4.        SOFA – expansion of layouts and shear distribution

4.1      Anchor layouts and shear distribution for static and seismic loading

The SOFA method includes the fib Bulletin 58 [2] provisions for shear distribution to all participating anchors within three rows in a group parallel 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 in both EN 1992-4 [1] and the fib Bulletin 58 [2], 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 explained in Table 4.1.

For both static and seismic loading, shear distribution for regular layouts of anchors (within and beyond 3x3) follows the same approach as defined in Table 4.1. However, limits are placed based on current knowledge and irregular layouts and large anchor groups () must resist shear entirely by the front row of anchor(s). For seismic shear loading, the bandwidth approach does not apply. In this document, n_j refers to the number of rows perpendicular to the edge and n_i refers to the number of anchors per row.

The layouts as mentioned in Table 4.1 are also applicable for anchors located far from edge, however shear distribution becomes irrelevant.

4.2     Bandwidth Approach for misaligned anchors

For orthogonal layouts in design, all anchors may perfectly align in a row, but onsite execution may not always be as “millimetre” 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 Fig. 4.1, the band includes any anchors within a quarter of the maximum spacing in the y-direction – identical for the x-direction  if an adjacent edge exists – thus extending the breakout body using the smallest edge distance and thereby increasing the concrete edge resistance.

4.3      Larger layouts and impacts on concrete breakout

As noted in Table 4.1, 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 [2] 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. By removing limitations on the layouts, the SOFA method enables the designer to model any layout, regular or irregular. However, expanding the possible layouts without considering the participation of the back rows in resisting concrete edge breakout would lead to illogical scenarios where, for instance, only the row nearest to the edge in a 4x2 layout would resist shear, meaning a 3x2 layout would provide higher resistance as it could engage all three rows parallel to the edge. The SOFA method avoids this by allowing the first three rows of a 4x2 anchor layout to participate in resisting edge breakout in shear.

Furthermore, the SOFA method also incorporates the work of Grosser [3], which demonstrated that a larger number of anchors (five) per row can participate in resisting shear, thereby enlarging the concrete breakout body, , and consequently generating a higher resistance. Again, this also requires no hole clearance between the anchor and the baseplate’s holes as all anchors must be loaded simultaneously to avoid a “shear lag” effect that may arise if the spacing becomes unduly large. Combined, these extensions are valid only for layouts up to 16 anchors as further experimental investigations are still required to validate the model for much larger groups.

An example of concrete edge break-out for a 5x3 anchor layout is shown in Fig. 4.2, where a shear force, , acts perpendicular to an edge, thereby activating the middle row (the concrete breakout bodies for the front and rear rows are not shown as a simplification).

If the anchors in the same group with two adjacent edges were now loaded with inclined shear, edge breakout must be verified for each edge, as shown in Fig. 4.3.

4.4      Shear distribution parallel and perpendicular to the edge

Before verifying each edge, knowing the shear that acts on each row, , is paramount. Here, Table 4.3-2 of [2] provides guidance. For instance, shear perpendicular to an edge is distributed as for first row,  for second row of anchors for necessary edge failure verification. For a maximum of three rows, the load would then be split as  for first row,  for second row of anchors, and finally for the third row.

The above does not apply shear acting parallel to an edge, as the failure load is typically twice the failure load perpendicular to the same edge and only the anchor row nearest to the edge is verified as per EN 1992-4 [1]. The SOFA method distributes the load equally between the anchor rows as . When the fastening is subject to biaxial shear, the shear distribution for anchors up to three rows parallel to the edge is calculated using following equations:

5.        Resistance verification in SOFA method for static and seismic shear loading

5.1      Resistance verification in SOFA method for static and seismic shear loading

Resistance verification for anchor layout regular up to 3x3

The resistance against static and seismic shear for anchor layout regular up to 3x3 follows the design criteria as mentioned in [1] (refer to Table 5.1). The resistance verifications to both tension and combined tension and shear loading are not mentioned in this section as they follow the requirements of [1] without modifications.

5.2      Verification against concrete edge break-out failure

The characteristic resistance for steel failure without lever arm  is taken directly from the product relevant ETA, with the resistance verified for the load on each anchor.

Concrete pry-out failure is verified according to the equations mentioned in [1].

Concrete edge break-out resistance with hole clearance:

The edge resistance for anchors with hole clearance is verified using the design criteria defined in [1], however the modified edge distance, and reference and projected areas  are calculated using the distance approach for regular and irregular layouts.

Concrete edge break-out resistance verification for anchors without hole clearance

The verification is performed per row according to the formula below and with the loads used to determine the eccentricity and the angle applied on the verified row. 

5.3      Verification against combined loading

The design verification is done separately for steel failure and for failures other than steel by the equations mentioned in Table 5.3.

Conclusion

It can be summarised that EN 1992-4 [1] provides a standardized and prescriptive approach suitable for routine designs whereas the SOFA method offers a more advanced research-based method for optimizing performance of anchors in critical and specialized projects. The flexibility and customization in design of anchor layouts along with integrated PROFIS Engineering provides detailed understanding of stress distributions, potential failure mechanisms and anchor performance.

·       Complex projects: Ideal for projects involving unique or complex loading conditions, dynamic loads, e.g., seismic zones or unusual geometries.

·       Optimized design: Suitable for projects where material optimization and economic designs are critical.

·       Customized solutions: Used in scenarios where standard prescriptive methods do not provide adequate solutions requiring a more tailored approach.

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