Eurocode 3. Example 6.6: Cross-section 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 1993-1-1.

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 cross-sectional 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

\(h = 467.2 mm\) \(b = 192.8 mm\) \(t_{w} \ = 11.4 mm\) \(t_{f} \ = 19.6 mm\) \(r = 10.2 mm\) \(A \ = 12 500 mm^{2}\) \(W_{pLy} \ = 2 230 000 mm^{3}\)

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]	2.346e-05
I2, [m^4]	4.533e-04
I12, [m^4]	0
Torsion Constant, [m^4]	1.160e-06
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

Cross-section 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 cross-section 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 cross-sectional 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.