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Calculate beam loads, bending moments, and shear forces for simply supported, cantilever, and fixed beams. Supports UDL and point loads. Free structural engineering calculator.
Optional: Total load distributed over beam length
Optional: Concentrated load
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Understand beam types, bending moments, shear forces, and deflection for structural engineering projects.
A structural beam is a horizontal or inclined load-bearing member designed to resist bending and shear forces. Beams transfer loads from slabs, floors, and walls to columns and foundations, forming the structural skeleton of buildings, bridges, and industrial frameworks.
The three primary analysis outputs for any beam are the Bending Moment Diagram (BMD), the Shear Force Diagram (SFD), and the Deflection Profile. Each governs a different failure mode: flexural failure, shear failure, and serviceability (excessive sag) respectively.
Modern beam design codes (IS456, ACI 318, Eurocode 2) require engineers to verify all three. Over-designed beams waste material; under-designed beams risk catastrophic collapse. This calculator provides the fundamental elastic analysis underpinning all beam design codes.
M_max = wL² / 8w = distributed load (kN/m), L = span (m). Max BM at midspan.
M_max = PL / 4P = point load (kN), L = span (m). Applies when load is at midspan.
M_max = wL² / 2Max BM occurs at the fixed support. Free end has zero moment.
δ = 5wL⁴ / (384EI)E = elastic modulus (GPa), I = second moment of area (m⁴).
| Support Type | Reactions | Max BM Location | Max Deflection | Common Use |
|---|---|---|---|---|
| Simply Supported | 2 vertical | Midspan (UDL) | 5wL⁴/384EI | Floor beams, bridges |
| Cantilever | 1 fixed support | Fixed end | wL⁴/8EI | Balconies, canopies |
| Fixed Both Ends | 4 reactions | At supports & midspan | wL⁴/384EI | Portal frames |
| Propped Cantilever | 3 reactions | At fixed support | Reduced vs cantilever | Continuous beams |
| Continuous Beam | 3+ supports | Over interior supports | Spans must be analysed | Multi-bay floors |
Galileo Galilei published 'Two New Sciences', documenting the first study of beam bending and cantilever failure — founding modern structural mechanics.
Leonhard Euler derived the column buckling formula and pioneered elastic beam theory that remains the basis of structural analysis today.
Claude-Louis Navier published the full flexure formula (σ = My/I), establishing the relationship between bending moment, section geometry, and stress.
Saint-Venant completed the theory of elastic bending and torsion, enabling analysis of non-prismatic beams and bridges.
Hardy Cross developed the Moment Distribution Method, allowing hand-calculation of statically indeterminate multi-bay frames.
Finite Element Analysis (FEA) software democratised complex beam and frame analysis, enabling 3D structural modelling at scale.
The Indian Standard covering RC beam design including limiting deflection to span/250 under live load and span/350 for finishes.
Read source →American Concrete Institute standard defining shear, flexure, and deflection requirements for RC beams used in US and internationally.
Read source →European Standard for concrete structure design with rules for beam bending, shear verification, crack control, and deflection limits.
Read source →A deeper beam is always stronger
Depth improves bending, but wide flanges (I-section) offer far better stiffness-to-weight ratio. Section shape matters more than depth alone.
Maximum moment always occurs at midspan
For cantilevers, max moment is at the fixed support. For continuous beams, it occurs over interior supports and must be checked at both locations.
Steel beams never deflect under design loads
Steel beams deflect elastically under load. Aesthetically unacceptable deflections require camber (pre-cambering) built into fabrication.
Shear failure is less critical than bending failure
Shear failure is brittle and sudden, while bending failure is often ductile. Codes require explicit shear checks — especially near supports.
Combine beam analysis with column load, concrete, and reinforcement calculators for complete structural design.