I I

Eurocode 3 Table of design properties for flanged steel profiles (IPE, HEA, HEB, HEM)

Description:
Design aid - Table of design properties for flanged steel profiles (IPE, HEA, HEB, HEM) including profile dimensions, cross-section properties (area A, second moment of area I, elastic modulus Wel, plastic modulus Wpl), strength properties (elastic moment Mel, plastic moment Mpl, plastic shear Vpl), and buckling properties (section class, buckling curves)
According to:
EN 1993-1-1:2005+AC2:2009 Sections 6.2 & 6.3
Supported National Annexes:
Nationally Defined Parameters (NDPs) automatically filled for supported countries (left blank otherwise)
All Calculations
Input
Steel partial material safety factor for cross-section resistance in accordance with EN1993-1-1 §6.1 and the National Annex for the case of steel buildings, or the relevant parts of EN1993 for other types of structures. It affects the resistance of profiles in axial force, shear, bending.
Notation for flanged profiles according to EN1993-1-1
Notation for flanged profiles according to EN1993-1-1
Tables
Design properties of IPE profiles for S235 steel class (γM0 = 1.00, units = mm)
Profile dimensionsArea propertiesInertia properties about major axis y-yInertia properties about minor axis z-zTorsional & warping propertiesAxial force & shear resistanceBending major axis y-yBending minor axis z-zBuckling curveSection classification
Profile Drawing Depth
h
[mm]
Width
b
[mm]
Web thickness
tw
[mm]
Flange thickness
tf
[mm]
Root radius
r
[mm]
Weight
m
[kg/m]
Perimeter
P
[m]
Area
A
[mm2]
Shear area z-z
Av,z
[mm2]
(for η=1.2)
Shear area y-y
Av,y
[mm2]
Second moment of area
Iy
[×106 mm4]
Radius of gyration
iy
[mm]
Elastic section modulus
Wel,y
[×103 mm3]
Plastic section modulus
Wpl,y
[×103 mm3]
Second moment of area
Iz
[×106 mm4]
Radius of gyration
iz
[mm]
Elastic section modulus
Wel,z
[×103 mm3]
Plastic section modulus
Wpl,z
[×103 mm3]
Torsion constant
IT
[×103 mm4]
Torsion modulus
WT
[×103 mm3]
Warping constant
Iw
[×106 mm6]
Warping modulus
Ww
[×103 mm4]
Design plastic axial force resistance
Npl,Rd
[kN]
Design plastic shear force resistance z-z
Vpl,Rd,z
[kN]
Design plastic shear force resistance y-y
Vpl,Rd,y
[kN]
Design elastic bending moment resistance
Mel,Rd,y
[kNm]
Design plastic bending moment resistance
Mpl,Rd,y
[kNm]
Design elastic bending moment resistance
Mel,Rd,z
[kNm]
Design plastic bending moment resistance
Mpl,Rd,z
[kNm]
Buckling about major axis y-y Buckling about minor axis z-z Web in pure bending about major axis y-y Web in pure uniform compression Flanges in uniform compression due to axial force or bending moment
IPE80 dxf 80 46 3.8 5.2 5 6.00 0.328 764 358 478 0.8014 32.4 20.03 23.22 0.08489 10.5 3.691 5.818 6.727 1.770 115.1 135.2 179.62 48.53 64.91 4.71 5.46 0.87 1.37 a b 1 1 1
IPE100 dxf 100 55 4.1 5.7 7 8.10 0.400 1032 508 627 1.710 40.7 34.20 39.41 0.1592 12.4 5.789 9.146 11.53 2.812 342.1 266.8 242.60 68.99 85.07 8.04 9.26 1.36 2.15 a b 1 1 1
IPE120 dxf 120 64 4.4 6.3 7 10.4 0.475 1321 631 806 3.178 49.0 52.96 60.73 0.2767 14.5 8.646 13.58 16.89 3.839 872.0 483.4 310.44 85.55 109.41 12.45 14.27 2.03 3.19 a b 1 1 1
IPE140 dxf 140 73 4.7 6.9 7 12.9 0.551 1643 764 1007 5.412 57.4 77.32 88.34 0.4492 16.5 12.31 19.25 24.01 5.109 1951 808.2 386.01 103.69 136.68 18.17 20.76 2.89 4.52 a b 1 1 1
IPE160 dxf 160 82 5.0 7.4 9 15.8 0.623 2009 966 1214 8.693 65.8 108.7 123.9 0.6831 18.4 16.66 26.10 35.30 7.060 3889 1252 472.15 131.03 164.66 25.54 29.11 3.92 6.13 a b 1 1 1
IPE180 dxf 180 91 5.3 8.0 9 18.8 0.698 2395 1125 1456 13.17 74.2 146.3 166.4 1.009 20.5 22.16 34.60 47.23 8.911 7322 1882 562.76 152.65 197.55 34.39 39.11 5.21 8.13 a b 1 1 1
IPE200 dxf 200 100 5.6 8.5 12 22.4 0.768 2848 1400 1700 19.43 82.6 194.3 220.6 1.424 22.4 28.47 44.61 68.46 12.22 12746 2683 669.38 189.95 230.65 45.66 51.85 6.69 10.48 a b 1 1 1
IPE220 dxf 220 110 5.9 9.2 12 26.2 0.848 3337 1588 2024 27.72 91.1 252.0 285.4 2.049 24.8 37.25 58.11 89.82 15.22 22310 3874 784.21 215.47 274.61 59.22 67.07 8.75 13.66 a b 1 1 1
IPE240 dxf 240 120 6.2 9.8 15 30.7 0.922 3912 1914 2352 38.92 99.7 324.3 366.6 2.836 26.9 47.27 73.92 127.4 20.55 36680 5354 919.23 259.74 319.11 76.21 86.16 11.11 17.37 a b 1 1 1
IPE270 dxf 270 135 6.6 10.2 15 36.1 1.041 4595 2214 2754 57.90 112.3 428.9 484.0 4.199 30.2 62.20 96.95 157.1 23.80 69469 7974 1079.71 300.37 373.66 100.79 113.74 14.62 22.78 a b 1 2 1
IPE300 dxf 300 150 7.1 10.7 15 42.2 1.160 5381 2568 3210 83.56 124.6 557.1 628.4 6.038 33.5 80.50 125.2 197.5 27.82 124260 11520 1264.58 348.44 435.52 130.91 147.66 18.92 29.43 a b 1 2 1
IPE330 dxf 330 160 7.5 11.5 18 49.1 1.254 6261 3081 3680 117.7 137.1 713.1 804.3 7.881 35.5 98.52 153.7 275.9 36.79 196090 15490 1471.25 418.00 499.29 167.59 189.02 23.15 36.11 a b 1 2 1
IPE360 dxf 360 170 8.0 12.7 18 57.1 1.353 7273 3514 4318 162.7 149.5 903.6 1019 10.43 37.9 122.8 191.1 370.8 46.35 309370 21070 1709.14 476.73 585.85 212.36 239.50 28.85 44.91 a b 1 2 1
IPE400 dxf 400 180 8.6 13.5 21 66.3 1.467 8446 4269 4860 231.3 165.5 1156 1307 13.18 39.5 146.4 229.0 504.1 58.62 482890 27930 1984.89 579.27 659.39 271.76 307.18 34.41 53.82 a b 1 3 1
IPE450 dxf 450 190 9.4 14.6 21 77.6 1.605 9882 5085 5548 337.4 184.8 1500 1702 16.76 41.2 176.4 276.4 660.5 70.27 780970 37970 2322.29 689.85 752.74 352.43 399.92 41.46 64.95 a b 1 3 1
IPE500 dxf 500 200 10.2 16.0 21 90.7 1.744 11552 5987 6400 482.0 204.3 1928 2194 21.42 43.1 214.2 335.9 886.2 86.88 1235400 51280 2714.76 812.35 868.33 453.07 515.62 50.33 78.93 a b 1 3 1
IPE550 dxf 550 210 11.1 17.2 24 105.5 1.877 13442 7234 7224 671.2 223.5 2441 2787 26.68 44.5 254.1 400.5 1217 109.6 1861500 66890 3158.78 981.51 980.13 573.54 654.95 59.70 94.13 a b 1 4 1
IPE600 dxf 600 220 12.0 19.0 24 122.4 2.015 15598 8378 8360 920.8 243.0 3069 3512 33.87 46.6 307.9 485.6 1646 137.2 2814700 88510 3665.63 1136.76 1134.26 721.32 825.41 72.37 114.13 a b 1 4 1
Notes
  1. The design resistances of the profiles correspond to cross-section resistances reduced by the partial material factor γM0 in accordance with EN1993-1-1 §6.2.3(2), §6.2.4(2), §6.2.5(2), §6.2.6(2). The aforementioned design resistances do not take into account a) flexural buckling, b) lateral torsional buckling, c) interaction effects of axial force, shear force, bending moment, and d) interaction effects of biaxial bending. Therefore the presented cross-section resistances are indicative values applicable for special cases. In general the overall element resistance is smaller and must be verified according to the relevant clauses of EN1993-1-1 Section 6.
  2. Torsional properties (IT, WT) and warping properties (Iw, Ww) are accurate results obtained from finite element analysis of the cross-section and they are reproduced from Table 1 of the following scientific paper: M.Kraus & R. Kindmann, 'St. Venants Torsion Constant of Hot Rolled Steel Profiles and Position of the Shear Centre'. The notation is described in EN1993-1-3 Annex C.
  3. Cross-section classification for webs and flanges is presented in accordance with EN1993-1-1 Table 5.2 for the cases of pure bending without axial force and pure uniform compression without bending moment. For the case of combined bending moment and compressive axial force the section class has an intermediate value that may be equal or between the presented values.
Details

Design properties for flanged steel profiles (IPE, HEA, HEB, HEM) according to EN1993-1-1

Definition of the cross-section

For typical steel profiles (IPE, HEA, HEB, HEM) the geometric properties of the cross-section are defined in the following standards:

  • Geometry of IPE profiles: Euronorm 19 – 57, DIN 1025/5

  • Geometry of HEA profiles: Euronorm 53 – 62, DIN 1025/3

  • Geometry of HEB profiles: Euronorm 53 – 62, DIN 1025/2

  • Geometry of HEM profiles: Euronorm 53 – 62, DIN 1025/4

The geometric properties that fully define the cross-section are: total height h, flange width b, web thickness tw, flange thickness tf, and root radius r. The notation is defined in EN1993-1-1 §1.7 which is reproduced in the figure above.

Geometric properties

The basic geometric properties of the cross-section are calculated by using the fundamental relations of mechanics. The geometric quantities include the total area of the cross section A and the second moments of the area about the major axis Iy and about the minor axis Iz, where the orientation of the major axis of bending y-y and the minor axis of bending z-z is specified in EN1993-1-1 §1.7 which is reproduced in the figure above. The root fillets are taken into account in the calculated geometric properties. Due to symmetry the centroid of the cross-section (center of mass) as well as the shear center are located in the middle of the height and width.

Shear area

For shear load parallel to the web the shear area Av,z, for the case of rolled I and H sections, is specified in EN1993-1-1 §6.2.6(3) as:

Av,z = max( A - 2btf + (tw + 2r)tf , ηtwhw )

where according to EN1993-1-1 §5.1 the value of the coefficient η is assumed equal to η = 1.2 for steel grades up to and including S460 and hw = h - 2tf is the height of the web.

For shear load parallel to the flanges the corresponding shear area Av,y is not specified in EN1993-1-1 for the case of rolled I and H sections. In the provided tables the shear area Av,y is assumed equal to the sum of areas of the flanges only, which is a reasonable conservative assumption:

Av,y = 2btf

Elastic section modulus

The elastic section modulii Wel,y and Wel,z about the major axis y-y and the minor axis z-z respectively are calculated by dividing the second moment of the area Iy and Iz with the corresponding distance from the centroid to the most distant edge:

Wel,y = Iy / (h / 2)

Wel,z = Iz / (b / 2)

Plastic section modulus

The plastic section modulii Wpl,y and Wpl,z about the major axis y-y and the minor axis z-z respectively correspond to the maximum plastic bending moment when the axial force of the cross-section is zero and the stress profile is fully plastic. Due to symmetry when the full plastic bending stress profile is reached with zero axial force the section is divided into two parts separated by the axis of symmetry. The plastic section modulus corresponds to the sum of first moments of the area of the two halves about the major axis y-y and the minor axis z-z respectively.

Torsional and warping properties

For open thin-walled cross-sections the torsional constant IT, torsional modulus WT, warping constant Iw, and warping modulus Ww may be calculated according to the procedure described in EN1993-1-3 Annex C. The values presented in the tables for the torsional and warping properties are accurate results obtained from finite element analysis of the cross-section and they are reproduced from Table 1 of the following scientific paper: M.Kraus & R. Kindmann, 'St. Venants Torsion Constant of Hot Rolled Steel Profiles and Position of the Shear Centre'. The presented values take into account the actual thickness of the cross-section elements and the presence of the root fillets.

Design cross-section resistance

The design resistance of the cross-section for axial force, shear force, and bending moment are calculated in accordance with EN1993-1-1 §6.2. They correspond to the gross cross-section resistance reduced by the steel partial material safety factor for cross-section resistance γM0 that is specified in EN1993-1-1 §6.1 for buildings, or the relevant parts of EN1993 for other type of structures, and the National Annex.

The aforementioned design resistances do not take into account a) flexural buckling, b) lateral torsional buckling, c) interaction effects of axial force, shear force, bending moment, and d) interaction effects of biaxial bending. Therefore the presented cross-section resistances are indicative values applicable for special cases. In general the overall element resistance is smaller and must be verified according to the relevant clauses of EN1993-1-1 Section 6.

Design axial force resistance

The design plastic resistance of the cross-section in uniform tension is specified in EN1993-1-1 §6.2.3(2). The design plastic resistance of the cross-section in uniform compression for cross-section class 1, 2, 3 is specified in EN1993-1-1 §6.2.4(2). The aforementioned axial force resistances correspond to the gross cross-sectional area A and the steel yield stress fy:

Npl,Rd = Afy / γM0

Design shear force resistance

The design plastic shear resistance of the cross-section is specified in EN1993-1-1 §6.2.6(2). It corresponds to the relevant shear area Av,z or Av,y, for shear force along the axis z-z and y-y respectively, multiplied by the steel yield stress in pure shear fy / √3 corresponding to the yield criterion in EN1993-1-1 §6.2.1(5)::

Vpl,Rd,z = Av,z ⋅ ( fy / √3 ) / γM0

Vpl,Rd,y = Av,y ⋅ ( fy / √3 ) / γM0

Design elastic bending moment resistance

The design elastic bending moment resistance of the cross-section is specified in EN1993-1-1 §6.2.5(2). It corresponds to the relevant elastic section modulus Wel,y or Wel,z, for bending about the major axis y-y or about the minor axis z-z respectively, multiplied by the steel yield stress fy:

Mpl,Rd,y = Wel,yfy / γM0

Mpl,Rd,z = Wel,zfy / γM0

The elastic bending moment resistance is applicable for class 3 cross-sections. For class 4 cross-sections the effective cross-section properties must be defined that take into account the reduced effective widths of the compression parts of the cross-section as specified in EN1993-1-1 §6.2.2.5.

Design plastic bending moment resistance

The design plastic bending moment resistance of the cross-section is specified in EN1993-1-1 §6.2.5(2). It corresponds to the relevant plastic section modulus Wpl,y or Wpl,z, for bending about the major axis y-y or about the minor axis z-z respectively, multiplied by the steel yield stress fy:

Mpl,Rd,y = Wpl,yfy / γM0

Mpl,Rd,z = Wpl,zfy / γM0

The plastic bending moment resistance is applicable for class 1 or 2 cross-sections.

Cross-section class

The classification of cross-sections is specified in EN1993-1-1 §5.5. The role of the classification is to identify the extent to which the resistance and rotation capacity of the cross-section are limited by local buckling of its parts.

Four section classes are identified:

  • Class 1: Plastic bending moment resistance develops and plastic hinge develops with rotation capacity adequate for plastic analysis.

  • Class 2: Plastic bending moment resistance develops but the rotation capacity is limited by local buckling.

  • Class 3: Elastic bending moment resistance develops but local buckling prevents the development of plastic resistance.

  • Class 4: Elastic bending moment resistance cannot develop because local buckling occurs before the yield stress is reached at the extreme fiber. Effective widths are used to account for the effects of local buckling of compression parts.

The classification of the cross-section parts (flanges and web) is specified in EN1993-1-1 Table 5.2. The class of the compression part depends on its width c to thickness t ratio, adjusted by the factor ε that takes into account the value of the steel yield stress fy:

ε = (235 MPa / fy)0.5

In general the class of the compression part is more unfavorable when it is subjected to uniform compression, as compared to pure bending. Indicative classification of the flanges and webs of the steel profiles is presented for the characteristic cases of pure uniform compression and pure bending moment. In general the class may have an intermediate value if the stress profile of the compression part occurs from a combination of compressive axial force and bending moment. The classification of the total cross-section is determined by the class of its most unfavorable compression part, web or flange.

The examined width to thickness limits c / t for cross-section classification according to EN1993-1-1 Table 5.2 are presented below:

Width to thickness limits for cross-section classification according to EN1993-1-1 Table 5.2
Class Web Outstand Flanges
Web in pure compression Web in pure bending Flanges in pure compression due to
axial force or bending moment
Class 1 c / t ≤ 33ε c / t ≤ 72ε c / t ≤ 9ε
Class 2 c / t ≤ 38ε c / t ≤ 83ε c / t ≤ 10ε
Class 3 c / t ≤ 42ε c / t ≤ 124ε c / t ≤ 14ε

For the classification of the webs t = tw and c = h - 2tf - 2r.

For the classification of the outstand flanges t = tf and c = b / 2 - tw /2 - r.

Buckling curves

The appropriate buckling curve for rolled flanged sections is specified in EN1993-1-1 Table 6.2 depending on the aspect ratio h/b, the flange thickness tf, the steel yield stress fy, and the orientation of bending axis.