Theoretical Analysis and Design of Prestressed CFRP-Reinforced Steel Columns

Data Availability Statement

Notation

A_ca

cross-sectional area of the cross arm or prestressing chair;

A_e

half-length of the major axis of the ellipse;

A_P

cross-sectional area of CFRP;

A_s

cross-sectional area of steel;

a

(final) supporting length;

a_max

maximum supporting length considering space limitations;

a_mix

(final) supporting length that makes the symmetric and antisymmetric buckling capacities equivalent;

a₀

initial supporting length;

B

bending stiffness of the steel column;

B_ca

bending stiffness of the cross arm or prestressing chair;

B_e

half-length of the minor axis of the ellipse;

b_ca

width of the prestressing chair;

b_P

CFRP width;

b_s

width of the I-section;

b_space

width for the space of the bolts and other components in the prestressing chair and anchorage;

b_x

distance from the center of the CFRP to the center of the bolt in the prestressing chair;

C₁₁

coefficient for calculating P_b;

D

quantity for calculating P_b;

E_ca

elastic modulus of the cross arm or prestressing chair;

E_P

elastic modulus of CFRP;

E_s

elastic modulus of steel;

e

eccentricity of compressive external loading;

f

design strength of steel;

f_P

CFRP strength;

f_y

yield point of steel;

h_s

height of the I-section;

I_ca

moment of inertia of the cross arm or prestressing chair;

I_P

moment of inertia of CFRP;

I_s

moment of inertia of steel;

K_ca

axial stiffness of the cross arm or prestressing chair;

K_la

spring stiffness;

K_la,1

spring stiffness before the concave-side CFRP becomes slack;

K_la,2

spring stiffness after the concave-side CFRP becomes slack;

K_P

axial stiffness of the steel stay or CFRP;

K_s

axial stiffness of the steel column;

k

a coefficient affected by initial imperfection v_om;

L

steel column length;

L_a

length of anchorage;

L_p

CFRP length;

L_P,0

initial CFRP length;

M

sum of the external bending moments of the steel section;

m

average value;

N

additional vertical compression force;

P

external compression force;

P_b

buckling capacity;

P_b,FEM

buckling capacity according to the FEM;

P_b,H

buckling capacity of the ideal prestressed stayed column (Hafez et al. 1979);

P_b,TH

buckling capacity using the theory of this paper;

P_b,TH,i

buckling capacity calculated by Buckling case i in this paper (i = 0, 1, 2, and 3);

P_b,max,d

design value of P_b,max,TH, which is ϕ_cP_b,max,TH;

P_b,max,FEM

maximum buckling capacity according to the FEM;

P_b,max,TH

maximum buckling capacity according to the theory of this paper;

P_b,test

buckling capacity from the test;

P_E

Euler buckling load;

P_max

maximum theoretical buckling capacity;

P_n

required compressive bearing capacity;

P_t

external force at the moment when both sides of the CFRPs become slack in the compressive deformation phase or at the moment when both sides of the CFRPs come under tension;

R

diameter of the thread bolt;

r

radius of the gyration of the steel section;

S

horizontal supporting force;

S_l

horizontal force provided by the CFRP on the left side;

S_r

horizontal force provided by the CFRP on the right side;

T_i

initial CFRP prestressing force;

T_l

left side initial CFRP prestressing force;

T_max,d

maximum design prestressing force considering the CFRP strength and maximum prestressing force that can be achieved with no prestressing machine;

T_min,H

minimum effective prestressing force (Hafez et al. 1979);

T_opt

optimal initial CFRP prestressing force;

T_opt,FEM

optimal initial CFRP prestressing force according to the FEM;

T_opt,H

optimal initial CFRP prestressing force (Hafez et al. 1979);

T_opt,TH

optimal initial CFRP prestressing force according to the theory of this paper;

T_r

right side initial CFRP prestressing force;

T_23b

initial CFRP prestressing force corresponding to the boundary of Buckling cases 2 and 3;

T_23b,d

design value of T_23b;

t_ca

thickness of the prestressing chair;

t_P

CFRP thickness;

t_sf

thickness of the I-section steel flange;

t_sw

thickness of the I-section steel web;

v_om

initial imperfection at the midspan of the steel column after prestressing the CFRP;

v_om,0

initial imperfection at the midspan of the steel column before prestressing the CFRP;

W_s

steel cross section modulus;

α

angle between the CFRP and the longitudinal axis of the steel column;

α₁, α₂, α₃

coefficients for calculating φ;

ΔT_c

reduction in the CFRP prestressing force caused by Δ_y;

ΔT_e

change in the CFRP force caused by the lateral displacement Δ_x;

Δ_x

lateral displacement of the steel column;

Δ_x,1

midspan lateral displacement at the moment when both sides of the CFRPs become slack in the compressive deformation phase;

Δ_x,2

midspan lateral displacement at the moment when both sides of the CFRPs come under tension;

Δ_x,M

lateral deformation due to column end rotation caused by the bending moment under eccentric compression;

Δ_x,y

lateral deformation of the midspan generated by Δ_y;

Δ_y

axial displacement of the steel column;

Δ_y,2

axial displacement of the steel column at the moment when both sides of the CFRPs come under tension;

Δ_y,c

axial displacement generated by the axial compression of the material;

Δ_y,x

axial displacement of the end generated by Δ_x;

η

reduction factor;

γ

coefficient of the section plastic development;

σ

mean square error;

λ

slenderness of the pure steel column;

λ_n

regularized slenderness of the pure steel column;

φ

stability coefficient of the pure steel column;

φ_s,TH

stability coefficient of PCRSC according to the theory of this paper;

φ_s,opt,TH

optimal value of φ_s,TH; and

ϕ_c

reduction factor in design.

References