Influence of Sectional Depth on Structural Behavior of Bridge Pier Caps

Acknowledgments

Notation

A_g

gross area of the concrete section;

A_s

area of nonprestressed longitudinal tension reinforcement;

A_st

nominal cross-sectional area of reinforcement;

A_s,min

minimal area of flexural bar reinforcement;

A_v

area of shear reinforcement;

A_v,min

minimal area of shear reinforcement;

a_v

shear span;

b_w

thickness of the pier cap;

C

coefficient for sectional configuration;

d

effective depth;

F_h

factored tensile force in a horizontal tie;

F_v

factored tensile force in a vertical tie;

f_ck

specified compressive strength of concrete;

$f_c^{\mathrm{\prime }}$

specified compressive strength of concrete;

f_n

stress caused by axial force;

f_r

concrete modulus of rupture;

f_vy

specified yield strength for vertical shear reinforcement;

f_y

specified yield strength for nonprestressed reinforcement;

f_yt

specified yield strength of transverse reinforcement;

h

sectional depth of the member;

M_cr

cracking moment;

M_n

nominal moment;

M_SLS

moment at SLS;

N_u

factored axial force normal to cross section occurring simultaneously with V_u;

n

number of reinforcing steel rebars;

P_FEA

maximal load from finite-element analysis;

P_guide

load resistance capacity using the larger of P_v-tie and P_Vn as a vertical tie force;

P_Max

maximal load from the test;

$P_{M_n}$

total load at the nominal moment;

P_STM

load resistance capacity among the lesser of the strut-and-tie element forces;

P_strut

load resistance capacity of the strut-to-node interfaces;

P_t-tie

load resistance capacity of the horizontal tensile tie;

P_ULS

total load in the ULS;

$P_{V_n}$

total load at nominal shear strength;

P_v-tie

load resistance capacity of the vertical tie;

s

longitudinal spacing of the shear reinforcement;

s_req

required spacing of the stirrups;

V_c

contribution of concrete to the shear strength;

V_n

nominal shear strength;

V_s

contribution of the reinforcement to the shear strength;

V_u

factored shear force at section;

w_eff

maximal effective width of the tie;

x

distance between the loading point and the inner edge of bearing support;

z

section modulus;

α

angle between the inclined stirrups and the longitudinal axis of the member;

${\epsilon }_{cu}$

compressive strain of concrete at maximal concrete stress;

${\epsilon }_y$

yield strain of steel reinforcement;

κ

coefficient of the size effect ( $=1+\sqrt{200/d}\le 2$);

λ

modification factor reflecting reduced mechanical properties of lightweight concrete;

λ_s

factor used to modify shear strength based on the size effect factor;

ρ

reinforcement ratio for flexural tensile reinforcement;

ρ_h

reinforcement ratio for horizontal shear reinforcement;

ρ_min

minimal flexural reinforcement ratio required in the design codes;

ρ_req

required flexural tensile reinforcement ratio;

ρ_v

reinforcement ratio for vertical shear reinforcement;

ρ_v,req

required shear reinforcement ratio;

ρ_w

ratio of A_s to b_wd; and

ϕ_s

resistance factor for the reinforcement.

References