# Influence of Slip of Standardized Joints in Steel Structures

### Technical Article

DIN EN 1993-1-8 [3] provides a model for the calculation as well as the classification of the connection stiffness and manages the resulting modeling of the semi-rigid joint in the structural model.

In practice, bending-resistant connections are usually defined as rigid in the determination of internal forces or in the structural model. The moment-rotation characteristics of the connection is thus not considered in the determination of internal forces. In most cases, it has to be, however, considered, depending on the stiffness of the structure, according to the standards in structural analysis.

In the following, the effect of the slip of the connection on the design results of frame structures will be shown in an example.

#### Structure

It is about a two-hinged frame with a span of 15.0 m and a height of 6.0 m plus 0.8 m attic.

For the first design step with rigid connections, the cross-sections as shown in Figure 01 are applied. Structural steel S235 according to DIN EN 1993-1-1 [2] will be used.

Figure 01 - Structure for the First Design Step and the Selected Connection

#### Loading

It will be calculated with the following simplified load assumptions:- Load width (distance from the fram) = 5.00 m
- Self-weight roof structure g = 0.40 kN/m²
- Snow load s = 1.30 kN/m²
- Wind load walls w = 0.60 kN/m² (c
_{p}= 0.8 snd -0.5) - Imperfections (in the frame plane) according to DIN EN 1993-1-1

#### Design ULS with Rigid Frame Joint

The calculation of the internal forces in the frame plane is performed according to the second-order analysis and with imperfections (inclination and precamber). The enveloping of the internal force M_{y }is shown in Figure 02.

Figure 02 - Enveloping of the Internal Force My with Rigid Connection

For the beam design with RF-/STEEL EC3, a lateral and torsional restraint at the member ends and a lateral support of the upper chord is applied at one-third division points.

The design of the frame joint is performed with RF-/JOINTS Steel - DSTV. The type IH3.1 and M20 will be used. With the existing internal forces, no design of the connection according to [1] is possible.

Figure 03 - Design of the Connection with RF-/JOINTS Steel - DSTV

Therefore, the beam section has to be increased to IPE 500 and the connections have to be selected as shown in Figure 01 to analyze the serviceability limit state.

#### Design ULS with Semi-Rigid Frame Joint

The requirement to consider the moment-rotation characteristics in structural analysis results from the classification of the connection according to DIN EN 1993-1-8.

For a movable frame, the classification "deformable" applies if:

$\frac12\;\cdot\;{\mathrm S}_\mathrm{Structure}\;<\;{\mathrm S}_{\mathrm j,\mathrm{ini}}\;<\;25\;\cdot\;{\mathrm S}_\mathrm{Structure}$

For the currently designed connection IH 3.1 E 50 20 6xM20 10.9 (see Figure 01) without stiffener and the column HE-B 240, this results in:

${\mathrm S}_{\mathrm j,\mathrm{ini}}\;=\;72,270\;\mathrm{kNm}/\mathrm{rad}$

The stiffness of the structure is calculated according to EN 1993-1-8 Section 5.2.2.5 as follows:

${\mathrm S}_\mathrm{Structure}\;=\;\frac{\mathrm E\;\cdot\;{\mathrm I}_\mathrm b}{{\mathrm L}_\mathrm b}\;=\:\frac{21,000\;\mathrm{kN}/\mathrm{cm}²\;\cdot\;48,200\;\mathrm{cm}^4}{1,500\;\mathrm{cm}}\;=\;6,748\;\mathrm{kNm}/\mathrm{rad}$

The connection can thus be classified as deformable:

3,374 kNm/rad < S_{ini} = 72,270 kNm/rad < 168,700 kNm/rad

Due to the redistribution of internal forces to be expected to the moment of span, a calculation and design with the original IPE 450 can be tried again.

The calculation of the internal forces in the frame plane is again performed according to the second-order analysis and with imperfections (inclination and precamber) as well as in consideration of the moment-rotation characteristics of the connection. The application is carried out according to DIN EN 1993-1-8 Sec. 5.1.2.(4), simplified with a linear rotational spring with S_{j,ini}/2. The enveloping of the internal force My is shown in Figure 04.

Figure 04 - Enveloping of the Internal Force My with Semi-Rigid Connection

Due to the consideration of the rotation stiffness, it results in a reduction of the corner moments of about 10 %. The design of the connection with RF-/JOINTS Steel - DSTV results in a positive design for the type IH 3.1 E 45 20 6xM20 8.8. The original section IPE 450 can be also designed as sufficiently resistant (see Figure 05).

Figure 05 - Design of Beam and Connection

#### Design SLS with Rigid Frame Joint

Only the design of the horizontal deformation of the frame will be performed here. The limit value is defined with w_{h,max} = h / 150 = 680 / 150 = 4.53 cm.

Due to the smaller load level for the SLS, it can be assumed that the moments are below 2/3 M_{j,Ed }and therefore, the elastic initial stiffness of the connection can be applied for the deformation analysis. It is possible to do this via the modification of the stiffness for the relevant load combinations in the calculation parameters (see Figure 06).

Figure 06 - Calculation Parameters - Modify Stiffness for LCs in SLS - Characteristic

By applying S_{j,ini}, it results in deformations in x-direction of 4.73 cm (see Figure 07).

Figure 07 - Enveloping of Deformations in X-Direction

The design is thus as follows:

w_{ex} / W_{h,max} = 4.73 / 4.53 = 1.04

#### Conclusion

The consideration of the moment-rotation characteristics of the connection results in a more realistic display of the structure and a more economical design with a saving of material of about 10 % in this example.

Furthermore, for the serviceability limit state design in the sense of an economical design, it is necessary to apply the elastic initial stiffness for the respective load comnbinations when performing the defomation analysis.

#### Keywords

slip connections dstv stiffness