.33+.m.34 = 250.47
Iteration 35
Time; t35 = t34+t = 17.500 min

15. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.35 = 20 + 345  log(8 t35/(1 min) + 1) = 761.48
Gas temperature increment; .g.35 = g.35 - g.34 = 4.31
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.35 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.34 - 1.6910-3
(Jkg-1
)  m.34
2
+ 2.2210-6
(Jkg-1
)  m.34
3
ca.35 = 547.5 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.35 = Cp  p / (ca.35  s)  dp  SF = 0.35
Increase of temeperature (3-1-2, exp. 4.27)
.m.35 = max(p  SF/(dp  ca.35  s)  (g.35 - m.34) / ( 1 + storage.35 / 3)  t - (exp(storage.35/10) -1)  .g.35, 0)
.m.35 = 6.87
Member temperature; m.35 = m.34+.m.35 = 257.34
Iteration 36
Time; t36 = t35+t = 18.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.36 = 20 + 345  log(8 t36/(1 min) + 1) = 765.67
Gas temperature increment; .g.36 = g.36 - g.35 = 4.19
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.36 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.35 - 1.6910-3
(Jkg-1
)  m.35
2
+ 2.2210-6
(Jkg-1
)  m.35
3
ca.36 = 549.8 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.36 = Cp  p / (ca.36  s)  dp  SF = 0.35
Increase of temeperature (3-1-2, exp. 4.27)
.m.36 = max(p  SF/(dp  ca.36  s)  (g.36 - m.35) / ( 1 + storage.36 / 3)  t - (exp(storage.36/10) -1)  .g.36, 0)
.m.36 = 6.81
Member temperature; m.36 = m.35+.m.36 = 264.16
Iteration 37
Time; t37 = t36+t = 18.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.37 = 20 + 345  log(8 t37/(1 min) + 1) = 769.75
Gas temperature increment; .g.37 = g.37 - g.36 = 4.08
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.37 = 425 (Jkg-1) + 7.7310-1 (Jkg-1)  m.36 - 1.6910-3 (Jkg-1)  m.36
2+ 2.2210-6 (Jkg-1)  m.36
3
ca.37 = 552.2 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.37 = Cp  p / (ca.37  s)  dp  SF = 0.34
Increase of temeperature (3-1-2, exp. 4.27)
.m.37 = max(p  SF/(dp  ca.37  s)  (g.37 - m.36) / ( 1 + storage.37 / 3)  t - (exp(storage.37/10) -1)  .g.37, 0)
.m.37 = 6.76
Member temperature; m.37 = m.36+.m.37 = 270.91
Iteration 38
Time; t38 = t37+t = 19.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.38 = 20 + 345  log(8 t38/(1 min) + 1) = 773.72
Gas temperature increment; .g.38 = g.38 - g.37 = 3.97

16. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.38 = 425 (Jkg-1) + 7.7310-1 (Jkg-1)  m.37 - 1.6910-3 (Jkg-1)  m.37
2+ 2.2210-6 (Jkg-1)  m.37
3
ca.38 = 554.5 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.38 = Cp  p / (ca.38  s)  dp  SF = 0.34
Increase of temeperature (3-1-2, exp. 4.27)
.m.38 = max(p  SF/(dp  ca.38  s)  (g.38 - m.37) / ( 1 + storage.38 / 3)  t - (exp(storage.38/10) -1)  .g.38, 0)
.m.38 = 6.70
Member temperature; m.38 = m.37+.m.38 = 277.61
Iteration 39
Time; t39 = t38+t = 19.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.39 = 20 + 345  log(8 t39/(1 min) + 1) = 777.59
Gas temperature increment; .g.39 = g.39 - g.38 = 3.87
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.39 = 425 (Jkg-1) + 7.7310-1 (Jkg-1)  m.38 - 1.6910-3 (Jkg-1)  m.38
2+ 2.2210-6 (Jkg-1)  m.38
3
ca.39 = 556.8 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.39 = Cp  p / (ca.39  s)  dp  SF = 0.34
Increase of temeperature (3-1-2, exp. 4.27)
.m.39 = max(p  SF/(dp  ca.39  s)  (g.39 - m.38) / ( 1 + storage.39 / 3)  t - (exp(storage.39/10) -1)  .g.39, 0)
.m.39 = 6.64
Member temperature; m.39 = m.38+.m.39 = 284.24
Iteration 40
Time; t40 = t39+t = 20.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.40 = 20 + 345  log(8 t40/(1 min) + 1) = 781.35
Gas temperature increment; .g.40 = g.40 - g.39 = 3.77
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.40 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.39 - 1.6910-3
(Jkg-1
)  m.39
2
+ 2.2210-6
(Jkg-1
)  m.39
3
ca.40 = 559.2 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.40 = Cp  p / (ca.40  s)  dp  SF = 0.34
Increase of temeperature (3-1-2, exp. 4.27)
.m.40 = max(p  SF/(dp  ca.40  s)  (g.40 - m.39) / ( 1 + storage.40 / 3)  t - (exp(storage.40/10) -1)  .g.40, 0)
.m.40 = 6.58
Member temperature; m.40 = m.39+.m.40 = 290.82
Iteration 41
Time; t41 = t40+t = 20.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.41 = 20 + 345  log(8 t41/(1 min) + 1) = 785.03
Gas temperature increment; .g.41 = g.41 - g.40 = 3.68
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.41 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.40 - 1.6910-3
(Jkg-1
)  m.40
2
+ 2.2210-6
(Jkg-1
)  m.40
3

17. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
ca.41 = 561.5 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.41 = Cp  p / (ca.41  s)  dp  SF = 0.34
Increase of temeperature (3-1-2, exp. 4.27)
.m.41 = max(p  SF/(dp  ca.41  s)  (g.41 - m.40) / ( 1 + storage.41 / 3)  t - (exp(storage.41/10) -1)  .g.41, 0)
.m.41 = 6.52
Member temperature; m.41 = m.40+.m.41 = 297.34
Iteration 42
Time; t42 = t41+t = 21.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.42 = 20 + 345  log(8 t42/(1 min) + 1) = 788.62
Gas temperature increment; .g.42 = g.42 - g.41 = 3.59
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.42 = 425 (Jkg-1) + 7.7310-1 (Jkg-1)  m.41 - 1.6910-3 (Jkg-1)  m.41
2+ 2.2210-6 (Jkg-1)  m.41
3
ca.42 = 563.8 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.42 = Cp  p / (ca.42  s)  dp  SF = 0.34
Increase of temeperature (3-1-2, exp. 4.27)
.m.42 = max(p  SF/(dp  ca.42  s)  (g.42 - m.41) / ( 1 + storage.42 / 3)  t - (exp(storage.42/10) -1)  .g.42, 0)
.m.42 = 6.46
Member temperature; m.42 = m.41+.m.42 = 303.79
Iteration 43
Time; t43 = t42+t = 21.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.43 = 20 + 345  log(8 t43/(1 min) + 1) = 792.13
Gas temperature increment; .g.43 = g.43 - g.42 = 3.50
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.43 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.42 - 1.6910-3
(Jkg-1
)  m.42
2
+ 2.2210-6
(Jkg-1
)  m.42
3
ca.43 = 566.1 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.43 = Cp  p / (ca.43  s)  dp  SF = 0.34
Increase of temeperature (3-1-2, exp. 4.27)
.m.43 = max(p  SF/(dp  ca.43  s)  (g.43 - m.42) / ( 1 + storage.43 / 3)  t - (exp(storage.43/10) -1)  .g.43, 0)
.m.43 = 6.40
Member temperature; m.43 = m.42+.m.43 = 310.19
Iteration 44
Time; t44 = t43+t = 22.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.44 = 20 + 345  log(8 t44/(1 min) + 1) = 795.55
Gas temperature increment; .g.44 = g.44 - g.43 = 3.42
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.44 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.43 - 1.6910-3
(Jkg-1
)  m.43
2
+ 2.2210-6
(Jkg-1
)  m.43
3
ca.44 = 568.4 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.44 = Cp  p / (ca.44  s)  dp  SF = 0.33

18. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
Increase of temeperature (3-1-2, exp. 4.27)
.m.44 = max(p  SF/(dp  ca.44  s)  (g.44 - m.43) / ( 1 + storage.44 / 3)  t - (exp(storage.44/10) -1)  .g.44, 0)
.m.44 = 6.34
Member temperature; m.44 = m.43+.m.44 = 316.52
Iteration 45
Time; t45 = t44+t = 22.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.45 = 20 + 345  log(8 t45/(1 min) + 1) = 798.90
Gas temperature increment; .g.45 = g.45 - g.44 = 3.35
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.45 = 425 (Jkg-1) + 7.7310-1 (Jkg-1)  m.44 - 1.6910-3 (Jkg-1)  m.44
2+ 2.2210-6 (Jkg-1)  m.44
3
ca.45 = 570.8 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.45 = Cp  p / (ca.45  s)  dp  SF = 0.33
Increase of temeperature (3-1-2, exp. 4.27)
.m.45 = max(p  SF/(dp  ca.45  s)  (g.45 - m.44) / ( 1 + storage.45 / 3)  t - (exp(storage.45/10) -1)  .g.45, 0)
.m.45 = 6.28
Member temperature; m.45 = m.44+.m.45 = 322.80
Iteration 46
Time; t46 = t45+t = 23.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.46 = 20 + 345  log(8 t46/(1 min) + 1) = 802.17
Gas temperature increment; .g.46 = g.46 - g.45 = 3.28
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.46 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.45 - 1.6910-3
(Jkg-1
)  m.45
2
+ 2.2210-6
(Jkg-1
)  m.45
3
ca.46 = 573.1 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.46 = Cp  p / (ca.46  s)  dp  SF = 0.33
Increase of temeperature (3-1-2, exp. 4.27)
.m.46 = max(p  SF/(dp  ca.46  s)  (g.46 - m.45) / ( 1 + storage.46 / 3)  t - (exp(storage.46/10) -1)  .g.46, 0)
.m.46 = 6.22
Member temperature; m.46 = m.45+.m.46 = 329.01
Iteration 47
Time; t47 = t46+t = 23.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.47 = 20 + 345  log(8 t47/(1 min) + 1) = 805.38
Gas temperature increment; .g.47 = g.47 - g.46 = 3.21
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.47 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.46 - 1.6910-3
(Jkg-1
)  m.46
2
+ 2.2210-6
(Jkg-1
)  m.46
3
ca.47 = 575.5 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.47 = Cp  p / (ca.47  s)  dp  SF = 0.33
Increase of temeperature (3-1-2, exp. 4.27)
.m.47 = max(p  SF/(dp  ca.47  s)  (g.47 - m.46) / ( 1 + storage.47 / 3)  t - (exp(storage.47/10) -1)  .g.47, 0)

19. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
.m.47 = 6.16
Member temperature; m.47 = m.46+.m.47 = 335.17
Iteration 48
Time; t48 = t47+t = 24.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.48 = 20 + 345  log(8 t48/(1 min) + 1) = 808.52
Gas temperature increment; .g.48 = g.48 - g.47 = 3.14
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.48 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.47 - 1.6910-3
(Jkg-1
)  m.47
2
+ 2.2210-6
(Jkg-1
)  m.47
3
ca.48 = 577.8 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.48 = Cp  p / (ca.48  s)  dp  SF = 0.33
Increase of temeperature (3-1-2, exp. 4.27)
.m.48 = max(p  SF/(dp  ca.48  s)  (g.48 - m.47) / ( 1 + storage.48 / 3)  t - (exp(storage.48/10) -1)  .g.48, 0)
.m.48 = 6.10
Member temperature; m.48 = m.47+.m.48 = 341.26
Iteration 49
Time; t49 = t48+t = 24.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.49 = 20 + 345  log(8 t49/(1 min) + 1) = 811.59
Gas temperature increment; .g.49 = g.49 - g.48 = 3.07
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.49 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.48 - 1.6910-3
(Jkg-1
)  m.48
2
+ 2.2210-6
(Jkg-1
)  m.48
3
ca.49 = 580.2 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.49 = Cp  p / (ca.49  s)  dp  SF = 0.33
Increase of temeperature (3-1-2, exp. 4.27)
.m.49 = max(p  SF/(dp  ca.49  s)  (g.49 - m.48) / ( 1 + storage.49 / 3)  t - (exp(storage.49/10) -1)  .g.49, 0)
.m.49 = 6.04
Member temperature; m.49 = m.48+.m.49 = 347.30
Iteration 50
Time; t50 = t49+t = 25.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.50 = 20 + 345  log(8 t50/(1 min) + 1) = 814.60
Gas temperature increment; .g.50 = g.50 - g.49 = 3.01
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.50 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.49 - 1.6910-3
(Jkg-1
)  m.49
2
+ 2.2210-6
(Jkg-1
)  m.49
3
ca.50 = 582.6 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.50 = Cp  p / (ca.50  s)  dp  SF = 0.33
Increase of temeperature (3-1-2, exp. 4.27)
.m.50 = max(p  SF/(dp  ca.50  s)  (g.50 - m.49) / ( 1 + storage.50 / 3)  t - (exp(storage.50/10) -1)  .g.50, 0)
.m.50 = 5.98
Member temperature; m.50 = m.49+.m.50 = 353.27

20. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
Iteration 51
Time; t51 = t50+t = 25.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.51 = 20 + 345  log(8 t51/(1 min) + 1) = 817.56
Gas temperature increment; .g.51 = g.51 - g.50 = 2.95
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.51 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.50 - 1.6910-3
(Jkg-1
)  m.50
2
+ 2.2210-6
(Jkg-1
)  m.50
3
ca.51 = 585.0 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.51 = Cp  p / (ca.51  s)  dp  SF = 0.33
Increase of temeperature (3-1-2, exp. 4.27)
.m.51 = max(p  SF/(dp  ca.51  s)  (g.51 - m.50) / ( 1 + storage.51 / 3)  t - (exp(storage.51/10) -1)  .g.51, 0)
.m.51 = 5.92
Member temperature; m.51 = m.50+.m.51 = 359.19
Iteration 52
Time; t52 = t51+t = 26.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.52 = 20 + 345  log(8 t52/(1 min) + 1) = 820.45
Gas temperature increment; .g.52 = g.52 - g.51 = 2.90
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.52 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.51 - 1.6910-3
(Jkg-1
)  m.51
2
+ 2.2210-6
(Jkg-1
)  m.51
3
ca.52 = 587.5 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.52 = Cp  p / (ca.52  s)  dp  SF = 0.32
Increase of temeperature (3-1-2, exp. 4.27)
.m.52 = max(p  SF/(dp  ca.52  s)  (g.52 - m.51) / ( 1 + storage.52 / 3)  t - (exp(storage.52/10) -1)  .g.52, 0)
.m.52 = 5.86
Member temperature; m.52 = m.51+.m.52 = 365.05
Iteration 53
Time; t53 = t52+t = 26.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.53 = 20 + 345  log(8 t53/(1 min) + 1) = 823.29
Gas temperature increment; .g.53 = g.53 - g.52 = 2.84
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.53 = 425 (Jkg-1) + 7.7310-1 (Jkg-1)  m.52 - 1.6910-3 (Jkg-1)  m.52
2+ 2.2210-6 (Jkg-1)  m.52
3
ca.53 = 590.0 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.53 = Cp  p / (ca.53  s)  dp  SF = 0.32
Increase of temeperature (3-1-2, exp. 4.27)
.m.53 = max(p  SF/(dp  ca.53  s)  (g.53 - m.52) / ( 1 + storage.53 / 3)  t - (exp(storage.53/10) -1)  .g.53, 0)
.m.53 = 5.80
Member temperature; m.53 = m.52+.m.53 = 370.84
Iteration 54
Time; t54 = t53+t = 27.000 min

21. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.54 = 20 + 345  log(8 t54/(1 min) + 1) = 826.08
Gas temperature increment; .g.54 = g.54 - g.53 = 2.79
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.54 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.53 - 1.6910-3
(Jkg-1
)  m.53
2
+ 2.2210-6
(Jkg-1
)  m.53
3
ca.54 = 592.5 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.54 = Cp  p / (ca.54  s)  dp  SF = 0.32
Increase of temeperature (3-1-2, exp. 4.27)
.m.54 = max(p  SF/(dp  ca.54  s)  (g.54 - m.53) / ( 1 + storage.54 / 3)  t - (exp(storage.54/10) -1)  .g.54, 0)
.m.54 = 5.74
Member temperature; m.54 = m.53+.m.54 = 376.58
Iteration 55
Time; t55 = t54+t = 27.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.55 = 20 + 345  log(8 t55/(1 min) + 1) = 828.82
Gas temperature increment; .g.55 = g.55 - g.54 = 2.74
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.55 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.54 - 1.6910-3
(Jkg-1
)  m.54
2
+ 2.2210-6
(Jkg-1
)  m.54
3
ca.55 = 595.0 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.55 = Cp  p / (ca.55  s)  dp  SF = 0.32
Increase of temeperature (3-1-2, exp. 4.27)
.m.55 = max(p  SF/(dp  ca.55  s)  (g.55 - m.54) / ( 1 + storage.55 / 3)  t - (exp(storage.55/10) -1)  .g.55, 0)
.m.55 = 5.68
Member temperature; m.55 = m.54+.m.55 = 382.26
Iteration 56
Time; t56 = t55+t = 28.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.56 = 20 + 345  log(8 t56/(1 min) + 1) = 831.50
Gas temperature increment; .g.56 = g.56 - g.55 = 2.69
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.56 = 425 (Jkg-1) + 7.7310-1 (Jkg-1)  m.55 - 1.6910-3 (Jkg-1)  m.55
2+ 2.2210-6 (Jkg-1)  m.55
3
ca.56 = 597.5 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.56 = Cp  p / (ca.56  s)  dp  SF = 0.32
Increase of temeperature (3-1-2, exp. 4.27)
.m.56 = max(p  SF/(dp  ca.56  s)  (g.56 - m.55) / ( 1 + storage.56 / 3)  t - (exp(storage.56/10) -1)  .g.56, 0)
.m.56 = 5.62
Member temperature; m.56 = m.55+.m.56 = 387.89
Iteration 57
Time; t57 = t56+t = 28.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.57 = 20 + 345  log(8 t57/(1 min) + 1) = 834.14
Gas temperature increment; .g.57 = g.57 - g.56 = 2.64

22. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.57 = 425 (Jkg-1) + 7.7310-1 (Jkg-1)  m.56 - 1.6910-3 (Jkg-1)  m.56
2+ 2.2210-6 (Jkg-1)  m.56
3
ca.57 = 600.1 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.57 = Cp  p / (ca.57  s)  dp  SF = 0.32
Increase of temeperature (3-1-2, exp. 4.27)
.m.57 = max(p  SF/(dp  ca.57  s)  (g.57 - m.56) / ( 1 + storage.57 / 3)  t - (exp(storage.57/10) -1)  .g.57, 0)
.m.57 = 5.56
Member temperature; m.57 = m.56+.m.57 = 393.45
Iteration 58
Time; t58 = t57+t = 29.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.58 = 20 + 345  log(8 t58/(1 min) + 1) = 836.74
Gas temperature increment; .g.58 = g.58 - g.57 = 2.59
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.58 = 425 (Jkg-1) + 7.7310-1 (Jkg-1)  m.57 - 1.6910-3 (Jkg-1)  m.57
2+ 2.2210-6 (Jkg-1)  m.57
3
ca.58 = 602.7 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.58 = Cp  p / (ca.58  s)  dp  SF = 0.32
Increase of temeperature (3-1-2, exp. 4.27)
.m.58 = max(p  SF/(dp  ca.58  s)  (g.58 - m.57) / ( 1 + storage.58 / 3)  t - (exp(storage.58/10) -1)  .g.58, 0)
.m.58 = 5.51
Member temperature; m.58 = m.57+.m.58 = 398.96
Iteration 59
Time; t59 = t58+t = 29.500 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.59 = 20 + 345  log(8 t59/(1 min) + 1) = 839.29
Gas temperature increment; .g.59 = g.59 - g.58 = 2.55
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.59 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.58 - 1.6910-3
(Jkg-1
)  m.58
2
+ 2.2210-6
(Jkg-1
)  m.58
3
ca.59 = 605.4 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.59 = Cp  p / (ca.59  s)  dp  SF = 0.31
Increase of temeperature (3-1-2, exp. 4.27)
.m.59 = max(p  SF/(dp  ca.59  s)  (g.59 - m.58) / ( 1 + storage.59 / 3)  t - (exp(storage.59/10) -1)  .g.59, 0)
.m.59 = 5.45
Member temperature; m.59 = m.58+.m.59 = 404.40
Iteration 60
Time; t60 = t59+t = 30.000 min
Gas temperature – (1-1-2, cl. 3.2.1(1)); g.60 = 20 + 345  log(8 t60/(1 min) + 1) = 841.80
Gas temperature increment; .g.60 = g.60 - g.59 = 2.51
Specific heat of steel - (3-1-2, cl. 3.4.1.2);
ca.60 = 425 (Jkg-1
) + 7.7310-1
(Jkg-1
)  m.59 - 1.6910-3
(Jkg-1
)  m.59
2
+ 2.2210-6
(Jkg-1
)  m.59
3

23. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
ca.60 = 608.0 J/kg
Heat storage – (3-1-2, cl. 4.2.5.2); storage.60 = Cp  p / (ca.60  s)  dp  SF = 0.31
Increase of temeperature (3-1-2, exp. 4.27)
.m.60 = max(p  SF/(dp  ca.60  s)  (g.60 - m.59) / ( 1 + storage.60 / 3)  t - (exp(storage.60/10) -1)  .g.60, 0)
.m.60 = 5.39
Member temperature; m.60 = m.59+.m.60 = 409.80
Critical temperature results
Critical temperature a,crit = 437
Time to reach critical temperature Tfire = 33.0 min

24. -
Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock
Mechanics, Foundation Engineering & Retaining
Structures.
Tel.: (+30) 210 5238127, 210 5711263-Fax:+30 210 4401717
Mobile: (+30) 6936425722
www.geodomisi.com - costas@sachpazis.info
Project: Steel Member Fire Resistance Design (EN1993)
In accordance with EN1993-1-2:2005 incorporating Corrigenda
December 2005, September 2006 and March 2009 and the
recommended values.
Job Ref. 0519025
www.geodomisi.com
info@geodomisi.com
Section
Civil & Geotechnical Engineering
Sheet no./rev. 1
Calc.
Dr. C. Sachpazis
Date
09 July 2023
Chk'd by Date App'd by Date
Required time of fire exposure Treq,fire = 30.0 min
Steel member temp. after fire exposure time a = 410
PASS - Critical temperature exceeds steel member temperature at required fire exposure time
Analysis and Design by
Dr. Costas Sachpazis
Civil Engineer
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock Mechanics,
Foundation Engineering & Retaining Structures.
Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461
- Mobile: (+30) 6936425722 & (+44) 7585939944,
www.geodomisi.com - costas@sachpazis.info