Roof Beam Span Calculator Example Calculation:

Scenario: Calculate the maximum span for a floor joist made of Douglas Fir-Larch No. 1, with a spacing of 16 inches on center, supporting a live load of 40 psf (pounds per square foot) and a dead load of 10 psf.

Step-by-Step Calculation:

1. Determine the Modulus of Elasticity (E) and Bending Strength (Fb):
   • For Douglas Fir-Larch No. 1, typical values are:
     • E = 1,900,000 psi (pounds per square inch)
     • Fb = 875 psi
2. Calculate the Maximum Span Using the Formula:
   • The general formula for the maximum span L (in inches) is given by:
     L = √((8 x Fb x I) / (W x S))
     where:
     • I is the moment of inertia
     • W is the uniform load (in pounds per linear foot, plf)
     • S is the section modulus
3. Calculate the Uniform Load (W):
   • Convert the live load and dead load to uniform load:
     W = (40 + 10) psf × (16/12) (spacing in feet)
     W = 50 psf × 1.33 feet
     W = 66.5 plf
4. Section Properties (for a typical 2×10 joist):
   • For a 2×10 (nominal), the actual dimensions are 1.5 inches by 9.25 inches.
   • The moment of inertia I is calculated as:
     I = (b × d³) / 12
     I = (1.5 × 9.25³) / 12
     I ≈ 98.57 in⁴
   • The section modulus S is:
     S = (b × d²) / 6
     S = (1.5 × 9.25²) / 6
     S ≈ 21.36 in³
5. Calculate the Maximum Span (L):
   • Substitute the values into the span formula:
     L = √((8 × 875 × 98.57) / (66.5 × 21.36))
     L = √((688420 × 98.57) / 1419.84)
     L ≈ √47700.94
     L ≈ 218.36 inches
   • Convert inches to feet:
     L ≈ 218.36 / 12 ≈ 18.2 feet

Conclusion: For a Douglas Fir-Larch No. 1 floor joist with a spacing of 16 inches on center, supporting a live load of 40 psf and a dead load of 10 psf, the maximum allowable span is approximately 18.2 feet.