Point Load Calculator

About the Point Load Calculator

A point load (concentrated load) is a force applied at a single location on a beam, such as a post landing on a beam, a heavy appliance, or a hung load. Unlike uniform loads that spread evenly, point loads create peak stress at the load location and unequal reactions at the supports.

This point load calculator analyzes a simple beam (two supports at the ends) with a single concentrated load at any position along the span. It computes the support reactions, the maximum bending moment, and the maximum deflection. When the load is at mid-span, the formulas simplify, but this calculator handles any position.

Point load analysis is essential when a post from an upper level lands on a beam, when a hot tub is concentrating load at one location, or when any heavy object creates a localized loading condition.

When This Page Helps

Point loads create stress concentrations that can govern beam design. This calculator gives you the exact reactions, moment, and deflection for any load position, which is essential for accurate beam sizing.

How to Use the Inputs

1. Enter the beam span in feet.
2. Enter the point load in pounds.
3. Enter the distance from the left support to the load.
4. Enter the beam's moment of inertia (I) and modulus of elasticity (E) for deflection.
5. Read the reactions, maximum moment, and maximum deflection.

Example Calculation

Tips & Best Practices

• A point load at mid-span creates the maximum possible moment: P×L/4.
• Moving the load off-center reduces the moment but creates unequal reactions.
• Multiple point loads can be analyzed by superposition—calculate each separately and add the results.
• Point loads at or near supports create high shear but low moment.
• When a post lands on a floor, the load distributes through the subfloor to nearby joists—it's not truly a single point on the beam below.
• For critical point loads, always have an engineer verify the beam and connection design.

Simple Beam Formulas

The simple beam (pin-pin) is the most common structural model in residential construction. Support reactions are determined by static equilibrium. For a point load P at distance a from the left support on a beam of span L: R1 = P(L−a)/L and R2 = Pa/L. The moment at the load location is P×a×(L−a)/L.

Combined Point and Uniform Loads

In practice, beams often carry both uniform loads (floor dead and live loads) and point loads (posts). The total effect is the sum of the individual cases by superposition. Calculate the moment and deflection for each load case separately, then add them together.

Post Bearing on Beams

When a post bears on a beam, a steel post base or bearing plate should distribute the load over a wider area to prevent crushing the beam fibers at the bearing point. The required bearing area depends on the load and the wood's perpendicular-to-grain compression strength (Fc⊥).

Frequently Asked Questions

• What if the load is at mid-span?

  At mid-span, reactions are equal (P/2 each), maximum moment is P×L/4, and maximum deflection is P×L³/(48×E×I). These are the standard formulas for a center-loaded simple beam.

• How do I handle multiple point loads?

  Use superposition: analyze each load separately and add the reactions, moments, and deflections. This method works for any number of point loads on a simple beam.

• What creates a point load in residential construction?

  Posts from upper levels, heavy equipment (hot tubs, pianos), concentrated reactions from headers, and any localized load. Jack studs under a header create point loads on the plate and framing below.

• Is a point load worse than a uniform load?

  For the same total load, a mid-span point load creates twice the bending moment of a uniform load (PL/4 vs. wL²/8 = PL/8 when P = wL). So yes, point loads are generally more severe.

• How does point load location affect deflection?

  Maximum deflection occurs at or near mid-span regardless of where the point load is applied. For a load at mid-span, the deflection is largest. Moving the load toward a support reduces deflection significantly.

• Do I need a post directly under a point load?

  Not necessarily. The beam distributes the load to its supports. But if the beam isn't large enough, adding a post or column at or near the point load converts it into a multi-span beam, reducing moment and deflection.