Eurocode 3. Example 6.9: Member resistance under combined major axis bending and axial compression

In this article we compare the resistance under combined major axis bending and axial 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 5.3 and calculated with FEMAP v2019.1.

Task:

A rectangular hollow section (RHS) member is to be used as a primary floor beam of 7.2 m span in a multi-storey building. Two design point loads of 58 kN are applied to the primary beam (at locations B and C) from secondary beams, as shown in Figure 6.27. The secondary beams are connected through fin plates to the webs of the primary beam, and full lateral and torsional restraint may be assumed at these points. The primary beam is also subjected to a design axial force of 90 kN.
Assess the suitability of a hot-rolled 200 100 16 RHS in grade S355 steel for this application.

Solution:

Model

Materials

TitleYoung Modulus [MPa]Shear Modulus [MPa]Poisson RatioShear [MPa]Mass Density [t/mm^3]Tensile Strength [MPa]Yield Stress [MPa]
1..S3552.10e+500.300007.850e-09455.0355.0

Property “1..RHS 200x100x16”

PropertyValueProperty Shape
Type / ElementsBeam / 30
Material1..S355
Mass [t]0.5
Gravity Center [mm][3600.00; 0.00; 10.00]
Area, [mm^2]8300.0000
I1, [mm^4]11470000.00
I2, [mm^4]36780000.00
I12, [mm^4]0
Torsion Constant, [mm^4]29820000.00
Y Shear Area, [mm^2]2150.1420
Z Shear Area, [mm^2]5779.1710
Nonstructural Mass, [t]0
Perimeter, [mm]600.00
Warping Constant, [mm^6]0
Y Neutral Axis Offset A, [mm]0
Z Neutral Axis Offset A, [mm]0
h [mm]200.000
w [mm]100.000
t [mm]16.000

Boundary Conditions

Load “1..Shear Y = -58kN”

DefinitionLoad TypeApplied OnValues
Force on NodeForceNodes: 42, 53(0; -58000; 0)

Load “2..Axial = 90kN”

DefinitionLoad TypeApplied OnValues
Force on NodeForceNodes: 64(-90000; 0; 0)

Constraint “1..fixed”

DefinitionCountDOF
Constraint on NodeNodes: 22Tx Ty Tz Rx
Constraint on NodeNodes: 64Ty Tz Rx

Cross-section classification

Check[S2] 6..Flange Classification
PropertyEpsilonLambda FlangeLimit1Limit2Limit3Class
1..RHS 200 x 100 x 160.813.2526.8530.9234.171.0000

Check[S2] 7..ClassificatonLoad SetLS1..Shear + Axial
SelectionBeam Member 2
ComponentsAlpha WebPhiLambda WebLimit1 WebLimit2 WebLimit3 WebWeb ClassClass
Beam Member 20.52-0.939.500055.1863.5494.881.001.00

Compresson resistance

Check[S2] 9..Axial CheckLoad SetLS1..Shear + Axial
SelectionBeam Member 2
ComponentsAxial Force [KN]Design Tension Resistance [KN]Design Compression Resistance [KN]Design Resistance [KN]Utilization Factor
Beam Member 2-90.02946.52946.52946.50.03

Bending resistance

Check[S2] 10..Bending CheckIndividual LoadIL1..Shear Y = -58kN.fixed
SelectionBeam Member 2
ComponentsBending Moment Y [KN mm]Bending Moment Z [KN mm]Bending Moment Resistance Y [KN mm]Bending Moment Resistance Z [KN mm]Utilization Factor YUtilization Factor ZUtilization Factor
Beam Member 20.0e+3-139.2e+3103.0e+3174.3e+30.000.800.80

Note: Section Plastic Modulus in SDC Verifier was adjusted using characteristic to match the section with fillets:

6..User Plastic Section Modulus Y

PropertyValue
TypeProperty ‘6..User Plastic Section Modulus Y’
AliasWplYUser
1..RHS 200 x 100 x 16290000

7..User Plastic Section Modulus Z

PropertyValue
TypeProperty ‘7..User Plastic Section Modulus Z’
AliasWplZUser
1..RHS 200 x 100 x 16491000

Shear Resistance

Check[S2] 8..Shear CheckLoad SetLS1..Shear + Axial
SelectionBeam Member 2
ComponentsShear Force Y [KN]Shear Force Z [KN]Shear Force Y Resistance [KN]Shear Force Z Resistance [KN]Utilization Factor YUtilization Factor ZUtilization FactorYieldReduced [MPa]
Beam Member 20.058.0567.11134.10.000.050.05355.0

Buckling resistance in compression

Check[S2] 12..Buckling CompressionLoad SetLS1..Shear + Axial
Selections2
ComponentsNcr_y [KN]Ncr_z [KN]Lambda YLambda ZFyFzXi_YXi_ZNb Rd Y [KN]
Beam Member 24127.21470.50.84491.41550.921.630.770.412266.0

Check[S2] 12..Buckling CompressionLoad SetLS1..Shear + Axial
Selections2
ComponentsLambda YLambda ZFyFzXi_YXi_ZNb Rd Y [KN]Nb Rd Z [KN]
Beam Member 20.84491.41550.921.630.770.412266.01209.2

Check[S2] 12..Buckling CompressionLoad SetLS1..Shear + Axial
Selections2
ComponentsLambda YLambda ZFyFzXi_YXi_ZNb Rd Y [KN]Nb Rd Z [KN]
Beam Member 20.84491.41550.921.630.770.412266.01209.2

Member buckling resistance in buckling

Check[S2] 14..Lateral torsional bucklingIndividual LoadIL1..Shear Y = -58kN.fixed
SelectionBeam Member 2
ComponentsL_LT [mm]C1GmMcr [KN mm]Lambda_LTX_LTMb_Rd [KN mm]Uf b
Beam Member 22400.0001.00080769.233152.9e+30.2350.973169.5e+30.82

Note: SDC Verifier does not apply rule λ<= λLT0, in results the Utilization is higher on 2% (0.82 vs 0.8).

Combined bending and axial compression part is not compared because Example uses alternative method 1 (Annex A) and SDC Verifier uses alternative method 2 (Annex B).

Results for member resistance under combined major axis bending and axial compression in SDC Verifier match with results in example 6.9.

Check other comparation of Eurocode3 design examples standard and SDC Verifier.