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For Students · Cantilever Balcony

Cantilever Balcony for a bridge girder

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a bridge girder live below — adjust the inputs and watch it respond, right in your browser.

Beam Deflection

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Beam Deflection & BendingLive

Euler-Bernoulli beam theory

Controls

Presets

Span L (m)

Load P (kN)

Flexural rigidity EI (kN·m²)

Euler-Bernoulli theory relates a beam's deflection and internal moment to its load, span, and flexural rigidity EI. Deflection grows with the cube or fourth power of span, which is why doubling a span is far worse than doubling the load. Educational tool — not a substitute for a stamped structural design.

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Data Inspector

Max deflection1.30 mm

Max moment12.5 kN·m

Span/deflectionL/3840

Governing equation

δ = \frac{P L ^{3}}{48 E I} = \frac{10 \cdot 5 ^{3}}{48 \cdot 20000} = 1.30 mm

Reading this result: At L/3840 this beam clears the usual L/360 serviceability limit, so strength (not deflection) is likely to govern the design.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Concrete Beam

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Reinforced Concrete BeamLive

flexural capacity (ACI)

Controls

Presets

Width b (mm)

Effective depth d (mm)

Steel area As (mm²)

Concrete f'c (MPa)

Steel fy (MPa)

A reinforced concrete beam resists bending through a compression block in the concrete and tension in the steel. Setting these forces equal gives the stress-block depth a, and the moment capacity Mn = As·fy·(d − a/2). A tension-controlled section (steel yields first) fails gradually — the ductile behavior codes require. Educational tool, not a design.

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Data Inspector

Stress block a82 mm

Nominal Mn289 kN·m

Design φMn260 kN·m

Behaviortension-controlled

Governing equation

a = \frac{A _{s} f _{y}}{0.85 f _{c}^{'} b} = 82 mm, M_{n} = A_{s} f_{y} (d - \frac{a}{2}) = 1500 \cdot 420 (500 - \frac{82}{2}) = 289 kN\cdotm

Reading this result: Tension-controlled: with ρ ≈ 0.0100 well under 0.75·ρ_bal the steel yields first and the beam warns before it fails, while Mn = As·fy·(d − a/2) rises almost linearly with steel here.

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Frequently asked questions

Is this good for students?: Yes — this version of "Cantilever Balcony for a bridge girder" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.