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

The reduced Euler buckling stress term used in the AWC NDS formula has the value
F
cE
=
0.822E′
( KL/ d)
0.822(400,000 psi)
= = 468.92 psi
(26.48)
min
2 2
Also,
F
F
cE
c
468.92 psi
= = 0.4809
975 psi
This ratio, along with the values F c = 975 psi and c = 0.8 (for sawn lumber), are used in
the AWC NDS formula to calculate the allowable compression stress for the timber
column:
σ
allow
⎧⎪
1 + ( F / F )
= Fc
⎨
−
⎩⎪ 2c
⎧
⎪
= (975 psi) 1 +
⎨
(0.4809) −
2(0.8)
⎩
⎪
2
⎡1 + ( F / F ) ⎤
⎫
F / F
⎣⎢
2c
⎦⎥ − ⎪
⎬
c
⎭⎪
⎡1 + (0.4809) ⎤
⎢ ⎥ −
⎣ 2( 0.8)
⎦
2
= (975 psi) 0.9256 − 0.9256 − 0.6011
= 409.5 psi
cE c cE c cE c
{ }
2
0.4809
0.8
The allowable axial load that may be supported by the column is therefore
P = σ A = (409.5 psi)(7.25 in.)(9.25 in.) = 27,462 lb = 27,500 lb Ans.
allow
allow
⎫
⎪
⎬
⎭
⎪
pRoBLEmS
p16.27 Use the AISC equations to determine the allowable
axial load P allow that may be supported by a W8 × 48 wide-flange
column for the following effective lengths: (a) KL = 13 ft and
(b) KL = 26 ft. Assume that E = 29,000 ksi and σ Y = 50 ksi.
z
x
P
y
p16.28 Use the AISC equations to determine the allowable
axial load P allow that may be supported by an HSS152.4 × 101.6 × 6.4
column for the following effective lengths: (a) KL = 3.75 m and
(b) KL = 7.5 m. Assume that E = 200 GPa and σ Y = 320 MPa.
p16.29 The 10 m long HSS304.8 × 203.2 × 9.5 (see Appendix B
for cross-sectional properties) column shown in Figure P16.29/30
is fixed at base A with respect to bending about both the strong and
weak axes of the HSS cross section. At upper end B, the column is
restrained against rotation and translation in the x–z plane (i.e.,
bending about the weak axis) and against translation in the x–y
plane (i.e., the column is free to rotate about the strong axis). Use
the AISC equations to determine the allowable axial load P allow that
may be supported by the column, on the basis of (a) buckling in
the x–y plane and (b) buckling in the x–z plane. Assume that
E = 200 GPa and σ Y = 320 MPa.
B
A
FIGURE p16.29/30
p16.30 The 25 ft long HSS6 × 4 × 1/8 (see Appendix B for
cross-sectional properties) column shown in Figure P16.29/30 is
L
z
Strong
axis
Weak
axis
y
704