Off-Center Load Distribution on Four Supports

Calculate each corner reaction and spring compression for an eccentric vertical load on a rigid rectangular frame with four identical elastic supports.

An off-center load shifts the reactions between the corners of a rigid frame. Enter the support spacing, load magnitude, load offsets from the footprint center, and the common vertical spring rate to calculate all four corner reactions and their corresponding elastic compressions using a closed-form rigid-body Winkler spring model.

Check the minimum reaction before using the result. A negative reaction means the assumed four-contact solution requires a support to pull downward; actual casters and pads cannot do that, so the frame will lift off a support and needs an active-contact analysis instead.

Inputs

Note

Frame, supports, and load position

Total vertical load (lbf)

Range: 0.01–1,000,000 lbf

Use the complete supported weight, including equipment and payload.

Support spacing in X (in)

Range: 0.01–1,000 in

Support spacing in Y (in)

Range: 0.01–1,000 in

Load offset from footprint center in X (in)

Range: -500–500 in

Positive X is toward the +X support edge. Keep the load point within the support footprint for this model.

Load offset from footprint center in Y (in)

Range: -500–500 in

Positive Y is toward the +Y support edge. Keep the load point within the support footprint for this model.

Vertical rate of each support (lbf/in)

Range: 0.01–100,000,000 lbf/in

Identical linear spring rate for each support. This calculates elastic deflection; reaction distribution is independent of the common rate.

Result

Reaction at -X, -Y support (lbf)

131.94

Reaction at -X, +Y support (lbf)

243.06

Reaction at +X, -Y support (lbf)

256.94

Reaction at +X, +Y support (lbf)

368.06

Maximum spring compression (in)

0.3681

Maximum support reaction (lbf)

368.06

Minimum spring compression (in)

0.1319

Minimum support reaction (lbf)

131.94

Four-support contact check

All four supports remain in compression; the four-support solution is admissible.

What to check

Use support center-to-center spacings and offsets from the footprint center.
Check that the load point is within the support footprint and that no calculated reaction is negative.
Use the maximum reaction to verify each actual support's rating and the frame's stiffness.