Lumber design values used to calculate maximum horizontal spans include modulus of elasticity (E), bending strength (Fb), and shear strength (Fv). Bearing strength in compression perpendicular to grain (Fcp) is used to determine the minimum required bearing length at each end of joists and rafters. Calculated spans incorporate design value adjustments appropriate for repetitive-member use (Cr = 1.15), duration of load (CD), lumber size (CF), wet service conditions (CM), and incised lumber (Ci). The 2012 National Design Specification® for Wood Construction (NDS®) specifies appropriate magnitudes for lumber design values and adjustment factors.
Maximum horizontal joist and rafter spans are taken as the smallest span (L) calculated from the following three formulas:
based on bending strength (Fb)
where s = spacing between joists or rafters
Sx = section modulus for strong-axis bending of joist or rafter
wT = total distributed load (D + L, or D + Lr, or D + S)
supported by joist or rafter, in terms of load per unit area
based on deflection limit and modulus of elasticity (E)
where Ix = strong axis moment of inertia for joist or rafter
wL = distributed live load (L or Lr) or distributed snow
load (S) supported by joist or rafter,
in terms of load per unit area
deflection constant = constant term in denominator of
deflection limit (e.g., L/360)
based on shear strength (Fv)
where A = cross-sectional area of joist or rafter
The minimum required bearing length (lb) at each end of a joist or rafter is determined from the following formula:
where t = thickness of joist or rafter
Live load (L), snow load (S), and roof live load (Lr) are assumed uniformly distributed over the horizontal projected span for sloped members, as specified in the model building codes. In addition, the dead load (D) is assumed uniformly distributed over the horizontal projected span (rather than being distributed over the true length of sloped members). The assumption regarding dead load distribution is based on historical and current criteria for Joist and Rafter Span Tables adopted in the model building codes.
The Span Calculator was designed and created by Cameron Knudson and Dr. David Pollock at Washington State University. Support for development of the Span Calculator was provided by American Wood Council.