Base Plate Anchor Rod Calculator

Purpose and model boundary

This calculator takes a column base plate drawn in plan with its anchor rods (up to 12), the column on it and the axial load, moment and shears at its base. For the plate as drawn it returns the concrete bearing pressure under the plate, the bearing length and the neutral axis, each anchor rod's tension and share of the shear, equilibrium checks, and the plate, rod, grout and pedestal quantities and weights, by the elastic rigid-plate method. It gives statics and quantities only, for learning and estimating. It makes no plate bending, weld, anchor, concrete bearing, breakout, pull-out or shear strength check and no code check, and it is not a connection design.

The spreadsheet is the calculation authority. The page sends the drawn geometry and the values you type to the workbook and draws only what the workbook returns; it computes no engineering value itself.

Inputs and units

Sign conventions: X runs along the plate length N and Y along its width B, both from the plate centre. P is compression positive, a positive M presses the +X edge, rod tension is positive and the bearing pressure is never negative.

Governing relationships

The plate is taken as rigid. The concrete under it bears with a pressure that varies linearly along X and is uniform across the full width B; a rod acts as n times its gross area where the plate lifts and carries nothing where the plate presses down. The bearing resultant, the rod tensions and the loads are in equilibrium in force and in moment about the plate centre.

• Full bearing, when P is positive and the eccentricity e = M / P is within the kern, |M| ≤ P N / 6: the pressure runs from P / (B N) + 6 M / (B N²) at the +X edge to P / (B N) − 6 M / (B N²) at the −X edge.
• Partial bearing, otherwise: part of the plate lifts, the rods on that side take tension in proportion to their distance from the neutral axis, and the neutral axis is found so that the forces and moments balance.
• No bearing, when the rods alone hold a lifting plate: the rods carry the load and moment by themselves.
• Each rod's share of the shear is the shear resultant divided equally among the rods.

Calculation sequence

1. The workbook checks the plate, each rod row, the column section and the loads, and refuses the first one that is wrong.
2. It classifies the bearing case: full bearing when the whole plate presses down; otherwise it looks for a partial bearing equilibrium by a bisection on the neutral axis, trying the moment's edge first and then the other; when the plate lifts clear, the rods alone hold it.
3. From the case it finds the bearing pressure at 21 points along X, the bearing length and resultant, the neutral axis, and each rod's tension and share of the shear.
4. It adds up the equilibrium checks and works out the quantities: the plate's area, volume and weight, the rod count, length and weight, the grout and pedestal volumes and the column's area.

Outputs and interpretation

• Bearing: the bearing case (full, partial or no bearing), the largest and smallest bearing pressure in ksi or MPa, the bearing length along X, the neutral axis position for partial bearing, the eccentricity M / P and the bearing resultant.
• Anchor rods: one line per rod, in the order drawn: its gross area, its tension, its share of the shear and the distance from its centre to the nearest plate edge; with the largest rod tension and the rod that carries it, the number of rods in tension and their total tension.
• Quantities: the plate area, volume and weight, the rod count, total length and weight, the grout and pedestal volumes in ft³ or m³, the column section's idealized area, and the plate and rod weight together.
• Equilibrium checks: the bearing resultant minus the rod tensions minus the axial load, and the moment balance about the plate centre; both are zero in exact arithmetic and read about 1e-15.

Reading the results:

• The minimum bearing pressure is zero unless the whole plate bears.
• A weight without a density, a rod length total without a rod length, and a grout or pedestal volume without its sizes read blank, never zero.
• Large loads on small plates give pressures and rod tensions far above any material's capacity: the results are statics only and nothing is compared with a strength.

On the drawing, the returned bearing pressure is drawn under the plate, the neutral axis is drawn where it falls, and each rod is marked with its returned tension and shear.

Validation and status logic

The status reads OK when the plate is solved, CHECK when a rod sits inside the column outline or the pedestal is smaller than the plate (the results still apply to the plate as drawn), or NOT VALID with the first input to fix. Under NOT VALID every result is blank.

Assumptions and limitations

• A rigid plate on elastic bearing: linear pressure over the full width B, with no rectangular stress block and no limiting bearing stress.
• Rods act at n times their gross area in tension only; they carry no compression.
• Shear is shared equally by all rods; friction and shear lugs are not modelled.
• The moment acts about the plate's Y axis only; there is no moment about X.
• The column stands at the plate centre; its outline is the idealized sharp-corner shape of the typed dimensions and is used for the footprint checks and its area only.
• No plate, weld, anchor, concrete or code check is made.

Restrictions and non-computing states

The limits on each input are enforced by this calculator from its contract; an input outside them is refused with the field named.

• Every rod lies fully on the plate, and no two rods are at the same point.
• The column section names a profile and gives every dimension that profile uses.
• The pedestal's plan dimensions are given together or not at all.

Errors and warnings

Each NOT VALID status names the first input to fix, for example a rod that is not fully on the plate, a column section without a dimension its profile needs, or only one of the two pedestal dimensions. A CHECK status names the geometry to look at, such as a rod inside the column outline or a pedestal smaller than the plate.

The governing method is the classical elastic analysis of a rigid column base plate on concrete under axial load and moment. The bearing pressure varies linearly along the plate and is uniform across its width. Anchor rods carry tension only, where the plate lifts, and act as a steel area n times their gross area, n being the modular ratio. The neutral axis follows from vertical-force and moment equilibrium. While the load stays within the kern (an eccentricity of at most one sixth of the plate length), the whole plate bears, with the pressure from the axial and bending stresses combined. When the rods alone hold a lifting plate, their tensions vary linearly across the rod pattern. The shear is shared equally by the rods. The column area is computed from the typed dimensions of an idealized sharp-corner outline; no shape table is used or reproduced.

Sources and further reading

• Column bases, in a classic design manual for welded steel structures: O. W. Blodgett, Design of Welded Structures, James F. Lincoln Arc Welding Foundation, Cleveland, 1966.
• Combined axial load and bending, the basis of the full-bearing pressure, and the transformed-section method, the basis of treating each rod in tension as n times its area: B. J. Goodno and J. M. Gere, Mechanics of Materials, 9th edition, Cengage Learning, 2018, chapter 5, section Beams with Axial Loads, chapter 6, section Transformed-Section Method, and chapter 8, section Combined Loadings. Publisher page
• Further reading on base plate and anchor rod design, which this calculator does not perform: A. Kanvinde, M. Maamouri and J. Buckholt, Base Connection Design for Steel Structures, AISC Design Guide 1, 3rd edition, American Institute of Steel Construction, 2024. AISC design guide list
• Further reading on the strength of anchors in concrete (steel, breakout, pull-out, side-face blowout and pryout), which this calculator does not check: ACI Committee 318, Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary, American Concrete Institute, 2019, chapter 17, Anchoring to Concrete.

No table, chart or text from any of these publications is reproduced, and none of their authors or publishers has reviewed or endorses this calculator.

The workbook was checked on every test case against a separate solution by closed forms (full bearing, pure uplift and partial bearing) and by an equilibrium solver.

Applicable design codes and a qualified engineer govern real structures.