Structural beam analysis calculator using Euler-Bernoulli beam theory. Calculate maximum deflection, bending moments, shear forces, reactions, and bending stress for simply supported, cantilever, and fixed beams under point and distributed loads.
Enter distance to extreme fiber to calculate maximum bending stress
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Analyze beams under various loading and support conditions using Euler-Bernoulli beam theory. Calculate maximum deflection, bending moments, shear forces, support reactions, and bending stress for structural engineering applications.
Beam analysis determines the internal forces and deformations in structural members subjected to loads. Using Euler-Bernoulli beam theory, engineers calculate bending moments (M), shear forces (V), deflections (δ), and stresses (σ) to ensure structural safety and serviceability. The analysis depends on support conditions (simply supported, cantilever, fixed) and load types (point loads, distributed loads).
Key Beam Formulas
M = PL/4, δ = PL³/(48EI), σ = Mc/IEnsure beams can safely support applied loads without failure.
Verify deflections meet code limits for occupant comfort.
Select the most efficient beam size for the application.
Design floor beams, roof rafters, and structural headers.
Analyze bridge deck beams and girders under traffic loads.
Size shafts and supports in mechanical equipment.
Ensure shelves and tables can support intended loads.
A simply supported beam rests on supports at both ends that allow rotation (like a plank on two sawhorses). A cantilever beam is fixed at one end and free at the other (like a diving board). Cantilevers experience higher moments and deflections for the same load and span.
Steel section properties are published in resources like the AISC Steel Manual. For rectangular sections, I = bh³/12. For circular sections, I = πd⁴/64. Wood beam properties are in species-specific tables. Our moment of inertia calculator can help compute I for various shapes.
Steel: ~200 GPa (29,000 ksi), Aluminum: ~70 GPa (10,000 ksi), Concrete: 25-35 GPa (varies with strength), Wood: 8-14 GPa (varies by species). Use values from material specifications or testing.
Compare calculated bending stress to allowable stress (typically 0.6×yield for steel). Check deflection against code limits (often L/360 for floor beams, L/240 for roofs). Ensure shear stress doesn't exceed allowable values. This calculator provides the values; building codes provide the limits.
This calculator uses Euler-Bernoulli beam theory which assumes: small deflections, linear elastic material, plane sections remain plane, and loads act in a principal plane. It's accurate for most structural applications but may not apply to deep beams, very flexible members, or non-linear materials.