Eurocode 3. Example 6.6: Crosssection resistance under combined bending and compression
In this article we compare the resistance under combined bending and compression according to SDC Verifier and Designer’s Guide to Eurocode3: Design of steel buildings EN 199311.
All results are generated with SDC Verifier 4.5 and calculated with FEMAP v11.3.1
Task:
A member is to be designed to carry a combined major axis bending moment and an axial force. In this example, a crosssectional check is performed to determine the maximum bending moment that can be carried by a UKB 457 x 191 x 98 in grade S275 steel, in the presence of an axial force of 1400 kN.
Figure 6.15. Section properties for a 457 × 191 × 98 UKB

Solution:
Model
Materials
Title  Young Modulus [Pa]  Shear Modulus [Pa]  Poisson Ratio  Shear [Pa]  Mass Density [kg/m^3]  Tensile Strength [Pa]  Yield Stress [Pa] 

1..S275  2.10e+11  0  0.3000  0  7850.0000  355.00e+6  265.00e+6 
Property “1..UKB 457x191x98”
Property  Value  Property Shape 

Type / Elements  Beam / 6  
Material  1..S275  
Mass [kg]  137.4  
Gravity Center [m]  [0.70; 0.00; 0.00]  
Area, [m^2]  0.0125  
I1, [m^4]  2.346e05  
I2, [m^4]  4.533e04  
I12, [m^4]  0  
Torsion Constant, [m^4]  1.160e06  
Y Shear Area, [m^2]  0.0081  
Z Shear Area, [m^2]  0.0051  
Nonstructural Mass, [kg]  0  
Perimeter, [m]  1.68  
Warping Constant, [m^6]  0  
Y Neutral Axis Offset A, [m]  0  
Z Neutral Axis Offset A, [m]  0  
h [m]  0.467  
wt [m]  0.193  
wb [m]  0.193  
tf2 [m]  0.020  
tw [m]  0.011  
tf1 [m]  0.020 
Boundary Conditions
Load “1..Shear Y = 1050kN”
Definition  Load Type  Applied On  Values 

Force on Node  Force  Nodes: 4  (0; 1050000; 0) 
Load “2..Axial 1400N”
Definition  Load Type  Applied On  Values 

Force on Node  Force  Nodes: 4  (1400000; 0; 0) 
Constaint “1..fixed”
Definition  Count  DOF 

Constraint on Node  Nodes: 1  Tx Ty Tz 
Constraint on Node  Nodes: 7  Ty Rx Ry 
Classificaton
Standard  2..Eurocode 3 Member Checks  Check  7..Classificaton 
Individual Load  1..Axial 1400kN  Direction  All 
Selection  All Entities 
Load  Alpha Web  Phi  Lambda Web  Limit1 Web  Limit2 Web  Limit3 Web  Web Class  Class 

Individual Load ‘1..Axial 1400kN’  1.0000  0.1547  35.7544  31.0760  35.7845  63.9012  2.0000  2.0000 
Crosssection classification under pure compression (clause 5.5.2)
\(\varepsilon =\sqrt{235/f_{y}} \ =\sqrt{235/265} \ =0.94\)
Outstand flanges (Table 5.2, sheet 2):
\(c_{f} \ = (b – t_{w} – 2r)/2 \ = 80.5 mm\)
\(c_{f}/t_{f} \ = 80.5/19.6 = 4.11\)
Limit for Class 1 flange = 9ε = 8.48
8.48 > 4.11 ∴ flange is Class 1
Web — internal part in compression (Table 5.2, sheet 1):
\(c_{w} \ = h – 2t_{f} – 2r \ = 407.6 mm\)
\(c_{w}/t_{w} \ = 407.6/11.4 = 35.75\)
Limit for Class 2 web = 38ε = 35.78
35.78 > 35.75 ∴ web is Class 2
Under pure compression, the overall crosssection classification is therefore Class 2 . Consequently, unlike Example 5.1, nothing is to be gained by using the more complex approach of considering the actual stress distribution.
11..Bending and Axial
Standard  2..Eurocode 3 Member Checks  Check  11..Bending and Axial 
Individual Load  1..Axial 1400kN  Direction  All 
Selection  1..Eurocode3 Shapes 
Extreme  n  Reduced Resistance Y  Reduced Resistance Z  Uf Reduced Y  Uf Reduced Z  Alpha  Beta  Uf Combined 

Minimum  0.42  100016.5  422113.0  0.00  0.00  2.00  2.11  0.00 
Maximum  0.42  100016.5  422113.0  0.00  0.00  2.00  2.11  0.00 
Absolute  0.42  100016.5  422113.0  0.00  0.00  2.00  2.11  0.00 
Conclusion
In order to satisfy the crosssectional checks of clause 6.2.9, the maximum bending moment that can be carried by a 457 x 191 x 98 UKB in grade S275 steel, in the presence of an axial force of 1400 kN is 425.3 kN m .
For class 2 elements in calculation take into account fillets. In shapes fillets are skipped and it gives the difference of 0.007% in results.
Check other comparation of Eurocode3 design examples standard and SDC Verifier.