Calculate beam reactions, maximum moment, and deflection from a single point load at any position along a simple beam span.
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.
Precise calculations are essential for meeting regulatory requirements, passing inspections, and ensuring the long-term structural integrity and safety of the completed project.
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. This quantitative approach replaces rule-of-thumb estimates with precise calculations, minimizing material waste and reducing the likelihood of costly change orders during construction.
R1 = P × (L − a) / L R2 = P × a / L Max Moment = P × a × (L − a) / L Max Deflection (at center, load at a) = P × a × (L² − a²)³² / (9√3 × E × I × L)
Result: R1 = 3,214 lbs, M = 17,857 ft-lbs
A 5,000-lb point load 5 ft from the left support on a 14-ft beam: R1 = 5000×(14−5)/14 = 3,214 lbs. R2 = 5000×5/14 = 1,786 lbs. Max moment = 5000×5×9/14 = 16,071 ft-lbs at the load location.
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.
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.
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⊥).
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.
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.
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.
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.
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.
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.