Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

For intermediate-length columns with effective-slenderness ratios between 9.5 and 66,
σ allow = [20.2 − 0.125( KL/ r)] ksi
KL
(16.27)
= [139 − 0.868( KL/ r)] MPa where 9.5 < ≤ 66
r
699
EMPIRICAL COLuMN
FORMuLAS—
CENTRIC LOAdINg
For long columns with effective-slenderness ratios greater than 66,
51,000
σ allow = ksi
2
( KL/ r)
351,000
KL
= MPa where > 66
2
( KL/ r)
r
(16.28)
Wood columns
The design of wood structural members is governed by the document National Design Specification
for Wood Construction with Supplement, published by the American Wood Council
(AWC). 3 The National Design Publication Specification (NDS) provides a single formula for
the design of rectangular wood columns. The format of this formula differs somewhat from
that of the formulas for steel and aluminum in that the effective-slenderness ratio is expressed
as KL/d, where d is the finished dimension of the rectangular cross section. The effectiveslenderness
ratio for wood columns must satisfy KL/d ≤ 50. The NDS formula is
σ =
allow
⎧⎪
1 + ( F / F )
Fc
⎨
−
2c
⎩⎪
⎡1 + ( F / F ) ⎤
⎣⎢ 2c
⎦⎥
− F / F ⎫⎪
⎬
c
⎭⎪
2
cE c cE c cE c
(16.29)
where
F c = allowable stress for compression parallel to grain,
0.822Emin
′
FcE
=
= reduced Euler buckling stress,
2
( KL/ d)
E′ min = adjusted modulus of elasticity for stability calculations, and
c = 0.8 for sawn lumber.
The effective-slenderness ratio KL/d is taken as the larger of KL/d 1 or KL/d 2 , where d 1 and
d 2 are the two finished dimensions of the rectangular cross section.
Local Instability
All of the discussion so far has been concerned with the overall stability of the column, in
which the entire column length deflects as a whole into a smooth curve. However, no discussion
of compression loading is complete without mentioning local instability. Local instability
occurs when elements of the cross section, such as a flange or a web, buckle because of the
compressive load acting on them. Open sections such as angles, channels, and W sections are
particularly sensitive to local instability, although it can be a concern with any thin plate or
shell element. To address local instability, design specifications typically define limits on the
acceptable width-to-thickness ratios for various types of cross-sectional elements.
3
National Design Specification for Wood Construction, American Wood Council, Leesburg, VA, 2015.