### Description

The objective of this study is verification of bolted portal frame eaves connection, as shown in Fig. 9.2.1. Rafter is bolted using end plate on the column flange. The column is stiffened with two horizontal stiffeners in levels of the beam flanges. Compressed plates, e.g. horizontal stiffeners of column, web panel in shear or compression, and compressed beam flange, are designed as cross-section class 3. Horizontal beam is 6 m long loaded by continuous load over the entire length.

*Fig. 9.2.1 Bolted portal frame eaves connection*

### Analytical model

Eight components are examined: fillet weld, web panel in shear, column web in transverse compression, column web in transverse tension, beam flange in compression and tension, column flange in bending, end plate in bending, and bolts. All components are designed according to EN 1993-1-8:2005. Design loads of components depend on the position. The web panel in shear is loaded by design loads on the vertical axis of the column. Other components are loaded by reduced design loads in column flange to which horizontal beam is connected.

#### Fillet weld

The weld is closed around the whole cross-section of the beam. The thickness of the weld on the flanges can differ from the thickness of the weld on the web. Vertical shear force is transferred only by welds on the web and plastic stress distribution is considered. Bending moment is transferred by whole weld shape, and elastic stress distribution is considered. Effective weld width depending on the horizontal stiffness of the column is considered (because of bending of the unstiffened column flange). Design of the weld is done according to EN 1993-1-8:2005, Cl. 4.5.3.2(6). The assessment is carried out in two major points: on the upper or lower edge of the flange (maximum bending stress) and in the crossing of the flange and the web (combination of shear force and bending moment stresses).

#### Web panel in shear

The thickness of the column web is designed to be third class at most; see EN 1993-1-8:2005, Cl. 6.2.6.1(1). Two contributions to the load capacity are considered: resistance of the column wall in shear and the contribution from the frame behavior of the column flanges and horizontal stiffeners; see EN 1993-1-8:2005, Cl. 6.2.6.1 (6.7 and 6.8).

#### Column web in transverse compression or tension

Effect of the interaction of the shear load is considered; see EN 1993-1-8:2005, Cl. 6.2.6.2 and Tab. 6.3. Influence of longitudinal stress in the wall of the column is considered; see EN 1993-1-8:2005, Cl. 6.2.6.2(2). Horizontal stiffeners prevent buckling and are included in the load capacity of this component with the effective area.

#### Beam flange in compression

The horizontal beam is designed to be maximally third class.

#### Column flange or end plate in bending

Effective lengths for circular and noncircular failures are considered according to EN 1993-1-8:2005, Cl. 6.2.6. Three modes of collapse according to EN 1993-1-8:2005, Cl. 6.2.4.1 are considered.

#### Bolts

Bolts are designed according to EN 1993-1-8:2005, Cl. 3.6.1. Design resistance considers punching shear resistance and rupture of the bolt.

### Numerical design model

T-stub is modeled by 4-node shell elements as described in Chapter 3 and summarized further. Every node has 6 degrees of freedom. Deformations of the element consist of membrane and flexural contributions. Nonlinear elastic-plastic material status is investigated in each layer of integration point. Assessment is based on the maximum strain given according to EN 1993-1-5:2006 by value of 5 %. Bolts are divided into three sub-components. The first is the bolt shank, which is modeled as a nonlinear spring and caries tension only. The second sub-component transmits tensile force into the flanges. The third sub-component solves shear transmission.

### Global behavior

Comparison of the global behavior of the joint, described by moment-rotation diagrams for both design procedures mentioned above, was done. Attention was focused on the main characteristics of the moment-rotation diagram: initial stiffness, design resistance, and deformation capacity. Beam IPE 330 is connected to column HEB 300 using extended end plate with 5 rows of the bolts M24 8.8. The results of both design procedures are shown in the graph in Fig. 9.2.2 and in Tab. 9.2.1. CM generally gives higher initial stiffness compared to CBFEM. CBFEM gives slightly higher design resistance compared to CM in all cases, as shown in Chapter 9.2.5. The difference is up to 10%. Deformation capacity is also compared. Deformation capacity was calculated according to (Beg et al. 2004) because EC3 provides limited background for deformation capacity of endplate joints.

*Fig. 9.2.2 Moment-rotation diagram*

*Tab. 9.2.1 Global behavior overview*

CM | CBFEM | CM/CBFEM | ||

Initial stiffness | [kNm/rad] | 67400 | 112000 | 0,60 |

Design resistance | [kNm] | 204 | 199 | 0,98 |

Deformation capacity | [mrad] | 242 | 47 | 5,14 |

### Verification of resistance

Design resistance calculated by CBFEM was compared with the results of the component method in the next step. The comparison was focused on the resistance and also the critical component. The study was performed for the column cross-section parameter. Beam IPE 330 is connected to the column by extended endplate with 5 bolt rows. Bolts M24 8.8 are used. The dimensions of the end plate P15 with bolt end distances and spacing in millimeters are the height 450 (50-103-75-75-75-73) and the width 200 (50-100-50). The outer edge of the upper flange is 91 mm from the edge of the end plate. Beam flanges are connected to the end plate with welds with the throat thickness of 8 mm. The beam web is connected with the weld throat thickness of 5 mm. The column is stiffened with horizontal stiffeners opposite to beam flanges. The Stiffeners are 15 mm thick, and their width corresponds to the column width. The thickness of the end plate stiffener is 10 mm, and its width is 90 mm. The results are shown in Tab. 9.2.2 and Fig. 9.2.3.

*Tab. 9.2.2 Design resistance for parameter – column profile*

Column cross section | CM | CBFEM | CM/ CBFEM | ||

Resistance | Component | Resistance | Component | ||

[kNm] | [kNm] | ||||

HEB 200 | 107 | Column web in shear | 106 | Column web in shear | 1,01 |

HEB 220 | 121 | Column web in shear | 136 | Column web in shear | 0,89 |

HEB 240 | 143 | Column web in shear | 155 | Column web in shear | 0,92 |

HEB 260 | 160 | Column web in shear | 169 | Column web in shear | 0,95 |

HEB 280 | 176 | Column web in shear | 187 | Column web in shear | 0,94 |

HEB 300 | 204 | Column web in shear | 199 | Beam flange in tension/compression | 0,98 |

HEB 320 | 222 | Column web in shear | 225 | Beam flange in tension/compression | 0,99 |

HEB 340 | 226 | Beam flange in tension/compression | 242 | Beam flange in tension/compression | 0,93 |

HEB 360 | 229 | Beam flange in tension/compression | 239 | Beam flange in tension/compression | 0,96 |

HEB 400 | 234 | Beam flange in tension/compression | 253 | Beam flange in tension/compression | 0,92 |

HEB 450 | 241 | Beam flange in tension/compression | 260 | Beam flange in tension/compression | 0,93 |

HEB 500 | 248 | Beam flange in tension/compression | 268 | Beam flange in tension/compression | 0,93 |

*Fig. 9.2.3 Design resistance depending on column cross-section*

To illustrate the accuracy of the CBFEM model, the results of the parametric studies are summarized in the graph comparing resistances predicted by CBFEM and by CM; see Fig. 9.2.4. The results show that CBFEM provides slightly higher design resistance compared to CM in nearly all cases. The difference between both methods is up to 10%.

*Fig. 9.2.4 Verification of CBFEM to CM*

### Benchmark example

**Inputs**

- Steel S235
- Beam IPE 330
- Column HEB 300
- End plate height
*h*_{p}= 450 (50-103-75-75-75-73) mm - End plate width
*b*_{p}= 200 (50-100-50) mm - End plate P15
- Column stiffeners 15 mm thick and 300 mm wide
- End plate stiffener 10 mm thick, 90 mm width and depth, chamfers 20 mm
- Flange weld throat thickness
*a*_{f}= 8 mm - Web and end plate stiffener weld throat thickness
*a*_{w}= 5 mm - Bolts M24 8.8

**Outputs**

- Design resistance in bending
*M*_{Rd}= 206 kNm - Corresponding vertical shear force
*V*_{Ed}= –206 kN - Collapse mode: yielding of the beam stiffener on upper flange
- Utilization of the bolts 90,2 %
- Utilization of the welds 99,0 %