What is beam bending?

Beam bending occurs when a transverse load is applied to a structural member, causing it to deflect. The beam develops internal bending moments and shear forces to resist the load. The bending stress varies linearly from zero at the neutral axis to maximum at the extreme fibers.

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

A simply supported beam rests on two supports at its ends and is free to rotate. A cantilever beam is rigidly fixed at one end and free at the other. Cantilevers generally experience higher deflections and moments at the fixed support compared to simply supported beams of the same span and load.

How do I calculate beam deflection?

Beam deflection depends on the load type, span, elastic modulus (E), and moment of inertia (I). For a simply supported beam with central point load P: δ_max = PL³/(48EI). For UDL w: δ_max = 5wL⁴/(384EI). For cantilever with tip load P: δ_max = PL³/(3EI).

What is the moment of inertia in beam calculations?

The moment of inertia (I) is a geometric property of the beam cross-section that measures its resistance to bending. A larger I means less deflection and lower stress for the same load. For a rectangle: I = bh³/12. For a circle: I = πd⁴/64.

What is the maximum allowable deflection for a beam?

Common deflection limits are L/360 for floor beams under live load, L/240 for total load, and L/180 for roofs. Industrial applications may use L/500 or stricter. Always check the applicable building code or design standard for your specific application.

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Calculadora de flexión de vigas

Calcule el momento flector máximo, la flecha y la tensión para vigas simplemente apoyadas y en voladizo bajo diversos tipos de carga.

Carga puntual Carga uniformemente distribuida (CUD) Voladizo #164

Caso de carga

Longitud de la viga L (m)

Carga puntual P (kN)

Módulo elástico E (GPa)

Momento de inercia I (cm⁴)

Distancia a la fibra extrema c (mm)

Preajustes rápidos

Resultados

Momento flector máximo

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Flecha máxima

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Tensión por flexión máxima

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Relación luz/flecha

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Caso de carga

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Simplemente apoyada — Carga puntual en el centro

Simplemente apoyada — CUD

Voladizo — Carga puntual en la punta

Tensión por flexión

Donde σ es la tensión por flexión, M es el momento flector, c es la distancia a la fibra extrema, y I es el momento de inercia.

Caso de carga	M_max	δ_max
SA — Punto central	PL/4	PL³/(48EI)
SA — Punto a a	Pa(L−a)/L	fórmula compleja
SA — CUD w	wL²/8	5wL⁴/(384EI)
Cantilever — Carga puntual en el extremo	PL	PL³/(3EI)
Cantilever — Carga distribuida uniforme (UDL) w	wL²/2	wL⁴/(8EI)

⚠️ Nota: Estas fórmulas asumen comportamiento lineal-elástico, pequeñas deflexiones y vigas prismáticas (de sección transversal constante). Para cargas complejas, utilice el principio de superposición.