000_[Jonathan_Ochshorn]_Structural_Elements_for_Architecture_400

Table A-3.6 (Continued)
F. Beam stability factor

The beam stability factor, CL, may apply to glulam and timber beams but not ordinarily to
dimension lumber—and only when the compression edge of the beam is unbraced by a roof or

floor deck. For continuously braced beams—that is, when le ϭ 0—CL ϭ 0. For glulam, use only
the smaller value of CL or CV. For timbers, combine CL with the size factor, CF. Use only when the
beam depth is greater than its width. For these conditions:

Where CL ϭ A Ϫ A2 Ϫ B
A ϭ 1 ϩ (FbE /F*b )

1.9

B ϭ (FbE /Fb*)
0.95

Fbe ϭ 1.20b2EmЈ in
led

F*b ϭ Fb with all adjustments except CV, CL, and Cfu
EmЈ in ϭ EminCM (see Table A-3.9 for adjustments to E and Emin)

d ϭ beam depth (in.)
b ϭ beam width (in.)
lu ϭ the unsupported (unbraced) length (in.), that is, the greatest distance between lateral

braces, including bridging or blocking, along the length of the beam

le ϭ the effective unsupported length (in.) where continuous lateral support is not provided as
shown in these selected loading patterns:

Load Arrangement Effective Length, le

le ϭ 2.06lu for lu /d < 7

Uniform load: no lateral support except at ends. le ϭ 1.63lu ϩ 3d for lu /d ≥ 7
le ϭ 1.80lu for lu /d < 7

Single point load at midspan: no lateral support except at le ϭ 1.37lu ϩ 3d for lu /d ≥ 7
ends. le ϭ 1.11lu

Single point load at midspan: lateral support under load and
ends only.

le ϭ 1.68lu

Point loads at third points: lateral support under loads and
ends only.

le ϭ 1.54lu

Point loads at quarter points: lateral support under loads and
ends only.

Notes:
1. CF ϭ 0.9 for all 2ϫ dimension lumber having nominal width greater or equal to 14. CF ϭ 1.0 for all 4ϫ
dimension lumber having nominal width greater or equal to 14.
2. CM ϭ 1.0 for dimension lumber when FbCF ≤ 1150 psi.

(Continued )