Bending stiffness of column base

Description

The bending stiffness of the open and hollow section column base loaded by a combination of axial force and bending moment is studied. The design numerical model is validated to experiments presented at a paper by Bajer et al. (2014) and verified to the research numerical model in ATENA code and results of the component method.

 Validation

Under project MERLION the column base of column HEB 240 was tested, with a concrete block of sizes 𝑎′=1000 mm, 𝑏′=1500 mm, ℎ=400 mm and concrete grade C20/25 with base plate 𝑎= 330 mm; 𝑏=440 mm; 𝑡=20 mm of steel grade S235, with cast-in anchor bolts 4 × M20, As = 245 mm2 from grade 8.8, head diameter a = 60 mm, offset at top 50 mm and left −20 mm and grout thickness approximately 30 mm.

\[ \textsf{\textit{\footnotesize{Fig. 10.3.1 Test set-up and deformed base plate and anchor bolts}}}\]

Two specimens of this column base were tested at the laboratory in Brno University of Technology; see (Bajer et al. 2014). The experimental initial stiffness was 10 MNm/rad. The specimens did not exhibit any significant damage until load combination with axial force −400 kN and bending moment 180 kNm, which created rotation 0,04 rad. Then, concrete cracked with steel yielding of anchor bolts, base plate, and column. At the end of loading, the joint was still able to transfer bending moment 190 kNm up to rotation 0,15 rad.
ATENA software (Červenka et al. 2014) was used for a research model of the column base. The software includes a fracture-plastic material model for concrete, a material model with von Mises failure criterion for steel, and a Mohr-Coulomb criterion for the interfaces. The base plate is modeled by shell elements, and anchors are presented as reinforcement elements without a longitudinal bond. The anchors are fixed to the concrete at the location of the anchor heads. Supports by the concrete block are realized by springs. The model was validated using data from the experiment. It represents well the progress of cracking in the concrete block and deformation of steel parts. However, the idealization of the model brings a higher initial stiffness compared to the measured one.

\[ \textsf{\textit{\footnotesize{Fig. 10.3.2 Stiffness comparison of HEB 240 column base}}}\]

The same column base was examined by the design-oriented model using CBFEM. For this comparison, all safety factors were set to 1 and anchor length for stiffness calculation to 12. The initial stiffness is also lower than 29 MNm/rad determined by CM. The concrete cone breakout failure according to EN 1992-4 should occur at load combination of axial force −400 kN and bending moment 100 kNm. Steel plates yield by more than 5 %, which is a recommended value by EN 1993-1-5:2006, at −400 kN and 153 kNm.
The comparison of moment-rotational diagrams predicted by design-oriented models, CM and CBFEM, and research-oriented model by ATENA code to the experimental results is in Fig. 10.3.2.

Verification

Examples overview

The verification is prepared for base plates with different cross-sections and dimensions. Examples overview is shown in Tab. 10.3.1-10.3.3. Joints geometry are shown in Drawings 10.3.1-10.3.2. Steel grade for all of the examples is S235. Concrete grade is C20/25. The member is connected to the base plate by fillet welds, a_w=8mm. The results of the verification are shown in Tab. 10.3.4-10.3.6 and in Fig. 10.3.3.-10.3.8. 

\[ \textsf{\textit{\footnotesize{Tab. 10.3.1 Examples overview(Variable column HEB beam height)}}}\]

\[ \textsf{\textit{\footnotesize{Tab. 10.3.2 Examples overview(Variable column SHS cross-section)}}}\]

\[ \textsf{\textit{\footnotesize{Tab. 10.3.4 Examples overview(Variable base plate thickness)}}}\]

\[ \textsf{\textit{\footnotesize{Drawing 10.3.1 HEB joint geometry with dimensions)}}}\]

\[ \textsf{\textit{\footnotesize{Drawing 10.3.2 SHS joint geometry with dimensions)}}}\]

Verification results

\[ \textsf{\textit{\footnotesize{Tab. 10.3.5 Verification CBFEM to CM - Variable column HEB beam height}}}\]

\[ \textsf{\textit{\footnotesize{Tab. 10.3.6 Verification CBFEM to CM - Variable column SHS cross-section}}}\]

\[ \textsf{\textit{\footnotesize{Tab. 10.3.7 Verification CBFEM to CM - Variable base plate thickness}}}\]

\[ \textsf{\textit{\footnotesize{Fig. 10.3.3 Verification of CBFEM to CM-Variable column HEB beam height}}}\]

\[ \textsf{\textit{\footnotesize{Fig. 10.3.4 Sensitivity study for the beam height}}}\]

\[ \textsf{\textit{\footnotesize{Fig. 10.3.3 Verification of CBFEM to CM-Variable column SHS cross-section}}}\]

\[ \textsf{\textit{\footnotesize{Fig. 10.3.4 Sensitivity study for the SHS column dimensions}}}\]

\[ \textsf{\textit{\footnotesize{Fig. 10.3.3 Verification of CBFEM to CM-Variable base plate thickness}}}\]

\[ \textsf{\textit{\footnotesize{Fig. 10.3.4 Sensitivity study for the base plate thickness}}}\]

Benchmark case

Input

Cross-section
• SHS 150×16
• Steel S420

Base plate
• Thickness 20 mm
• Offsets top 100 mm, left 100 mm
• Full penetration butt welds
• Steel S420

Anchors
• Type M20 8.8
• Anchoring length 300 mm
• Offsets top layers 50 mm, left layers −20 mm
• Shear plane in thread

Foundation block
• Concrete C20/25
• Offset 200 mm
• Depth 800 mm
• Shear force transfer friction
• Mortar joint thickness 30 mm

Loading
• Axial force N = −756 kN
• Bending moment My = 56 kNm

Output

Stiffness
• Initial stiffness

\[ \textsf{\textit{\footnotesize{Fig. 10 Benchmark case for welded eaves moment joint (IPE 400 to HEB 300)}}}\]