Find the tension and shear on each anchor under a rigid base plate, with bearing pressure, for AS 5216:2021 anchor checks. Up to three load cases. Try it.
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About this Anchor Forces under a Rigid Base Plate Calculator
This calculator works out the tension and shear on each anchor of a rectangular group under a rigid base plate, together with the bearing pressure on the concrete beneath it, for one of up to three load cases. These are the demands the AS 5216:2021 failure-mode checks take: the most heavily loaded anchor for steel and pull-out, the group tension and its eccentricities for the concrete cone, and the group shear for pry-out and edge failure.
- Structural engineer turns column base actions, including biaxial moment and torsion, into the anchor forces each AS 5216 check needs.
- Steel connection designer compares grouted bearing with an ungrouted stand-off plate on levelling nuts and sees how the compression path changes the anchor tensions.
- Plant and equipment engineer checks base plates for skids, frames and supports under several load combinations on one page.
It is an engineering-grade CalcTree calculation: the solution, the plan of the plate and the anchor force table update together, and the page can be kept with the anchor checks that use its results.
More info on Anchor Forces under a Rigid Base Plate
Inputs and sign convention
The anchors form a grid of n_x by n_y at spacings s_x and s_y, and every offset is measured from the centre of the plate, including the anchor group and the load point. Actions are entered at the load point for up to three cases: axial force, shear in both directions, moments about both axes and torsion. Signs follow a right-handed x, y, z with z up and N* positive in tension. The anchor's stressed cross-section, the steel modulus and the concrete modulus set the relative stiffness of the anchors and the bearing.
Rigid plate solution
The plate stays plane, so the anchor forces and the bearing follow from one plane of uplift that satisfies equilibrium for N*, M*x and M*y. Anchors act as axial springs in tension, and the concrete is linear elastic in compression only. Because the compression zone depends on the answer, the page solves it iteratively and reports whether the solution is in equilibrium with the actions. On an ungrouted stand-off the anchors carry the compression too and the concrete carries nothing.
Tension results for the anchor checks
The group tension N* is the sum of the anchor tensions, which the concrete cone, splitting and bond checks take. Its eccentricities are the offsets of the tension resultant from the centroid of the anchors in tension, as the cone check's eccentricity factor takes them. The lever arm runs from the tension resultant to the compression resultant, for the cone check when there is compression under the fixture. The summary also gives the tension on the highest-loaded anchor and the peak elastic bearing pressure.
Shear working, plan and equilibrium
Each anchor takes an equal share of the shear. The torsion about the centroid of the group, including the shear's own offset from it, is shared through the polar moment of the group, so a corner anchor carries the most. The page reports the shear on that anchor, the group shear V*, and the eccentricities of the shear resultant from the centroid of the group that the pry-out check takes. Friction under the plate and shear lugs are not counted.
A plan of the plate shows the bearing pressure contour, the neutral axis, each anchor's tension and shear, and the tension and compression resultants. A table lists the forces on every anchor, numbered from one corner, with compression on a stand-off shown as a negative tension. Finally the anchor forces and bearing are summed back and compared with the actions; a solution that does not close means the plate cannot carry the case, for example a tension applied outside the reach of the anchors.
Common Calculation Errors to Avoid
- Transferring moments by hand when the load point is offset risks double counting. Enter the load point's offset from the plate centre and let the page move the actions.
- Using a stand-off model for a grouted plate, or the reverse, puts the compression in the wrong place and changes every anchor tension.
- Mixing sign conventions for the moments flips which side of the plate is in tension. Check the stated convention for M*x, M*y and M*z.
- Assuming a thin plate behaves as rigid misplaces the forces. A plate that bends puts more tension on the anchors near the member and moves the compression towards its edges, and the page does not check plate stiffness.
- Treating the bearing pressure as a bearing check confuses two things. It is an elastic value for the distribution, not a check on the concrete or the grout.
- Ignoring oversized clearance holes breaks the shear distribution. Equal sharing needs the clearance holes within the limits of AS 5216:2021 Table 4.2.2.1.
- Using the group tension for the steel check understates the demand. Steel and pull-out take the highest-loaded anchor; the concrete cone takes the group tension and its eccentricities.
Engineering templates
Common calculators
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FAQs
How are anchor tensions found under a rigid base plate?
The plate is assumed to stay plane, so its uplift varies linearly across it. Anchors in tension act as springs and the concrete bears in compression only, and the page finds the plane that balances the axial force and both moments.
Why does the concrete stiffness matter?
Only the ratio of anchor stiffness to concrete stiffness affects the result, and only once part of the plate bears on the concrete. Under pure uplift every anchor is in tension and the concrete does nothing.
When should I choose the stand-off compression path?
Choose it for a plate on levelling nuts with no grout, where the anchors carry compression as well as tension and the concrete carries none.
How is the shear shared between anchors?
The direct shear is shared equally, and the torsion about the group centroid, including the shear's own offset from it, is shared through the polar moment of the group. A corner anchor carries the most, and the page reports the shear on it.
What does the equilibrium check tell me?
It sums the anchor forces and bearing back about the plate centre and compares them with the actions. If it fails, the plate cannot carry that load case, for example a tension outside the reach of the anchors.
Which AS 5216 checks use these results?
Steel failure and pull-out use the highest-loaded anchor. The concrete cone, splitting and bond checks use the group tension and its eccentricities, and pry-out and concrete edge failure use the group shear.
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