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

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

TitleYoung Modulus [Pa]Shear Modulus [Pa]Poisson RatioShear [Pa]Mass Density [kg/m^3]Tensile Strength [Pa]Yield Stress [Pa]
1..S2752.10e+1100.300007850.0000355.00e+6265.00e+6

Property “1..UKB 457x191x98”

PropertyValueProperty Shape
Type / ElementsBeam / 6
Material1..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”

DefinitionLoad TypeApplied OnValues
Force on NodeForceNodes: 4(0; -1050000; 0)

Load2..Axial 1400N”

DefinitionLoad TypeApplied OnValues
Force on NodeForceNodes: 4(1400000; 0; 0)

Constaint “1..fixed”

DefinitionCountDOF
Constraint on NodeNodes: 1Tx Ty Tz
Constraint on NodeNodes: 7Ty Rx Ry

Classificaton

Standard2..Eurocode 3 Member ChecksCheck7..Classificaton
Individual Load1..Axial 1400kNDirectionAll
SelectionAll Entities
LoadAlpha WebPhiLambda WebLimit1 WebLimit2 WebLimit3 WebWeb ClassClass
Individual Load ‘1..Axial 1400kN’1.0000-0.154735.754431.076035.784563.90122.00002.0000
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

Standard2..Eurocode 3 Member ChecksCheck11..Bending and Axial
Individual Load1..Axial 1400kNDirectionAll
Selection1..Eurocode3 Shapes
ExtremenReduced Resistance YReduced Resistance ZUf Reduced YUf Reduced ZAlphaBetaUf Combined
Minimum0.42100016.5422113.00.000.002.002.110.00
Maximum0.42100016.5422113.00.000.002.002.110.00
Absolute0.42100016.5422113.00.000.002.002.110.00

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.