Beam Load Calculator

For Simply Supported Beams with Point Load:

Where RA and RB are reactions at left and right supports, P is the point load, a is distance from left support to load, and b is distance from load to right support (L = a + b).

For Uniformly Distributed Load:

For symmetric loading, reactions at both ends are equal to half the total load (w × L).

Equilibrium Equations:

Simply Supported Beam

A beam supported at both ends, free to rotate at supports. This is the most common beam type in buildings and bridges. Reactions act vertically upward at each support. The beam experiences maximum bending moment at mid-span.

Cantilever Beam

A beam fixed at one end and free at the other. Common in overhanging structures, balconies, and brackets. Fixed support provides both vertical reaction and restraining moment. Deflection is typically larger than simply supported beams.

Fixed-Fixed Beam (Both Ends Fixed)

A beam with both ends fixed, preventing rotation at supports. Both vertical reactions and moment reactions occur. This condition provides the most rigid support and lowest deflections. Common in reinforced concrete structures.

Fixed-Pinned Beam

A beam with one fixed end and one pinned end. This intermediate condition between simply supported and fixed-fixed provides better load distribution. Used in composite structures and certain bridge designs.

Point Load

A concentrated load applied at a single point along the beam. Common examples include column reactions, equipment loads, or concentrated wheel loads. Creates maximum bending moment at the point of application for cantilever beams, and at specific locations for simply supported beams.

Uniformly Distributed Load (UDL)

A load uniformly distributed over a length of the beam (lb/ft or kN/m). Examples include floor slabs, snow loads, or self-weight. Results in a parabolic bending moment diagram with maximum at mid-span for simply supported beams.

Uniformly Varying Load (UVL)

A load that increases or decreases uniformly along the beam length. Common in hydraulic structures, soil pressure on walls, or triangular load distribution. Creates cubic bending moment diagrams with specific peak locations depending on beam type.

What is the difference between simply supported and cantilever beams?

Simply supported beams are supported at both ends and are free to rotate at the supports. Cantilever beams are fixed at one end and extend freely from that point. Cantilevers experience larger deflections and bending moments at the fixed end for the same load, while simply supported beams experience maximum moment at mid-span.

How do you calculate beam deflection?

Beam deflection is calculated using the formula δ = (Load × L³) / (E × I), where L is the span, E is elastic modulus, and I is the moment of inertia. The exact formula depends on beam type and load configuration. Deflection increases with the fourth power of length, making long spans especially prone to deflection issues.

What is the maximum allowable deflection for beams?

Maximum allowable deflection is typically L/360 for floor beams (where L is span in inches), L/240 for roof beams, and L/480 for sensitive applications. For a 12-foot beam, L/360 = 0.4 inches. Building codes specify limits to prevent structural and aesthetic damage.

What is a uniformly distributed load (UDL)?

A UDL is a load spread uniformly across the entire length of a beam, measured in pounds per foot (lbs/ft) or kilonewtons per meter (kN/m). Examples include floor slabs, snow loads, and dead load from the beam itself. This creates a parabolic bending moment diagram.

How do you calculate shear force in a beam?

Shear force at any section is calculated by summing all vertical forces to one side of that section. For a simply supported beam with UDL, maximum shear occurs at the supports and equals (w × L) / 2. The shear force diagram helps identify critical sections and design requirements.

What is bending moment in structural engineering?

Bending moment is the internal moment that develops in a beam to resist applied loads. It causes the beam to bend, with the top fiber in compression and bottom fiber in tension. Maximum bending moment determines the required beam strength. The moment diagram shows moment values along the beam length.

What is the difference between elastic modulus and moment of inertia?

Elastic modulus (E) is a material property representing stiffness (psi or MPa). Moment of inertia (I) is a geometric property representing resistance to bending (in⁴ or mm⁴). Both affect deflection: deflection is inversely proportional to (E × I). Higher E or I results in less deflection.

When do you need a structural engineer for beam design?

Always consult a structural engineer for critical applications, building code compliance requirements, unusual loading patterns, long spans, or when calculations indicate marginal safety. This calculator provides estimates but is not a substitute for professional structural design and analysis for real projects.