# 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.