1.0 Introduction

The enhanced role of post-installed fasteners safely connecting steel members to concrete in increasingly complex scenarios has led to anchorages regularly exceeding the regular geometrical layouts specified in national and international fastening design guidelines such as EN 1992-4 [1]. For instance, an anchorage connecting a primary structural steel beam to concrete column loaded in shear, such as in Figure 1 may need a higher-level flexibility in resisting applied static and seismic load combinations as compared to the current scope of the available design standards. Here, engineers and designers struggle in finding solutions that ensure the reliability of the connection within the boundaries of EN 1992-4.


Figure 1: Primary steel beam supporting a composite floor deck attached to a concrete column

This article presents an expansion to the design provisions contained in the current EN 1992-4 under the “Hilti SOFA Method” (Solutions for Fastening), which allows shear distribution beyond the front row for concrete edge breakout verification for static and seismic conditions and ultimately provides more design flexibility when considering of the number of anchors in a group loaded in shear close to one or more concrete edges.

2.0 Anchor configurations and the design provisions covered by EN 1992-4

EN 1992-4 contains design provisions for fastenings in concrete that reflect the foundational empirical evidence accounting for various uncertainties that ensure a high level of safety but may not always lead to a feasible design. One outcome is the limitation of the anchor group configurations in EN 1992-4 is shown in Figure 2. Although all these groups can be designed for tension and / or shear if the nearest anchor in the group is positioned sufficiently far enough from a concrete edge (with an edge distance of 𝑐 ≥ 𝑚𝑎𝑥{10ℎ𝑒𝑓;60𝑑𝑛𝑜𝑚}), EN 1992-4 limits design of the specified anchor groups in shear close to a concrete edge unless the annular gap (also called “hole clearance”) between the anchor and baseplate is completely nullified by a grout, welding (mostly applicable to cast-in headed anchors), or special means such as the Hilti Filling Set.


Figure 2: Fasteners without hole clearance for all edge distances and for all load directions and fasteners with hole clearance in accordance with Table 6.1 (EN1992-4) remote from the edge for all load directions and fasteners with hole clearance in accordance with Table 6.1 close to an edge. 

2.1 Anchor layouts and static shear load distribution

Table 1: Differences between anchor groups loaded in shear close to the edge with and without hole clearance. 

Table 1 illustrates the differences between the anchor groups with and without hole clearance when positioned close to an edge and loaded in shear towards that edge. The two factors – hole clearance and edge distance – determine the effectiveness of the individual anchors in resisting edge breakout, represented by a semi-conical concrete surface. For a group of anchors loaded in shear perpendicular to the edge, shear is divided equally between the row of anchors nearest to the edge and the breakout body, is resisted only by the front row per EN 1992-4. This conservative assumption of only the front row of anchors in a group resisting the entire shear applied on a baseplate can lead to unfeasible solutions. The other two failure modes – steel and concrete pry-out – account for the shear acting on the highest loaded anchor in the group and on the entire group, respectively.

3.0 State-of-the-art Approach for Shear Load distribution in fib Bulletin 58

The EN 1992-4 approach to fastening design based on prescribed anchor layouts is often inadequate and unfeasible when larger anchor groups are required, such as for fastening a steel column close to the edge of a concrete foundation. In certain circumstances, depending upon parameters such as edge distance, anchor spacing, concrete member thickness, and the hole clearance, edge breakout may start from either the anchors closest or furthest from the edge, necessitating a verification of all anchors.

The fib Bulletin 58 [2], Section 4.3.1.3, includes the possibility of designing for such cases and allows for shear acting perpendicular to the edge to be evenly distributed beyond the first row parallel to that edge, underpinned by the presence of no hole clearance between the annular gap of the baseplate and anchors. In practice, this translates to verifying the resistance of the breakout body potentially generated by each row of anchors parallel to an edge as the governing failure plane may not always be the front row. An illustration of this effect is provided by Figure 3.


a) Edge failure initiates    b) Edge failure initiates           c) Edge failure initiates  
at the front row at the second row at third row

Figure 3: Shear load distribution perpendicular to an edge and the failure surfaces

As Figure 4 illustrates, the same principle applies to shear acting parallel to an edge, with breakout verified for all rows perpendicular to that edge, bringing consistency to the shear distribution principle.


a) Edge failure initiates    b) Edge failure initiates           c) Edge failure initiates at third
at the front row at the second row row (Front two rows assumed to fail)
(front row assumed to fail) 

Figure 4: Shear load distribution parallel to an edge and the failure surfaces

Note that applying the same approach with a normal (non-zero) hole clearance will result in an unacceptable loss in serviceability.

Although the fib Bulletin 58 allows distribution of shear beyond the front rows for edge breakout, the anchor groups are still restricted to a 3x3 grid without hole clearance and to 2x2 with hole clearance, see Figure 4.3-1 of [2]. Anchor layouts beyond 3x3 and irregular configuration, such as triangular and circular, are covered in neither EN 1992-4 nor the fib Bulletin 58. 

4.0 SOFA method for anchor layouts & shear distribution in static and seismic loading

The SOFA method applies the fib Bulletin 58 provisions for shear distribution to all participating anchors within three rows in a group parallel and perpendicular to the edge and expands the layouts to which it applies. This enables the designer to model fastening layouts loaded in shear towards the edge that exceed those prescribed in both EN 1992-4 and the fib Bulletin 58, with the prerequisite that no hole clearance exists between both anchor and baseplate. For the different anchor arrangements, the static and seismic shear distribution for anchors close to edge allowed in SOFA are captured in Table 2.

  
Table 2: Shear load distribution for anchors close to an edge for static and seismic conditions 

For both static and seismic loading, the SOFA method permits shear distribution for regular layouts of anchors (within and beyond 3x3). However, limits are placed based on current knowledge on larger layouts, with irregular and large anchor groups (𝑛𝑖 × 𝑛𝑗 > 16) still resisting shear entirely through the front row of anchor(s), with 𝑛𝑗 and 𝑛𝑖 referring to the number of rows perpendicular and parallel to the edge, respectively. The maximum number of anchors in a row is limited to 5 in order to assume the contribution of the back row. This limit is justified by the available research background (Grosser, 2012). Under seismic loading, the distribution to the rear row(s) of anchors requires nullifying the hole clearance.

4.1 Larger layouts and impacts on shear distribution per row

As noted in Table 2, while shear transfer beyond the front row of anchors is possible up to three rows parallel to edge, Figure 4.3-1 of the fib Bulletin 58 explicitly limits the anchor groups to a rectangular 3x3 layout, limiting, by extension, the number of anchors per row to three. Such restrictive layouts may be insufficient for fastening primary structural steel elements that typically resist high shear forces. Expanding the layouts through the SOFA method enables the designer to model any layout, regular or irregular. 

An example of edge breakout beyond the front row for a 5x3 anchor layout positioned near an edge with no hole clearances is shown in Figure 5, where a shear force, 𝑉𝐸𝑑, acts at perpendicular to the edge. Here, edge breakout per SOFA is verified for each row parallel to each edge, with only the breakout body of the middle row shown as a simplification.

Note that the SOFA method does not require an equal number of anchors per row.


Figure 5: Concrete breakout body for the middle row when loaded perpendicular to the edge. 

4.2 The SOFA approach for unaligned anchors

For orthogonal layouts in design, all anchors may perfectly align in a row, but onsite execution may not always be as “millimeter” precise, leading to an overestimation of resistance if the failure plane were to initiate from the anchor nearest to the edge. However, the failure plane for concrete edge breakout does not require perfect alignment of all anchors in a row and the failure plane may encompass other anchors as they activate within a defined virtual “band”. As shown in Figure 6, the band includes any anchors within a quarter of the maximum spacing between the nearest and furthest anchor in the y- (𝑠𝑦,𝑚𝑎𝑥) and x-directions (𝑠𝑥,𝑚𝑎𝑥) if an adjacent edge exists. This extends the breakout body while using the smallest edge distance between all anchors in the band, 𝑐𝑦,1, to increase the concrete edge resistance. 

Note that this approach applies only under static load conditions and the regular EN 1992-4 approach of edge breakout from the anchor nearest to the edge applies for seismic conditions even if the hole clearance is nullified.


Figure 6: Definition of the “band” demarcated by the red box, shown for one edge

5.0 Verifying concrete edge breakout resistance according to the SOFA method

While the verification for steel and pry-out under both static and seismic loading remain unaffected, the SOFA method verifies the edge breakout resistance of each row, 𝑉𝑅𝑘,𝑐,𝑟𝑜𝑤 𝑖, using the provisions of EN 1992-4 [1] with modifications from the fib Bulletin 58 [2] to cover larger anchor groups. The only difference between the two design provisions relates to the calculation for 𝜓𝛼,𝑉, which is reflected more accurately for larger groups by the fib Bulletin 58, as illustrated by Figure 7. 


Figure 7: Illustration of the parameter 𝜓𝛼,𝑉 in the fib Bulletin 58 vs. EN 1992-4
 

6.0 Design options in PROFIS Engineering

In Hilti’s PROFIS Engineering, the engineer can find options for designing a wide range of fastenings covered in this article according to either EN 1992-4, ETAG 001: Annex C, or the SOFA method: 



Customizing the layouts is possible via the “2D Editor” and PROFIS provides a warning message with an option to change the method to SOFA when selecting or positioning anchors in layouts beyond the limits of EN 1992-4: 

7.0 Conclusion

The result of extensive internal and external research over the years has resulted in the SOFA method offering engineers enhanced flexibility and enabling feasible solutions when designing fastenings of increased complexity under both static and seismic conditions. Integrated into PROFIS Engineering’s Concrete module, the SOFA method provides designers with:

•       A fastening design approach extending the limits of EN 1992-4 for anchor layouts beyond 3x3.
•       Higher resistance to concrete edge failure by transferring shear load beyond the row of anchors nearest to the edge up to a maximum of three rows, with a maximum of five anchors per each row.
•       Using a notional “band” to unify unaligned anchors in irregular layouts into a row to increase resistance to edge breakout.

To know more, refer to our Whitepaper further detailing this article. Link to the Whitepaper: SOFA Method Whitepaper W4607(EN)

To start designing, visit https://profisengineering.hilti.com/

8.0 References

1.    EN 1992-4:2018: Eurocode 2 – Design of concrete structures – Part 4: Design of fastenings for use in concrete, Brussels: CEN, 2018. 
2.    fib bulletin 58: Design of anchorages in concrete, Lausanne: IFSC, 2011.
3.    P. R. Grosser, Load-bearing behavior and design of anchorages subjected to shear and torsion loading in uncracked concrete, Germany: Institut für Werkstoffe im Bauwesen der Universität Stuttgart, 2012.