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Check shelf or tabletop deflection

A shelf can carry a load yet deflect too much for its purpose. Define the supports first, then check stress and deformation separately.

Side view of a uniformly loaded shelf on two continuous supported edges; section inset shows width and thickness.mgδLSectionBt
Side-view concept of a uniform plate, continuously supported across the full width at both ends with a uniformly distributed payload. The red deflection line is exaggerated.

What you will understand

  • Support conditions and load distribution
  • Deflection versus stress
  • The plate model versus the complete frame

Blue: defined conditions · Red: calculated quantities. Diagrams are schematic.

  • L: support span / t: thickness
  • m: added payload mass
  • δ: deflection

The examples below are illustrative. Each example button loads its fixed values, units and mode. Ordinary calculator links do not load an example.

Match the actual supports

The tabletop calculator treats the plate as a one-way beam of width B. Two-edge support is continuous over each full edge. A table on four isolated legs or a plate supported on all four edges is a different model.

  • Use the unsupported support-to-support span for L
  • Distinguish uniform loading from a central line load spread over the full width
  • Check concentrated loads from small feet or objects separately

Define material and section orientation

Young’s modulus E describes stiffness; allowable stress is a strength comparison criterion. A higher E does not automatically mean higher strength. Check condition, temperature and material direction. Direction-dependent wood/plywood behavior and long-term deformation are outside this homogeneous model.

For practical review

At the same payload, ignoring self-weight, doubling thickness increases I eightfold and reduces bending deflection to one eighth. Actual self-weight and supports also matter. Direction-dependent wood/plywood behavior and long-term creep are outside this homogeneous beam model.

I = Bt³/12, Z = Bt²/6

Compare deflection and stress separately

Deflection and stress are separate results for the same load. Set their limits from the intended use and design criteria; defaults are not product ratings.

Example: homogeneous shelf on two continuous supports

Inputs

  • Uniform payload; L = 500 mm, B = 200 mm, t = 10 mm
  • Added payload m = 10 kg; density ρ = 2,700 kg/m³
  • E = 70 GPa; allowable stress 80 MPa; deflection limit 1 mm (assumed)

Results

  • Plate self-mass = 2.7 kg
  • Maximum deflection including self-weight ≈ 0.174 mm
  • Bending stress including self-weight ≈ 2.335 MPa

Both results are within the entered limits for this model. Leg/frame/joint strength and local deformation are not assessed. Properties and comparison limits are illustrative assumptions.

Load the fixed values, units and mode for this illustration. Then edit them for your conditions.

Review the rest of the structure and long-term use

The plate result is not the load rating of the entire table. Eccentric loading, reinforcement and people leaning on the table require checks along the actual load path.

  • The load path through frame, legs, joints and floor
  • Local indentation, lateral movement, vibration and tipping
  • Long-term loading, temperature, humidity and corrosion

Keep a review checklist

This checklist is a personal reminder, not a safety score or an automatic approval. It is not sent or saved.

Continue with another guide

Reference information and illustrative calculations. This content does not guarantee suitability or safety of a design. Confirm the actual materials, component specifications and operating conditions.