Beam Response Lab
Set a left pin and right roller, constant flexural rigidity E·I, one downward point load and/or a downward uniform load across the entire span. Closed-form Euler–Bernoulli expressions calculate support reactions, shear, sagging moment and downward deflection; the loads are superposed. Inspect the point-load shear jump explicitly. This limited browser model is for learning and checking assumptions, not approving a structure.
Key features
- Exact static support reactions for one point load and/or a full-span uniform load
- Piecewise shear and bending moment with explicit left/right limits at the point load
- Closed-form Euler–Bernoulli downward deflection and a solved maximum location
- Shear, moment and deflection diagrams plus a sampled numeric table
- Download SVG diagrams, dense CSV samples and settings/results JSON
- Visible unit conversions, sign convention and a large-deflection heuristic warning
How to use
- Choose the centre-point or mixed-load example, or enter a span L in metres and constant elastic modulus E and second moment I.
- Set a nonnegative point load P in kN and its location a strictly inside the span, and/or a nonnegative full-span uniform load w in kN/m.
- Calculate the simply supported response and check the two upward reactions and flexural rigidity E·I.
- Read the shear jump, peak moment, peak downward deflection and the three position diagrams; the numeric table shows both sides of a point load.
- Download SVG diagrams, numeric CSV or model JSON only after checking units and model limits.
Use cases
- Check a classroom midspan point-load formula against the full response diagram
- Compare a concentrated equipment load with a distributed load on the same idealized span
- Locate peak sagging moment and maximum downward displacement under an off-centre load
- Export transparent position samples for independent engineering review
Frequently asked questions
Which supports and load directions does this model use?
A vertical pin at the left end and roller at the right end carry one downward point load P and/or a downward uniform load w over the full span. Reactions act upward. It cannot represent cantilevers, multiple supports, moments, inclined loads or partial-span UDLs.
What are E, I and the units?
E is the constant elastic modulus in GPa, I is the constant second moment of area in cm⁴, and E·I is converted to N·m². Span and point location are metres; P and reactions are kN, w is kN/m, moment is kN·m and deflection is mm.
How are the diagrams and peaks calculated?
The solver superposes closed-form point and uniform load solutions. It evaluates moment at the load position and at any interior zero-shear point, and finds the downward deflection maximum from the continuous analytic slope. Diagram and CSV points are samples; the reported peaks are not chosen from the sample grid.
Why are there two shear values at the point load?
An ideal concentrated load causes a discontinuity in shear. The table and diagram show the limit just before and just after that load; the difference is P. Moment and displacement remain continuous.
Does this certify a real beam or tell me whether it is safe?
No. This small-deflection, linearly elastic Euler–Bernoulli model ignores shear deformation, self-weight unless entered as w, cross-section stress, lateral stability, connections, load combinations and code limits. The >1% span deflection flag is only a model-validity heuristic. An independent qualified structural review is required for design or construction decisions.
Are my beam dimensions uploaded?
No. Calculation and requested SVG, CSV and JSON creation run in this browser tab; the tool has no model-data upload endpoint.
Privacy
The entered beam values and calculations remain in browser memory. Files are generated locally only when you choose a download.
Comments & questions