What is the difference between a simply supported beam and a cantilever?

A simply supported beam rests on two supports that provide vertical reactions but no moment resistance. A cantilever is fixed at one end (providing both a vertical reaction and a moment reaction) and free at the other. Cantilevers experience their maximum moment at the fixed support, while simply supported beams have zero moment at both ends.

What causes beam failure — stress or deflection?

Beams can fail by yielding (bending stress exceeds yield strength), shear failure (shear stress exceeds shear strength), or excessive deflection (serviceability limit). In most structural applications, deflection limits (typically L/300 to L/360 for floors) govern the design rather than stress limits. Always check both strength and serviceability.

Beam Stress & Deflection Calculator – Bending, Shear & Moment | CalcEngines

Structural Engineering · CalcEngines

Beam Stress & Deflection Calculator

Compute bending stress, shear stress, max deflection, reactions, and section modulus for simply supported, cantilever, and fixed beams under point loads, UDL, and applied moments.

6 beam configs SFD & BMD diagrams Material library Utilisation check Deflection limits Free to use

Beam Configuration

Beam Geometry & Load

Beam Length L (mm) Total span length

Point Load P (N) Applied point force

Load Position a (mm) Distance from left / fixed end

Cross-Section

Section Preset Or enter custom values below

Section Shape

Width b (mm) Flange width / diameter

Height h (mm) Overall depth

Material

Deflection Limit (L/n)

Live Beam Diagram

Primary Results

Max Deflection

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Press Calculate

Bending Stress

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Max Moment

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Max Shear

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Enter beam parameters above and click Calculate.

Shear Force & Bending Moment Diagrams

Utilisation & Safety

Utilisation = actual / allowable. Values below 100% are acceptable. Deflection check uses the selected L/n serviceability limit.

Detailed Results

Reaction Rₐ

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Left / fixed end (N)

Reaction Rₑ

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Right end (N)

Moment @ Fixed

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N·mm (cantilever)

Deflection @ Load

—

mm at load point

Slope @ A

—

radians

Slope @ B

—

radians

Section Properties

I (mm⁴)

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2nd Moment of Area

Z (mm³)

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Section Modulus

yₘₐₓ (mm)

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Extreme Fibre Distance

A (mm²)

—

Cross-Section Area

I_rect = bh³/12 · I_circ = πd&sup4;/64 · I_I-sec (approx) = bh³/12 − (b−t_w)(h−2t_f)³/12 · Z = I/y_max

Material Reference

Material	E (GPa)	Yield / f_y (MPa)	UTS (MPa)	Density (kg/m³)	Poisson ν	Notes
Structural Steel S275	200	275	430	7850	0.30	EN 10025 S275
Structural Steel S355	200	355	490	7850	0.30	High-strength structural
Aluminium 6061-T6	69	276	310	2700	0.33	Aerospace / structural
Aluminium 7075-T6	72	503	572	2810	0.33	High-strength aluminium
Timber C24	11	24	40	420	0.38	EN 338 softwood
Concrete C30/37	33	30	37	2400	0.20	Characteristic cube
Cast Iron	170	250	400	7200	0.26	Grey cast iron typical
Titanium Ti-6Al-4V	114	880	950	4430	0.34	Aerospace grade

Formula Reference

σ = M · y / IBending stress at fibre distance y

τ = V · Q / (I · b)Shear stress at neutral axis

δ(SS, P central) = PL³/48EIMax deflection, SS beam, central load

δ(SS, UDL) = 5wL&sup4;/384EIMax deflection, SS beam, full UDL

δ(Cant, P free end) = PL³/3EIMax deflection, cantilever, tip load

δ(Cant, UDL) = wL&sup4;/8EIMax deflection, cantilever, UDL

I_rect = bh³/122nd moment of area, rectangle

Z = I / y_maxElastic section modulus

Common Questions

How do you calculate beam deflection? +

Maximum deflection depends on beam type and loading. For a simply supported beam with a central point load: δ = PL³/(48EI). For a UDL on a simply supported beam: δ = 5wL&sup4;/(384EI). For a cantilever with tip load: δ = PL³/(3EI). E is Young’s modulus and I is the second moment of area. Larger I (deeper or wider sections) dramatically reduce deflection.

What is the bending stress formula? +

Bending stress: σ = M · y / I, where M is the bending moment (N·mm), y is the distance from the neutral axis to the point of interest (mm), and I is the second moment of area (mm&sup4;). Maximum bending stress occurs at the extreme fibres (y = h/2 for symmetric sections). It equals M/Z where Z is the section modulus.

What is the section modulus and why does it matter? +

The elastic section modulus Z = I/y_max. It directly links bending moment to stress: σ_max = M/Z. A higher Z means greater moment capacity for the same stress. Doubling the beam depth quadruples I and doubles Z, which is why deep I-beams are so efficient. The plastic section modulus S (for steel design) is higher, giving additional reserve capacity beyond first yield.

What are typical deflection limits for beams? +

Common serviceability deflection limits: L/200 for general structural elements; L/300 for floor beams; L/360 for floors with plaster ceilings; L/500 for sensitive equipment or precision structures. In most building designs, deflection governs rather than stress. Always check the governing code (EN 1993 for steel, EN 1995 for timber, AISC for US practice).

How does a fixed beam differ from a simply supported beam? +

A fixed beam has moment reactions at both ends (preventing rotation), which reduces midspan moment and deflection significantly compared to a simply supported beam. Under a UDL, a fixed beam’s max midspan moment is wL²/24 vs wL²/8 for simply supported — a factor of 3 reduction. However, fixed ends develop hogging moments of wL²/12, so both the supports and midspan must be designed for bending.

Formulae based on Euler-Bernoulli beam theory. For composite, curved, or deep beams consult specialist analysis.
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