Influence of Slip of Standardized Joints in Steel Structures
Technical Article
DIN EN 199318 [3] provides a model for the calculation as well as the classification of the connection stiffness and manages the resulting modeling of the semirigid joint in the structural model.
In practice, bendingresistant connections are usually defined as rigid in the determination of internal forces or in the structural model. The momentrotation 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 twohinged 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 crosssections as shown in Figure 01 are applied. Structural steel S235 according to DIN EN 199311 [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
 Selfweight 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 199311
Design ULS with Rigid Frame Joint
The calculation of the internal forces in the frame plane is performed according to the secondorder 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 onethird 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 SemiRigid Frame Joint
The requirement to consider the momentrotation characteristics in structural analysis results from the classification of the connection according to DIN EN 199318.
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 HEB 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 199318 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 secondorder analysis and with imperfections (inclination and precamber) as well as in consideration of the momentrotation characteristics of the connection. The application is carried out according to DIN EN 199318 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 SemiRigid 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 xdirection of 4.73 cm (see Figure 07).
Figure 07  Enveloping of Deformations in XDirection
The design is thus as follows:
w_{ex} / W_{h,max} = 4.73 / 4.53 = 1.04
Conclusion
The consideration of the momentrotation 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
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Figure 01  Structure for the First Design Step and the Selected Connection

Figure 02  Enveloping of the Internal Force My with Rigid Connection

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

Figure 04  Enveloping of the Internal Force My with SemiRigid Connection

Figure 05  Design of Beam and Connection

Figure 06  Calculation Parameters  Modify Stiffness for LCs in SLS  Characteristic

Figure 07  Enveloping of Deformations in XDirection

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

Figure 02  Enveloping of the Internal Force My with Rigid Connection

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

Figure 04  Enveloping of the Internal Force My with SemiRigid Connection

Figure 05  Design of Beam and Connection

Figure 06  Calculation Parameters  Modify Stiffness for LCs in ULS  Characteristic

Figure 07  Enveloping of Deformations in XDirection