Resilient Posttensioned Bridge Bent with Buckling Restrained Brace

Acknowledgments

Notation

A_PT

area of PT bars;

A_BRB

area of steel core of BRB;

BRBF

Buckling-Restrained Brace Frame;

C

adjusted BRB strength in compression;

c_b

depth of neutral axis at the bottom of the column;

c_t

depth of neutral axis at the top of the column;

d

diameter of the column;

d_PT

distance between PT bars;

E_so

strain energy;

E_D

hysteretic energy;

E_BRB

modulus of elasticity of steel core of BRB;

E_PT

modulus of elasticity of PT bars;

F_AF

axial force;

F_PT

posttensioning force;

$F_{\mathrm{BRB}\mathrm{\_}\mathrm{C}}$

strength of BRB in compression;

$F_{\mathrm{BRB}\mathrm{\_}\mathrm{T}}$

strength of BRB in tension;

$F_{\mathrm{BRB}\mathrm{\_}\mathrm{U}}$

ultimate strength of the BRB;

$F_{\mathrm{BRB}\mathrm{\_}\mathrm{Y}}$

yield strength of the BRB;

$F_{\mathrm{PT}\mathrm{\_}\mathrm{U}}$

ultimate strength of PT-Bent;

$F_{\mathrm{PT}\mathrm{\_}\mathrm{Y}}$

yield strength of PT-Bent;

$F_{\mathrm{PT}\mathrm{\_}\mathrm{BRB}\mathrm{\_}\mathrm{U}}$

ultimate strength of hybrid bent;

$F_{\mathrm{PT}\mathrm{\_}\mathrm{BRB}\mathrm{\_}\mathrm{Y}}$

yield strength of hybrid bent;

$F_{z\mathrm{\_}ec}$

vertical reaction forces in the east column;

$F_{z\mathrm{\_}wc}$

vertical reaction forces in the east column;

H

column height;

H_b

beam height;

H_f

footing height;

K_BRB

BRB stiffness;

K_PT

PT-Bent stiffness;

$K_{\mathrm{PT}\mathrm{\_}\mathrm{BRB}}$

hybrid bridge bent stiffness;

L

center-to-center distance between columns;

L_BRB

length of the yielding steel core of the BRB;

L_PT

length of PT bars;

M_s

bending moment from energy dissipator;

M_N

bending moment due to gravity load;

M_PT

bending moment from PT bars;

M_tot

total bending moment;

P_max

maximum BRB compressive force;

P_ysc

actual yield strength of steel core;

R_y

ratio of expected yield stress to specified minimum yield stress;

T_max

maximum BRB tensile force;

T

adjusted BRB strength in tension;

T_PT

initial posttensioning forces;

Z₁

distance from the edge of the column toe to the first PT bar;

Z₂

distance from the edge of the column toe to the second PT bar;

u_o

maximum displacement;

α

ratio of the yielding force of the BRB to the yielding force of the PT-Bent;

α₀

material overstrength factor;

β

compressive adjustment factor;

β_max

maximum value of compressive adjustment factor;

γ

angle at which BRB is inclined in the bent with respect to the horizontal axis;

${\mathrm{\Delta }}_{\mathrm{BRB}\mathrm{\_}\mathrm{Y}}$

yield displacement of the BRB;

Δ_D

difference in the yield displacement of the PT-Bent and the BRB;

${\mathrm{\Delta }}_{\mathrm{PT}\mathrm{\_}\mathrm{Y}}$

yield displacement of the PT-Bent;

${\mathrm{\Delta }}_{\mathrm{PT}\mathrm{\_}\mathrm{BRB}\mathrm{\_}\mathrm{Y}}$

yield displacement of the PT-BRB bent;

ɛ_BRB

BRB strain;

θ_b

rotation of column at the bottom;

θ_t

rotation of column at the top;

θ_r

equal rotation of column at the top and bottom;

${\theta }_{\mathrm{r}\mathrm{\_}\mathrm{BRB}\mathrm{\_}\mathrm{U}}$

rotation of column at which BRB fractures;

θ_PT,y

rotation at which the PT bars yield;

θ_T

design target rotation;

λ

moment contribution ratio;

ξ_eq

equivalent viscous damping ratio;

ω

strain hardening adjustment factor; and

ω_max

maximum value of strain hardening adjustment factor.

References