How are ordinary tensioned bolts verified using the new Advance Design Steel Connections module?

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This verification appears in the bolted connections loaded in tension (loaded from bending moment and / or axial force). For non-preloaded bolts, Eurocode 3 (EN 1993-1-8:2005) contains these connections in category D (see chapter 3.4.2 from EN 1993-1-8:2005). For this category, bolts from class 4.6 up to and including 10.9 should be used and no preloading is required. This category should not be used where the connections are frequently subjected to variations of tensile loading.

As an example, we have the steel frame from the following figure loaded with a concentrated force applied at the middle of the main beam. All frame members are made of steel S355.

Figure 1. Details of the analyzed frame

We create rigid beam to column connections (from the "Connection creation" toolbar we choose "Create a standard beam-column fixed connection", and the connection type is "Moment end plate").

After the Finite Element analysis is done, the model is exported to Advance Design Steel Connections (more information can be found in the FAQ: How are steel joints calculated using the new Advance Design Steel Connections module?). The loading state in the analyzed frame is presented in the following figures.

Figure 2. Axial efforts (F_x) in frame members

Figure 3. Shear forces (F_z) in frame members

Figure 4. Bending moment (M_y) in frame members

After configuring the connection properties it is necessary to update them to correspond to the ones set in Advance Design. This can be done by clicking on "Calculate". The proposed connection for verification is presented in Figure 5.

Figure 5. Perspective of the analyzed joint

Figure 6. Details of the analyzed connection

Note: Advance Design Steel Connections will automatically generate connection details in the "Detail" window.

We will explicitly check the tensile strength of bolts. The short version of this verification can be found in the "Report" window of the Advance Design Steel Connections module (an updated report appears only after clicking "Calculate").

The verification relationship according to EN 1993-1-8:2005 table 3.2 is:

F_t,Ed ≤ F_t,Rd, where F_t,Ed is the design tensile force per bolt for the ultimate limit state;
                                    F_t,Rd is the design tension resistance per bolt.

It is expected that the plate rotates as a rigid body around the centre of the compressed flange of the beam.
The bolt internal force distribution depends on the distance to the centre of rotation.

EN 1993-1-8:2005 provides that in a bolted connection with more than one bolt-row in tension, the bolt-rows are numbered starting from the bolt-row furthest from the centre of compression (see Figure 7).

The maximum force, F_t,Ed, appears in bolt-row 1; therefore the force in a bolt will be:

- design tension force from bending moment for one bolt from bolt- row 1;

Figure 7. Efforts and the numbering of bolt-rows of the analyzed connection

M_Ed - design bending moment (according to bending moment diagram from Figure 4, M_Ed = 51.59 kNm).

- design axial force for one bolt from bolt-row 1 ;

k₂ = 0.9 (according to table 3.4 from EN 1993-1-8:2005);
f_ub - nominal ultimate tensile strength of the bolt; ;

A_s - tensile stress area of the bolt; ;

Verification is accomplished!
Comparing the results obtained by manual calculation to the one displayed in the "Report" window in the Advance Design of Steel Connections module, you can see that the results are identical.