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Beam Deflection Calculator

// DEFLECTION • STRESS • MOMENT • REACTIONS

Not a structural design tool Teaching and first-pass estimating only, and not engineering advice. Do not use it to size, verify, or approve any load-bearing member. Open for the full scope limits.

What this tool actually solves

Small-deflection Euler-Bernoulli bending for a straight, prismatic, homogeneous, isotropic, linearly elastic beam under a single static load, in one plane, about the strong axis.

Every one of those words is a restriction, and real members routinely break at least one of them.

Not checked, at all

  • Stability: buckling of any kind, lateral-torsional stability, local and flange buckling, web crippling and bearing.
  • Other actions: shear capacity, torsion, biaxial or skew bending, axial load and combined stress.
  • Joints: connections, welds, bolts, anchors, fixings, and whether the support can carry the reactions this page reports.
  • Time and environment: fatigue, vibration, impact, seismic, wind, snow drift, ponding, temperature, creep, shrinkage, corrosion, fire.
  • Real geometry: notches, holes, penetrations, stress concentrations, residual stress, initial camber or bow, construction tolerance, erection stability.
  • Compliance: every code requirement of every jurisdiction.

A member can satisfy every number reported here and still be unsafe.

One load, unfactored

  • A single load case only. Loads are not superposed and combinations are not formed.
  • No load or resistance factors, and no distinction between service and ultimate limit states.
  • Real design works from the load combinations in the governing code, not one load typed into a box.

Material values are representative, not guaranteed

  • Wood: values depend on species, grade, size, moisture and load duration. The NDS adjustment factors are not applied here.
  • Polymers: stiffness falls under sustained load, so a polymer result is a lower bound on the deflection you will actually get.
  • Brittle materials: no yield plateau, and rupture strength is a statistical quantity rather than a property. Glass quoted at its mean modulus of rupture breaks half the time.
  • Everything else: one published figure per row, with its source. Real material has scatter; your certificate governs.

Theory limits

  • Shear deformation is neglected, which under-predicts deflection for short deep beams.
  • Small-deflection theory assumes deflection stays small against the span. Past roughly a fiftieth of the span it no longer holds.
  • Beyond yield every deflection number is wrong, and not by a small margin.
  • Deflection limits like L/360 are conventions from building practice for particular situations. They are not requirements, they do not apply to machine parts, and meeting one is not evidence that anything is adequate.

Get a professional engineer for

  • Anything load-bearing or safety-critical: beams, joists, lintels, rafters, purlins, mezzanines, platforms, guardrails, lifting points, temporary works.
  • Anything where failure means property damage, injury, or a regulatory problem.
  • Anything needing a certified calculation or a PE stamp.

No warranty. No liability. You assume all risk. This page, its numbers, diagrams, material library and independent check are provided as-is and as-available, without warranty of any kind, express or implied, including accuracy, completeness, timeliness, reliability, fitness for a particular purpose, merchantability, engineering or professional suitability, regulatory or code acceptability, or non-infringement. To the maximum extent permitted by law, the author accepts no liability for any loss, injury, damage, cost or claim arising from use of or reliance on this page.

Independent verification required. Check every value against the governing design standard, the actual material specification and test certificates, and a competent structural engineer before acting on anything. The standard, the certificate and professional judgement control; where this page disagrees with them, this page is wrong.

Consequential damages excluded. To the maximum extent permitted by law, in no event will the author or maintainers be liable for any direct, indirect, incidental, special, exemplary, punitive or consequential damages, including loss of use, data, profits or business interruption, however caused and on any theory of liability, whether in contract, strict liability or tort including negligence, arising out of or in connection with this page, even if advised of the possibility of such damage.

Indemnity. By using this page you agree to indemnify and hold harmless the author and maintainers against any claim, demand, loss or expense arising out of your use of it or of anything derived from it.

Severability. If any part of this notice is held unenforceable, the remainder continues to apply, and the unenforceable part is limited to the least extent necessary rather than struck out.

Beam, load, and section

Pick the boundary condition from its diagram. "Supported on both sides" means two different things, and under a uniform load they differ by a factor of five.

Worked examples

Support case

Is a bolted end fixed or pinned?

Almost always pinned. A standard bolted shear connection, a shear tab or clip angles or a single vertical line of bolts, is detailed so the beam end can rotate, and AISC designs it as a simple connection. Two or three bolts do not change that when they all sit on one vertical line: the end pivots about that line.

A bolted end is fixed only if it was built to be, with bolts at both flanges spread over the depth of the beam so they form a couple. Bolts clustered at the web are a pin. The AISC criterion is on connection stiffness: with Ks the secant stiffness at service load, Ks L / EI at or below 2 may be taken as simple, and at or above 20 as fully restrained. Ordinary bolted connections sit near the bottom of that range.

Fixity is also a chain. A perfect moment connection into a column that can itself rotate is not a fixed end, and a fixed end generates a real end moment that whatever it bolts to has to carry.

What to do here: bracket it. Use simply supported for deflection, since assuming fixed under-predicts it by 5x under a distributed load and 4x under a central point load, in the unconservative direction. Use fixed-fixed to size the connection, since that gives the end moment it would have to carry. If the truth is partial fixity the real answer sits between the two, and finding where needs a frame analysis with a rotational spring at each end, which this tool does not do.

Load

Span and material

Cross-section

Bending is about the strong (horizontal) axis. Weak-axis bending is not offered.

Checks

A safety factor of 1 reports raw utilization against the published strength. Wood rows already carry NDS reference design values, which are reduced values, so leave the factor at 1 for those.