structural / loading analysis
Choose the support condition and load case.
Start with the structural model: support condition, applied loading, and stiffness assumptions. The expanded beam library is grouped by supports before load take-off, stress, and stability screens.
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Structural analysis tools.
Choose the closest idealised model. If the real structure does not match the stated support or loading assumptions, use a more suitable analysis method.
Simply supported beams
Determinate beams, from textbook single loads to flexible combinations.
- UDL + central point loadMaximum shear, moment, and elastic deflection.
- UDL + point load at any positionLeft and right reactions and critical positive moment.
- Full-span one-way triangular loadAsymmetric reactions, moment, and elastic deflection.
- Central triangular “tent” loadSymmetric reactions and maximum positive moment.
- One or two partial UDL zonesCentral, end, separated, or overlapping loaded lengths.
- Up to three point loadsEqual or unequal loads with equal or unequal spacing.
- UDL, point load, and prescribed end momentsSigned boundary moments with a transparent statics envelope.
Cantilever beams
Fixed-free members under individual or superimposed actions.
- Free-end point loadFixed-end action, rotation, and free-end deflection.
- Point load at any positionLoad-point and free-end movement, including the unloaded tail.
- Full-span uniform loadFixed actions and elastic free-end movement.
- Triangular load rising to free endPeak intensity, resultant, moment, rotation, and deflection.
- UDL + point load + end momentSame-sense elastic superposition with component deflections.
Fixed & propped beams
Indeterminate idealisations that require rotational restraint or displacement compatibility.
- Fixed-fixed full-span UDLEnd hogging, midspan sagging, reactions, and deflection.
- Fixed-fixed central point loadSymmetric end and midspan response.
- Fixed-fixed point load at any positionOff-centre reactions, end moments, and load-point deflection.
- Propped cantilever full-span UDLCompatibility reactions, hogging, sagging, and deflection.
- Propped cantilever point loadLoad-position-dependent prop reaction and moments.
Overhang & continuous beams
Support arrangements that can create both sagging and hogging regions.
- Single or double overhang beamFull-length UDL, one point load, reaction uplift, and moment envelope.
- Two-span continuous beamIndependent span UDLs, centre-support hogging, and span sagging.
Load path
Convert area loading into a transparent member line load.
- Slab load to beamSelf-weight, superimposed actions, tributary width, and beam line load.
Stress & stability screens
Simple elastic checks before detailed material and code verification.
- Elastic bending stressStress and utilisation from moment and section modulus.
- Column axial stressGross-area compression stress and utilisation.
- Euler column bucklingIdeal critical load, effective length, radius, and slenderness.
beam library / coverage
One parameterized calculator can cover several diagram tiles.
The library now groups equivalent textbook cases into flexible tools—for example, partial UDL zones cover central, end, separated, and overlapping uniform loads. Every live page declares its support model, sign convention, equations, limitations, and numerical regression fixture.
- Live now: 19 beam-response tools across six support families.
- Next: partial triangular patches and reversed cantilever UVLs.
- Next: three- and four-span continuous-beam cases.
- Later: stiffness-varying members and frame analysis, which require a general solver rather than closed-form shortcuts.