Simple Moment–Rotation Methodology for Predicting the Capacity of Concrete-Filled Steel Pipe Piles to Concrete Cap Connections

Acknowledgments

Notation

A_ij

area over which radial concrete stresses act;

A_Ubar,k

cross-sectional area of U-bar, k;

c_i

distance from the axis of rotation;

c_Ubar,k

distance from the axis of rotation to each U-bar, k;

d_{Pile_Infl.}

assumed inflection point location along the length of the pile;

d_rot.axis

assumed distance to the axis of rotation;

F_{conc_x-dir}

resultant forces in the x-direction from the radial concrete stresses;

F_{frict_x-dir}

resultant forces in the x-direction from the friction stresses;

F_ij

resultant forces from the radial concrete stresses;

F_{InterfaceShear}

interface shear force component at the top of the pile;

F_{surf-frict,ij}

surface-friction forces;

F_Ubar,k

force from U-bar, k;

F_Ubars

resultant force from all U-bars;

$f_{cc}^{\mathrm{\prime }}$

ultimate stress of the concrete;

f_u

ultimate stress of the steel;

f_y

yield stress of the steel;

L_eff

effective length factor;

L_eff,Ubar

effective length factor of the U-bar;

L_emb

embedment length of the pile in the cap;

M_conn

external moment from the pile;

M_{z_conc}

moment around the point of rotation resulting from the radial forces;

M_{z_frict}

moment around the point of rotation resulting from the friction forces;

M_{z_shear}

moment due to the interface shear force;

M_{z_Ubar}

resultant moment from the U-bars;

n_rad

number of layers in the radial discretization;

n_Ubar

number of U-bars;

n_vert

number of layers in the vertical discretization;

V_conn

external shear from the pile;

β

imposed angle of rotation;

Δ_i

lateral displacement at a given layer;

Δ_Ubar

displacement at the location of the U-bar;

ɛ_cu

ultimate strain of the concrete;

ɛ_i

lateral strain in the surrounding concrete at layer i;

ɛ_ij

radial strain distribution in the concrete along the surface of the pile at layer i;

ɛ_uar,k

longitudinal strains in the reinforcing steel of U-bar, k;

ɛ_y, ɛ_sh, ${\epsilon }_{su}^R$, and ɛ_su

strain limits for the steel;

μ

effective coefficient of friction between the pile steel and the cap concrete;

σ_ij

radial concrete stresses;

σ_Ubar,k

U-bar, k, stresses; and

θ_j

angle measured to radial division j of layer i.

References