Steel column anchored to concrete foundation beam - Calculation example CUR10
The example from CUR/BmS Report 10 forms the basis for the elaboration in IDEA StatiCa Connection and 3D Detail. However, we do not compare all tests, partly because the book was written in 2009 and the current EN 1992-4 was not in force at that time.
Connection loaded for compression, bending and shear
The steel column with cross section IPE240 is placed on a narrow foundation beam of 450x800 mm2. A normal pressure force, a shear force and a bending moment act on the column. In combination with the short edge distances, this makes for a challenging design. The task consists of testing the various failure mechanisms and determining the reinforcement required to prevent concrete cone fracture and splitting. See below for the information given.
Fig. 1: Calculation example from CUR10.
The model is first modeled in the Connection application, where the steel section, including base plate and welds, is tested based on the CBFEM calculation. The anchor forces and compressive stresses in the concrete are then used to test the anchorage according to the applicable standards EN 1992-4, EN 1992-1-1 and EN 1993-1-8, depending on the type of anchor and the failure mechanism involved.
In the Connection application, calculations are made according to EN 1992-4, assuming unreinforced concrete. When certain failure mechanisms cannot be prevented by this, it is necessary to include additional reinforcement in the design. This can be done by exporting the column base plate connection from Connection to the 3D Detail application, in which the reinforcement is explicitly included in the calculation.
Connection model
See Figure 2 for the detailing of the connection. The footplate has a thickness of 35 mm with a mortar joint of 25 mm. The anchors are designed with anchor plates and have an edge distance of 70 mm to the center of the anchor. The anchor plates have a maximum dimension of 80x80 mm2, ensuring a minimum concrete cover of 30 mm between anchor plate and concrete edge.
The anchors transmit the shear force and the length of the anchors was chosen to be 350 mm. The concrete beam is modeled as unreinforced, cracked concrete with a length of 4 m.
Fig. 2: Column footplate connection worked out in Connection.
*Theexact length of the concrete beam and the method of support cannot be unambiguously derived from the calculation example [1]. To determine the required reinforcement, the beam was modeled with a length of 4 m and truncated on both sides. In practice, the beam may be longer.
The stress-strain calculation is performed in IDEA StatiCa Connection. In the next step, we analyze the results.
Connection results
The bending moment creates tensile forces in the left two anchors. These amount to approximately 114.3 kN each, resulting in a total tensile force of 228.6 kN. This agrees well with the tensile force of 120.7 kN per anchor determined in the calculation example [1].
On the other side, the load is transferred to the concrete via the base plate as pressure. IDEA StatiCa tests the compressive stresses in the concrete based on an effective surface and the resulting compressive force. Here, a compressive strength of fjd = 12.6 MPa is calculated, which is lower than the value of 18.7 MPa from the calculation example [1]. This difference is mainly explained by a lower concentration factor ¢(k_j = ¢frac{A_{c1}}{A_{eff}}.¢).
The tests of the column, welds, footplate, and compressive stresses in the concrete are satisfactory. However, the anchors do not comply, with a Unity Check of 960%.
Fig. 3: Results of the CBFEM calculation in Connection.
A closer look at the results shows that the test for steel rupture under tensile and shear stresses, as well as the pullout of the anchors, is satisfactory. However, the dimensional control is determined by the concrete, which fails according to three mechanisms: concrete cone failure, lateral breakout and concrete edge failure. These are three distinct failure mechanisms that inevitably occur in a calculation with unreinforced concrete and this combination of anchor forces and edge breaks.
Since the dimensions of the concrete beam and column base plate cannot be changed, it is necessary to include reinforcement in the calculation. This is determined in accordance with EN 1992-4 Art. 7.2.1.2 & 7.2.2.2, to avoid the failure mechanisms mentioned.
Export to 3D Detail
The Connection model is exported to IDEA StatiCa 3D Detail, so that the reinforcement can be explicitly included in the analysis and concrete failure can be prevented. In this way, all norm tests for both anchors and concrete are fully covered.
Through the RC check, the complete model is transferred, including forces, concrete block, base plate and anchors. The next step is to design the reinforcement and correctly define the boundary conditions. As will be shown, these boundary conditions are crucial for a reliable finite element calculation.
Fig. 4: Export from Connection to 3D Detail.
- Concrete Block
The concrete element is taken from the Connection model, and can be further modified here if necessary. For modeling more complex concrete forms, see this article.
- Supports
When exporting, a surface support is automatically created. This is located at the bottom, but must be adjusted so that a support is present at both ends of the beam. It is assumed that the beam is actually longer and is truncated here. The longitudinal reinforcement thereby runs through the support providing stiffness in compression & tension.
- Anchors
The 4 x M24 anchors with anchor plates are taken from the Connection model. Only the thickness of the anchor plates is still set, as it is now explicitly included in the model. A thickness of 20 mm is assumed so that the forces can be transferred properly. See this article for all anchor options.
Fig. 5: Modeling of the 3D Detail model with supports and anchor plate thickness.
- Load
The forces in the anchors and on the base plate are automatically exported from IDEA StatiCa Connection. As a result, the force effects are accurately applied in the 3D Detail model without the need for manual input. For more information on exporting forces, see this article.
- Main reinforcement
The concrete in 3D Detail has no tensile strength, and therefore reinforcement must always be modeled. No reliable results can be obtained without reinforcement, since all tensile energy must be absorbed by steel.
We first model the main reinforcement, assuming that:
- Longitudinal reinforcement Ø16
- Brackets Ø12-250.
This reinforcement may differ, as it cannot be directly derived from the calculation example [1]. This reinforcement is not central to the testing, but is required to correctly calculate the model in 3D Detail.
Additional reinforcement
The most important part of this calculation example is the design of the additional reinforcement to prevent the breakout of the unreinforced concrete.
- Tensile reinforcement
When considering concrete cone failure due to anchors under tension, the reinforcement should be designed to absorb the full anchor forces. In this case, the total tensile force isFt = 2 × 114.3 kN = 228.6 kN. Based on this, the required reinforcementAs,req is determined.
- Ft = 2 × 114.3 = 228.6 kN
- Axis,req = 【{F_t}{f_{yd}}} = 【{228600}{435}} = 526 mm2
In the example, 4 x Ø16 brackets are applied symmetrically around the anchors as suspension reinforcement at 70 mm spacing. Based on the available reinforcement area and the acting tensile force, this results in a stress in the brackets of approximately 284 N/mm².
- 4Ø16shaft = 804 mm2.
- σs = Ω( Ωfrac{F_t}{A_s} = Ωfrac{228600}{804}) = 284 N/mm2
With brackets 4Ø16, the following characteristic resistance is calculated according to equation 7.31 from EN1992-4 art. 7.2.1.9:
\N_{Rk,re} = ˜sum_{i=1}^{n_{re}} A_{s,re,i} \cdot f_{yk,re} = A_{s,re} \cdot f_{yk,re} \⌫ = 804 cdot 500 = 402 kN
The resulting design resistance appears to be sufficient to withstand the acting tensile force in the two anchors.
\N_{Rd} = ≈ 350 kN >Ft
Fig. 6: Additional reinforcement designs for tensile, shear and splitting according to EN1992-4.
- Shear reinforcement
In addition to tensile forces, shear forces also act on the anchors, leading to concrete edge failure. The prescribed brackets 4Ø16 also act as shear reinforcement and can easily absorb the shear force of Fv = 37.5 kN.
- Shear reinforcement
The example [1] also considers concrete splitting, for which reinforcement must be designed in the direction of the splitting force. Two situations are distinguished for splitting, indicated as (a) and (b) in Figure 6. The reinforcement required to prevent splitting is calculated according to equation 7.22 in EN1992-4 art. 7.2.1.7, where k4 has a value of 0.50 for anchors with anchor plates.
\Λ(˜sum A_{s,˜mathrm{re}} = k_4 Λ, ˜frac{sum N_{Ed}}{f_{yk,˜mathrm{re}} / ˜gamma_{Ms,˜mathrm{re}}
(a) The split crack from one anchor to the concrete edge in lateral direction. This can be accommodated by the longitudinal reinforcement.
(b) Split crack between the anchors. This can be accommodated by the additional brackets 2Ø16 between the anchors.
Fig. 7: The 3D Detail model with the reinforcement modeled.
For a correct calculation in 3D Detail, it is essential to observe the reinforcement detailing rules and prepare a preliminary design of the required reinforcement. This forms the basis for obtaining reliable results.
For exact dimensions and modeling of reinforcement, please refer to the 3D Detail model that can be downloaded at the bottom of the page.
3D Detail Results
Once the 3D Detail model is built, including the reinforcement, the CSFM calculation can be performed. During the design phase, we recommend increasing the mesh factor to 3 or 4 to speed up the calculation. However, for final reporting, the calculation should be performed with mesh factor 1. The figure below shows a summary of the results.
Fig. 8: Summary of the results of the CSFM calculation in 3D Detail.
The UGT tests are shown in the upper left corner and are satisfactory. The stresses in both concrete and reinforcement are within the design values, and the anchors and reinforcement are adequately anchored. The deformations are within expectations and no undesirable deformations or stability problems occur.
Results for Concrete
Looking at the stress distribution, we see compressive stresses in the concrete develop around the anchors and below the base plate, locally reaching -13.3 MPa. Using a Cut, the stress distribution in the concrete element can be analyzed in more detail.
Other valuable results to analyze are the principal stresses and principal racks, found under the Supplementary tab. In particular, the main racks ε₁ in the concrete are relevant because they provide insight into where tensile stresses occur and thus where reinforcement is required to absorb them.
Fig. 9: Results of the CSFM calculation for concrete.
Results for Steel - Anchors & Reinforcement.
The stress distribution in the anchors is as expected. Because the anchors with anchor plate do not transfer force through attachment, a nearly constant stress value occurs along the length of the anchor.
Furthermore, we see that the additional reinforcement can absorb the tensile forces from the anchors. Interestingly, however, the stresses in the 4Ø16 brackets are lower than the previously calculated approximately 284 N/mm².
This difference can be explained by the fact that in the CSFM model all modeled reinforcement contributes to the force transfer and the load is distributed over multiple reinforcement bars. The existing Ø12 braces are also part of this force mechanism and function as a truss that absorbs part of the tensile stresses. This shows an important feature of working with IDEA StatiCa Detail and explains why the results may differ from a simplified hand calculation.
In practice, we recommend including all reinforcement present in the model, including the main reinforcement. This provides the most realistic result, since in reality this reinforcement also contributes to the force transfer.
Fig. 10: Results of the CSFM calculation for steel reinforcement & anchors.
In order to still verify the calculated reinforcement, the model can be slightly modified. For this purpose, some cooperating brackets were removed. The results of this are shown in Figure 11. In this situation, stresses of 259 N/mm2 arise in the Ø16 brackets, which is closer to the calculated value of 284 N/mm2.
The hand calculation assumes the situation with the black arrows in Figure 11. The anchors are under tension and transfer their force through the anchor plate. From this plate, a pressure diagonal forms toward the top of the additional brackets. These brackets then direct the force downward, creating a second pressure diagonal towards the next bracket, and in this way the forces are finally transferred to the bearings.
Fig. 11: Modified 3D Detail model to compare the hand calculation.
Some of the tensile forces from the anchors are still transferred to the first bracesvia a direct pressure diagonal, indicated by the white arrow in Figure 11. Although this behavior can be partially mitigated, further removal of braces is not useful, as this may cause other failure mechanisms to occur, e.g., torsion in the beam.
These findings show that the behavior of the connection is not only determined by the forces or anchors, but also strongly depends on the modeling and boundary conditions. Factors such as beam length, type of supports, and reinforcement modeling are all important to evaluate because they affect the force behavior.
The importance of boundary conditions
Direct force transfer to the bearing
The modeling chosen largely determines how the forces are transferred through the concrete and whether the resulting stresses are representative of the real situation. In the example we already saw that the forces from the anchors do not always follow what we had assumed in the manual calculation. A similar behavior occurs when the beam is modeled too short and supported at both ends. In that case, the tensile forces from the anchors find a direct path to the bearing, hardly addressing the suspension reinforcement (Figure 12).
To ensure a realistic force progression, it is therefore necessary to include sufficient length in the model. In the calculation example, a beam length of 4 m was chosen so that the forces can develop realistically and the action of the reinforcement is correctly accounted for.
Fig. 12: If the beam is too short, the anchor forces are directly derived to the bearings.
Wrong choice of bearing arrangement
Another situation that can occur is that the model is set up as if it were a foundation beam resting entirely on the foundation, with only a support at the bottom. In this case, the shear force and bending moment present will cause the concrete element to tip over. To prevent this, it is necessary to apply appropriate boundary conditions at both ends, tailored to the actual bearing situation.
Fig. 13: A surface support that simulates only the subsurface leads to overturning of the concrete beam.
Conclusion
This calculation example demonstrated that the combination of IDEA StatiCa Connection and 3D Detail provides a reliable workflow for calculating anchorages in concrete. By first testing the steel-concrete connection in Connection and then exporting the model to 3D Detail for analyzing concrete with reinforcement, all relevant failure mechanisms according to the Eurocode are understood and verified. The results show that both the anchors and the concrete comply, provided the correct reinforcement is applied. This method thus provides a practical and reliable picture of the actual force progression in the structure.
View the articles below and download the IDEA StatiCa models for more information.
Literature:
[1] Hordijk, D.A. & Stark, J.W.B. (2009). Column footplate connections - Recommendations for calculation according to the Eurocodes. CUR/BmS report 10, Bouwen met Staal & CUR Bouw & Infra, Zoetermeer/Gouda.
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