Anchor Group Force Distribution Calculator

How is force shared in an anchor group?

When a base plate carries tension and moment, the anchors do not all take the same force. If the plate is taken as rigid it stays plane as it rotates, so the elongation of each anchor, and with it the force, varies linearly with distance from the centroid of the group. The axial force is shared equally and the moment gives a larger share to anchors far from the centre.

Formula

N_i = N / n + M_x × y_i / Σy² + M_y × x_i / Σx². Here x and y are the anchor coordinates measured from the centroid of the group. A positive result means the anchor is in tension. A negative result means compression at that point: it is carried by the concrete and not by the anchor, so the anchor tension is taken as zero.

Example

Four anchors sit at the corners of a 300 × 200 mm rectangle under 40 kN of tension and a moment of 6 kN·m (M_x). The axial share is 40 / 4 = 10 kN. With Σy² = 4 × 100² = 40 000 mm² the moment share is 6000 × 100 / 40 000 = 15 kN. The top row anchors carry 10 + 15 = 25 kN of tension. The bottom row gives 10 − 15 = −5 kN: those anchors are not in tension and 10 kN of compression goes into the concrete. The calculator opens with this example.

How to use the tool

Enter the anchor coordinates or use the grid and circle generators. Type the axial force (tension positive), the moments about both axes and the shear if needed. If the column axis is not at the middle of the anchor group, give the position of the axial force and the tool adds the moment from the eccentricity. The result shows the force in each anchor, the most loaded anchor, the total tension and the position of the neutral axis.

What are the limits of this calculation?

This is the simplest anchor distribution model and it assumes compression is transferred at the anchor positions. Under a grouted base plate the compression really concentrates near the compression edge of the plate or under the column flange. If that zone lies outside the anchor rows this calculation is conservative. If it lies inside, the tension is underestimated. For moment resisting column bases, use the result for preliminary sizing only.

Concrete cone failure, pull out, edge distance and group effects are not part of this tool. Those checks are made with EN 1992-4 and the technical approval document of the anchor manufacturer.