Help >

Benchmark 21: ECCS N°119 Worked Example 5

Project file: Benchmark_(EC_EN_1993)_21.esa

SCIA Engineer Version R18.1

Introduction

This benchmark concerns Worked Example 5 of ECCS N°119 Rules for Member Stability in EN 1993-1-1, Background documentation and design guidelines, ECCS, 2006.

This fifth worked example deals with spatial behaviour. The beam-column is subjected to compression and biaxial bending. The transverse loading is assumed to act through the shear center. Lateral torsional buckling is a potential mode of failure according to the shape of the cross-section.

The interaction factors k_ij for combined bending and compression are determined using both alternative method 1 (Annex A) and alternative method 2 (Annex B).

Reference Results

The reference gives following results:

Classification:

Flanges
c/t_f	4,6
Class 1 limit	9,0
=> Flanges Class 1

Web
c/t_w	41,8
Class 1 limit	45,6
=> Web Class 1

Compression resistance
N_c,Rd	2715 kN

Bending resistance
M_c,y,Rd	516 kNm
M_c,z,Rd	78,9 kNm

Shear resistance
A_v,z	5990 mm²
V_pl,z,Rd	814 kN
A_v,y	6718 mm²
V_pl,y,Rd	912 kN
Shear buckling does not need to be considered

Resistance to combined bending, shear and axial force
M_y,N,V,Rd	516 kNm
M_z,N,V,Rd	78,9 kNm
α	2
β	1

Member buckling resistance in compression
N_cr,y	71038 kN	N_cr,z	3157 kN
Relative slenderness λ_y	0,195	Relative slenderness λ_z	0,927
α_y	0,21	α_z	0,34
χ_y	1,00	χ_z	0,644

Member buckling resistance in bending (General)
C₁	1,2
M_cr	1079 kNm
Relative slenderness λ_LT	0,691
Alpha_LT	0,34
Chi_LT	0,789
k_c	0,907
f	0,955
Chi_LT,mod	0,826

Member buckling resistance in bending (Rolled)
Relative slenderness λ_LT	0,697
α_LT	0,49
χ_LT	0,827
k_c	0,907
f	0,954
χ_LT,mod	0,867

Verification according to Method 1
μ_y	1,00
w_y	1,138
μ_z	0,937
w_z	1,5
C_my,0	0,999
C_my	1,00
C_mz,0	0,771
C_mz	0,771
M_cr,0	899 kNm
λ₀	0,757
a_LT	0,998
b_LT	0,043
c_LT	0,468
d_LT	0,347
e_LT	0,719
C_yy	0,981
C_yz	0,863
C_zy	0,843
C_zz	1,014
eq. (6.61)	0,964
eq. (6.62)	0,870

Verification according to Method 2
C_my	0,925
C_m,LT	0,925
C_mz	0,6
k_yy	0,924
k_yz	0,489
k_zy	0,961
k_zz	0,815
eq. (6.61)	0,752
eq. (6.62)	0,974

SCIA Engineer results

Verification according to Method 1:

Verification according to Method 2:

Comments

The results correspond to the benchmark results.
The classification in the Reference uses for the stability checks class 1 determined from the section checks. SCIA Engineer uses for the stability checks the most negative class along the member (Class 3) but this has been manually modified to class 1 in order to have the same classification as the Reference.
There are some small round-off differences between the cross-section properties. In SCIA Engineer the cross-section according to the Arcelor catalogue has been used.
The reference calculates a wrong value for the shear area in the shear resistance check. The result shown above for the shear area is that corrected by manual calculation.
In the verification according to method 1, the reference uses the ‘General Case’ for LTB. However, the reference also applies the reduction factor f to calculate Chi_LT,mod in this case. In EN 1993-1-1 this reduction is only specified for the ‘Rolled sections and equivalent welded sections Case’ and not for the ‘General Case’. Due to the differences in the LTB reduction factor, the eventual verification formulas have differences.
In the verification according to method 1, both the reference and SCIA Engineer use the modified formula for calculation of C_zz.as given in correction sheet EN 1993-1-1:2005/AC:2009.

SCIA web

Downloads

SCIA is part of the Nemetschek group

Open topic with navigation