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

Title Young Modulus [MPa] Shear Modulus [MPa] Poisson Ratio Shear [MPa] Mass Density [t/mm^3] Tensile Strength [MPa] Yield Stress [MPa]
1..S355 2.10e+5 0 0.3000 0 7.850e-09 455.0 355.0

Property “1..RHS 200x100x16”

Property Value Property Shape
Type / Elements Beam / 30
Material 1..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”

Definition Load Type Applied On Values
Force on Node Force Nodes: 42, 53 (0; -58000; 0)

Load “2..Axial = 90kN”

Definition Load Type Applied On Values
Force on Node Force Nodes: 64 (-90000; 0; 0)

Constraint “1..fixed”

Definition Count DOF
Constraint on Node Nodes: 22 Tx Ty Tz Rx
Constraint on Node Nodes: 64 Ty Tz Rx

Cross-section classification

Check [S2] 6..Flange Classification
Property Epsilon Lambda Flange Limit1 Limit2 Limit3 Class
1..RHS 200 x 100 x 16 0.81 3.25 26.85 30.92 34.17 1.0000

Check [S2] 7..Classificaton Load Set LS1..Shear + Axial
Selection Beam Member 2
Components Alpha Web Phi Lambda Web Limit1 Web Limit2 Web Limit3 Web Web Class Class
Beam Member 2 0.52 -0.93 9.5000 55.18 63.54 94.88 1.00 1.00

Compresson resistance

Check [S2] 9..Axial Check Load Set LS1..Shear + Axial
Selection Beam Member 2
Components Axial Force [KN] Design Tension Resistance [KN] Design Compression Resistance [KN] Design Resistance [KN] Utilization Factor
Beam Member 2 -90.0 2946.5 2946.5 2946.5 0.03

Bending resistance

Check [S2] 10..Bending Check Individual Load IL1..Shear Y = -58kN.fixed
Selection Beam Member 2
Components Bending Moment Y [KN mm] Bending Moment Z [KN mm] Bending Moment Resistance Y [KN mm] Bending Moment Resistance Z [KN mm] Utilization Factor Y Utilization Factor Z Utilization Factor
Beam Member 2 0.0e+3 -139.2e+3 103.0e+3 174.3e+3 0.00 0.80 0.80

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

6..User Plastic Section Modulus Y

Property Value
Type Property ‘6..User Plastic Section Modulus Y’
Alias WplYUser
1..RHS 200 x 100 x 16 290000

7..User Plastic Section Modulus Z

Property Value
Type Property ‘7..User Plastic Section Modulus Z’
Alias WplZUser
1..RHS 200 x 100 x 16 491000

Shear Resistance

Check [S2] 8..Shear Check Load Set LS1..Shear + Axial
Selection Beam Member 2
Components Shear Force Y [KN] Shear Force Z [KN] Shear Force Y Resistance [KN] Shear Force Z Resistance [KN] Utilization Factor Y Utilization Factor Z Utilization Factor YieldReduced [MPa]
Beam Member 2 0.0 58.0 567.1 1134.1 0.00 0.05 0.05 355.0

Buckling resistance in compression

Check [S2] 12..Buckling Compression Load Set LS1..Shear + Axial
Selections 2
Components Ncr_y [KN] Ncr_z [KN] Lambda Y Lambda Z Fy Fz Xi_Y Xi_Z Nb Rd Y [KN]
Beam Member 2 4127.2 1470.5 0.8449 1.4155 0.92 1.63 0.77 0.41 2266.0

Check [S2] 12..Buckling Compression Load Set LS1..Shear + Axial
Selections 2
Components Lambda Y Lambda Z Fy Fz Xi_Y Xi_Z Nb Rd Y [KN] Nb Rd Z [KN]
Beam Member 2 0.8449 1.4155 0.92 1.63 0.77 0.41 2266.0 1209.2

Check [S2] 12..Buckling Compression Load Set LS1..Shear + Axial
Selections 2
Components Lambda Y Lambda Z Fy Fz Xi_Y Xi_Z Nb Rd Y [KN] Nb Rd Z [KN]
Beam Member 2 0.8449 1.4155 0.92 1.63 0.77 0.41 2266.0 1209.2

Member buckling resistance in buckling

Check [S2] 14..Lateral torsional buckling Individual Load IL1..Shear Y = -58kN.fixed
Selection Beam Member 2
Components L_LT [mm] C1 Gm Mcr [KN mm] Lambda_LT X_LT Mb_Rd [KN mm] Uf b
Beam Member 2 2400.000 1.000 80769.23 3152.9e+3 0.235 0.973 169.5e+3 0.82

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.