Beam Load Span Calculator

How to Use the Beam Load Span Calculator

This calculator performs a simplified bending stress analysis for a simply supported beam carrying a uniformly distributed load. Enter the clear span in feet, the total load in pounds per linear foot (PLF) which includes both dead and live loads, and select the beam material. The calculator determines the maximum bending moment using the formula M = wL²/8, then divides by the material's allowable bending stress (Fb) to find the required section modulus. It recommends the smallest standard lumber size whose section modulus meets or exceeds the requirement.

The total load in PLF represents everything the beam must carry per foot of its length. For a floor beam, this includes the weight of the floor itself (dead load, typically 10-20 PLF) plus the live load from occupants and furniture (typically 40 PLF for residential floors). If the beam supports a tributary width of 12 feet with a 50 PSF total load, the beam load would be 600 PLF.

Beam Materials and Allowable Stresses

Different beam materials have different allowable bending stresses. Douglas Fir-Larch No. 2 is the most common structural lumber with an Fb of 1,350 PSI. Southern Pine No. 2 is slightly stronger at 1,500 PSI. Spruce-Pine-Fir is more economical at 1,150 PSI but requires larger members. LVL (Laminated Veneer Lumber) offers significantly higher strength at 2,600 PSI, making it ideal for long spans and heavy loads where solid lumber would be impractically large. Steel A36 beams have an allowable bending stress of 21,600 PSI and are used where wood beams cannot meet the structural requirements.

Understanding Section Modulus

The section modulus (S) is a geometric property that measures a beam's resistance to bending. For rectangular sections like lumber, S = bd²/6, where b is the width and d is the depth. Because depth is squared, doubling the depth of a beam increases its section modulus by four times. This is why deeper beams are much stronger in bending than wider beams. A 2x12 has a section modulus of 31.64 cubic inches, more than four times the 7.56 cubic inches of a 2x6, even though the cross-sectional area is only about twice as large.

Limitations of This Calculator

This calculator checks bending stress only. A complete beam design must also verify deflection (typically limited to L/360 for floors), shear stress at the supports, bearing capacity where the beam sits on its supports, and lateral-torsional buckling for deep, narrow beams. For critical structural members, always have a licensed engineer perform the complete design, including load path analysis and connection details.

Frequently Asked Questions

How do I determine beam size for a span?

Calculate the maximum moment M = wL²/8, then divide by the allowable stress to get the required section modulus. Select the smallest beam whose section modulus exceeds this value. A 12-foot span with 200 PLF in Douglas Fir needs about 24 in³, satisfied by a 2x12 or 4x8.

What is the max span for a 2x10?

A Douglas Fir 2x10 (S = 21.39 in³) carrying 50 PLF can span approximately 10-12 feet. Higher loads or lower-grade lumber reduce the allowable span. Always check deflection limits as well.

What does PLF mean?

Pounds per linear foot (PLF) is the total distributed load along each foot of beam length. It includes dead load (structure weight) plus live load (occupants, furniture, snow). Multiply tributary width by per-square-foot loads to get PLF.

What is section modulus?

Section modulus measures a beam cross-section's resistance to bending, in cubic inches. For rectangular beams, S = bd²/6. Deeper beams have much higher section moduli because depth is squared.

What is the difference between LVL and solid lumber?

LVL has an allowable bending stress of about 2,600 PSI vs 1,350 PSI for Douglas Fir, meaning it can span farther or carry heavier loads at the same size. LVL is also more consistent with fewer natural defects.