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
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
Loading...
error loading table!
Design properties of IPE profiles for S235 steel class (<i>&gamma;</i><sub>M0</sub> = 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
column 0column 1column 2column 3column 4column 5column 6column 7column 8column 9column 10column 11column 12column 13column 14column 15column 16column 17column 18column 19column 20column 21column 22column 23column 24column 25column 26column 27column 28column 29column 30column 31column 32column 33column 34column 35
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 resitance 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 indermediate 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 respectivelly 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 respectivelly 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 respectivelly.

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 in 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 resitance 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-sectionial 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 orienation of bending axis.