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

From this allowable stress, the allowable axial load can be computed as
2 2
P = σ A = (91.43 N/mm )(804 mm ) = 73,510 N = 73.5 kN Ans.
allow
allow
(b) Allowable axial load P allow for KL = 2,750 mm: For an effective length KL = 2,750 mm,
the effective-slenderness ratio is
KL
r
= 2,750 mm
27.38 mm = 100.4
Since this slenderness ratio is greater than 66, the allowable compression stress is determined
from Equation (16.28):
351,000 351,000
σ allow = MPa = = 34.82 MPa
2 2
( KL/ r)
(100.4)
The allowable axial load is therefore
2 2
P = σ A = (34.82 N/mm )(804 mm ) = 27,995 N = 28.0 kN Ans.
allow
allow
ExAmpLE 16.7
A sawn rectangular timber of visually graded No. 2 Spruce–Pine–Fir (SPF) wood has
finished dimensions of 7.25 in. by 9.25 in. For this wood species and grade, the allowable
compression stress parallel to the wood grain is F c = 975 psi and the modulus of elasticity
is E′ min = 400,000 psi. The timber column has a length L = 16 ft, and pinned connections
are used at each end of the column. Use the AWC National Design Specification for Wood
Construction (NDS) column design formula to determine the allowable axial load P allow
that may be supported by the column.
Plan the Solution
The AWC NDS column design formula given in Equation (16.29) will be used to compute
the allowable axial load.
z
y
7.25 in.
9.25 in.
SolutioN
The AWC NDS column design formula is
where
⎧⎪
1 + ( F / F )
σ allow = Fc
⎨
−
⎩⎪ 2c
2
⎡1 + ( F / F ) ⎤
⎫
( F / F )
⎣⎢
2c
⎦⎥ − ⎪
⎬
c
⎭⎪
cE c cE c cE c
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 finished dimensions of the timber column are 7.25 in. by 9.25 in. The smaller of
these two dimensions is taken as d in the term KL/d. Since the column has pinned ends,
the effective-length factor is K = 1.0; therefore,
KL
d
(1.0)(16 ft)(12 in./ft)
= = 26.48
7.25 in.
703