Geotechnical Engineering Circular No. 9 Design, Analysis, and Testing of Laterally Loaded Deep Foundations that Support Transportation Facilities

Step 2: Determine the elastic critical buckling resistance, P

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Step 2: Determine the elastic critical buckling resistance, P
e
.
In determination of the nominal compressive resistance, buckling may occur with alack of sufficient bracing. AASHTO (2014) requires both flexural and torsional modes of buckling be checked if applicable. For fully embedded piles, the flexural buckling mode will be used. However, when the pile extends through water or air, doubly symmetric open section members (e.g., H-piles) must be evaluated for torsional buckling as well. The critical failure mode is the lesser buckling resistance, and is employed to define the nominal compressive resistance.
Flexural buckling
𝑃𝑃
𝑒𝑒
= Equation 11-30) Where P = Elastic critical buckling resistance (kips. t = Elastic modulus of steel (ksi).
= Gross cross-sectional area (in.
𝐾𝐾 = Effective length in the plane of buckling (Table 11-1) (dimensionless.
𝑙𝑙 = Unbraced length in the plane of buckling, or laterally unsupported length plus d f
where d f
is the depth to fixity below the ground (ins Radius of gyration about axis normal to plane of buckling (in. Torsional buckling
𝑃𝑃
𝑒𝑒
= �
𝜋𝜋
2
𝐸𝐸
𝑠𝑠𝑡𝑡
𝐶𝐶
𝑤𝑤
(𝐾𝐾
𝑘𝑘
𝐼𝐼
𝑘𝑘
)
2
+ 𝐺𝐺𝐺𝐺�
𝐴𝐴
𝑔𝑔
𝐼𝐼
𝑥𝑥
+ Equation 11-31)

165 In which
𝐶𝐶
𝑤𝑤
=
𝐼𝐼
𝑦𝑦
ℎ
2 4
𝐺𝐺 = Equation 11-32) Equation 11-33) Where
P𝑒 = Elastic critical buckling resistance (kips.
Est = Elastic modulus of steel (ksi).
Cw = Warping torsional constant (doubly symmetric open sections) (in.
Kz = Effective length for torsional buckling (dimensionless.
Iz = Unbraced length for torsional buckling (in.
G = Shear modulus (ksi).
J = St. Venant torsional constant (in.
Ag = Gross cross-sectional area (in.
I
𝑥𝑥
, I
y
= Moments of inertia about the major and minor principal axes of cross section, respectively (in.
ℎ = Distance between flange and centroids (in.

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