How are ordinary tensioned bolts verified using the new Advance Design Steel Connections module?
Question:How are ordinary tensioned bolts verified using the new Advance Design Steel Connections module?
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 (Fx) in frame members
Figure 3. Shear forces (Fz) in frame members
Figure 4. Bending moment (My) 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:
Ft,Ed ≤ Ft,Rd, where Ft,Ed is the design tensile force per bolt for the ultimate limit state;
Ft,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, Ft,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
MEd - design bending moment (according to bending moment diagram from Figure 4, MEd = 51.59 kNm).
nv - number of vertical bolt-rows; nv = 2 ;
Σr2 - sum of vertical distances between bolt-row 'r' and the center of compression axis; only tensioned bolt-rows are taken into account (the bolt-rows that are above the center of compression axis) ;
r - the number of the tensioned bolt-row; r = 1..nh.t ;
nh.t - the number of the first bolt-row above the center of compression axis (bolt-row 3);
- design axial force for one bolt from bolt-row 1 ;
nobj - number of end plates, nobj = 1 ;
nt - number of bolts from connection between the column and end plate.
fub - nominal ultimate tensile strength 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.