Effective Length for Bending Formula and Calculator

Related Resources: calculators

Effective Length for Bending Formula and Calculator

Civil Engineering and Design
Beam Deflection and Stress Calculators Formulas & Structural Analysis

Wood Structural Design Effective Length for Bending Members Formula and Calculator

Preview: Wood Structural Design Effective Length Calculator

Effective Length, l_e , for Bending Members

Cantilever¹	where l_u /d < 7	where l_u /d ≥
eq. 1, Uniformly distributed load	l_e = 1.33 l_u	l_e = 0.90 l_u
eq. 2, Concentrated load at unsupported end	l_e = 1.83 l_u	l_e = 1.44 l_u
Single Span Beam ^{1, 2}
eq. 3, Uniformly distributed load	l_e = 2.06 l_u	l_e = 1.63 l_u
eq. 4, Concentrated load at center with no intermediate lateral support	l_e = 1.80 l_u	l_e = 1.37 l_u
eq. 5, Concentrated load at center with lateral support at center	l_e = 1.11 l_u
eq. 6, Two equal concentrated loads at 1/3 points with lateral support at 1/3 points	l_e = 1.68 l_u
eq. 7, Three equal concentrated loads at 1/4 points with lateral support at 1/4 points	l_e = 1.54 l_u
eq. 8, Four equal concentrated loads at 1/5 points with lateral support at 1/5 points	l_e = 1.68 l_u
eq. 9, Five equal concentrated loads at 1/6 points with lateral support at 1/6 points	l_e = 1.73 l_u
eq. 10, Six equal concentrated loads at 1/7 points with lateral support at 1/7 points	l_e = 1.78 l_u
eq. 11, Seven or more equal concentrated loads, evenly spaced, with lateral support at points of load application	l_e = 1.84 l_u
eq. 12, Equal end moments	l_e = 1.84 l_u

¹ For single span or cantilever bending members with loading conditions not specified in Table above:
e = 2.06 l_u where l_u/d < 7
e = 1.63 l_u + 3d where 7 ≤ l_u/d ≤ 14.3
e = 1.84 l_u where l_u/d > 14.3
2. Multiple span applications shall be based on table values or engineering analysis.

Where

l_u = laterally unsupported span length of bending member, in
d = least dimension of compression member, in.

Source:

National Design Specification for Wood Constuction
American Wood Council