Sections 6.3.1 and 6.3.2 apply to overall member behavior while 6.3.3 and 6.3.4 apply to local buckling.
6.3.2 Combined Axial Compression and Bending 6.3.2.1 Cylindrical Members
Cylindrical members subjected to combined compression and flexure shall be proportioned to satisfy both the following requirements at all points along their length.
C f f
f .
F f
F F
+ + ≤
−
′
2 2
m bx by
a
a a
e b
1 0 1
(6.20)
f f
f .
. F F
+ + ≤
2 2
bx by
a
y b
0 6 1 0 (6.21)
where the undefined terms used are as defined by the AISC 335-89.
When f F
a a
≤ 0.15, Equation (6.22) may be used in lieu of Equations (6.20) and (6.21).
f f
f .
F F
+ + ≤
2 2
bx by
a
a b
1 0 (6.22)
Equation (6.20) assumes that the same values of Cm and Fe′ are appropriate for fbx and fby. If different values are applicable, Equation (6.23), or other rational analysis, should be used instead of Equation (6.20):
C f C f
f f
F F
f .
F F
+
− −
′ ′
+ ≤
2 2
my by mx bx
a a
ex ey
a
a b
1 1
1 0 (6.23)
6.3.2.2 Cylindrical Piles
Column buckling tendencies should be considered for piling below the mudline. Overall column buckling is normally not a problem in pile design, because even soft soils help to inhibit overall column buckling.
However, when laterally loaded pilings are subjected to significant axial loads, the load deflection (P – Δ) effect should be considered in stress computations. An effective method of analysis is to model the pile as a beam column on an inelastic foundation. When such an analysis is utilized, the following interaction check shown in Equation (6.24), with the one-third increase where applicable, should be used:
f f
f .
. F F
+ + ≤
2 2
bx by
a
xc b
0 6 1 0 (6.24)
where Fxc is given by Equation (6.5).
6.3.2.3 Pile Overload Analysis
For overload analysis of the structural foundation system under lateral loads (see 9.8), the following interaction equation may be used to check piling members:
P A M Z .
F π F
+ ≤
xc xc
2 arcsin 1 0 (6.25)
where the arcsin term is in radians and
A is the cross-sectional area, m2 (in.2);
Z is the plastic section modulus, m3 (in.3);
P, M are the axial loading and bending moment computed from a nonlinear analysis, including the (P – Δ) effect;
Fxc is the critical local buckling stress from Equation (6.5) with a limiting value of 1.2Fy considering the effect of strain hardening.
Load redistribution between piles and along a pile may be considered.
6.3.2.4 Member Slenderness
Determination of the slenderness ratio Kl r for cylindrical compression members should be in accordance with AISC 335-89. A rational analysis for defining effective length factors should consider joint fixity and joint movement. Moreover, a rational definition of the reduction factor should consider the character of the cross section and the loads acting on the member. In lieu of such an analysis, the values in Table 6.1 may be used.
6.3.2.5 Reduction Factor
Values of the reduction factor Cm referred to in Table 6.1 are as follows (with terms as defined by AISC 335-89):
a) 0.85;
b) M
. . M
−
1 2
0 6 0 4 , but not less than 0.4, nor more than 0.85;
c) f
. F
−
′
a e
1 0 4 , or 0.85, whichever is less.
6.3.3 Combined Axial Tension and Bending
Cylindrical members subjected to combined tension and bending shall be proportioned to satisfy Equation (6.21) at all points along their length, where fbx and fby are the computed bending tensile stresses.
6.3.4 Axial Tension and Hydrostatic Pressure
When member longitudinal tensile stresses and hoop compressive stresses (collapse) occur simultaneously, the following interaction equation shall be satisfied:
A2+B2+2ν A B≤1 0. (6.26) where
( )(see Footnote 3) ( )SF
a b h
x y
0 5
f f . f
A F
+ −
= × 3
3 This implies that the entire closed-end force due to hydrostatic pressure is taken by the tubular member. In reality, this force depends on the restraint provided by the rest of the structure on the member and the stress may be more or less than 0.5fh. The stress computed by a more rigorous analysis may be substituted for 0.5fh.
Table 6.1—Values of K and Cm for Various Member Situations
Situation
Effective Length Factor
K
Reduction Factor Cm a
Superstructure legs
Braced 1.0 See 6.3.2.5 a)
Portal (unbraced) K b See 6.3.2.5 a)
Jacket legs and piling
Grouted composite section 1.0 See 6.3.2.5 c)
Ungrouted Jacket Legs 1.0 See 6.3.2.5 c)
Ungrouted piling between shim points 1.0 See 6.3.2.5 b) Deck truss web members
In-plane action 0.8 See 6.3.2.5 b)
Out-of-plane action 1.0 See 6.3.2.5 a) or b) c Jacket Braces
Face-to-face length of main diagonals 0.8 See 6.3.2.5 a) or c) c Face of leg to centerline of joint length
of K-braces
0.8 See 6.3.2.5 c) Longer segment length of X-braces 0.9 See 6.3.2.5 c)
Secondary horizontals 0.7 See 6.3.2.5 c)
Deck truss chord members 1.0 See 6.3.2.5 a), b), or c) c For K-braces and X-braces, at least one pair of members framing into a joint shall be in tension if the joint is not braced out-of-plane.
a Defined in 6.3.2.5.
b Use Figure C-C2.2 in commentary of AISC 335-89. This may be modified to account for conditions different from those assumed in developing the chart.
c Whichever is more applicable to a specific situation.
the term “A” shall reflect the maximum tensile stress combination,
( )SF
B f F
= ×
h h
hc
ν is Poisson’s ratio, equal to 0.3;
Fy is the yield strength, MPa (ksi);
fa is the absolute value of acting axial stress, MPa (ksi);
fb is the absolute value of acting resultant bending stress, MPa (ksi);
fh is the absolute value of hoop compression stress MPa (ksi);
Fhc is the critical hoop stress [see Equation (6.18)];
SFx is the safety factor for axial tension (see 6.3.6);
SFh is the safety factor for hoop compression (see 6.3.6).
6.3.5 Axial Compression and Hydrostatic Pressure
When longitudinal compressive stresses and hoop compressive stresses occur simultaneously, the following equations shall be satisfied:
( )(see Footnote 3) ( )SF ( )SF
a h b
x b
xc y
0 5 1 0
f . f f
F f .
+ × + ≤ (6.27)
SF f
F .
× h ≤
h hc
1 0 (6.28)
Equation (6.27) should reflect the maximum compressive stress combination.
The following equation should also be satisfied when fx > 0.5Fha
f . F f
F . F F .
− + ≤
−
2
x ha h
aa ha ha
0 5 1 0
0 5 (6.29)
where Faa =
SF Fxe
x
;
Fha = SF Fhe
h
;
SFx is the safety factor for axial compression (see 6.3.6);
SFb is the safety factor for bending (see 6.3.6);
fx = fa + fb + (0.5fh)(see Footnote 3); fx should reflect the maximum compressive stress combination.
Fxe, Fxc, Fhe, and Fhc are given by Equations (6.4), (6.5), (6.16), and (6.18), respectively. The remaining terms are defined in 6.3.4.
If fb > fa + 0.5fh, both Equation (6.26) and Equation (6.27) shall be satisfied.
6.3.6 Safety Factors
To compute allowable stresses within 6.2.5, 6.3.4, and 6.3.5, the safety factors in Table 6.2 should be used with the local buckling interaction equations.
Table 6.2—Safety Factors
Design Condition
Loading Axial
Tension Bending Axial Comp. a Hoop Comp.
1) Where the basic allowable stresses would be used, for example, pressures that will definitely be encountered during the installation or life of the structure.
1.67 Fy/Fbb 1.67 to 2.0 2.0
2) Where the one-third increase in allowable stresses is appropriate, for example, when considering interaction with storm loads.
1.25 Fy/1.33Fb 1.25 to 1.5 1.5
a The value used should not be less than the AISC 335-89 safety factor for column buckling under axial.
b The safety factor with respect to the ultimate stress is equal to 1.67 and illustrated in Figure B.6.3.