Residual Flexural Capacity of Composite Beams with Corroded Studs after Fatigue

Acknowledgments

Notation

A

surface area of the stud;

A_c

section area of the concrete wing plate;

A_ft

upper flange area of the steel beam;

A_s

section area of the steel beam;

A_st(t)

cross-sectional area of studs after t time;

$A_{ft}^{\mathrm{\prime }}$

lower flange area of the steel beam;

A₀

initial section area of the stud;

a

height of the compression zone of the steel beam;

b_eff

effective width of the concrete wing plate;

b_f

width of the upper flange of the steel beam;

D_c(n)

fatigue damage degree of concrete;

D_cor(t)

degree of corrosion damage of the stud after t time;

D_s(n)

fatigue damage degree of the steel beams;

D_st(n)

fatigue damage of the studs;

d₁

distance between the force point and the top surface of the steel beam considering the strength reduction of the lower flange of the steel beam;

F

Faraday constant whose value is 96,484 C/mol;

F_c

pressure of the concrete compression zone;

F_s

ultimate tension of the whole steel section;

F_sc

twice pressure in the compression zone of the upper flange of the steel beam;

$F_{sc}^{\mathrm{\prime }}$

twice compression zone pressure of the steel beam web;

f(n/N)

degenerate function of residual strength;

f_c

initial compressive strength of concrete;

f_s

initial tensile strength of the steel;

f_st

shear strength of the stud;

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

compressive strength of the concrete cylinder;

h_c

height of the concrete wing plate;

h_s

steel beam height;

I

electric current of the stud;

I₀

conversion of the section inertia moment of the composite beam;

i

anode current density passing through the anode area;

L

calculation span for the composite beams;

L_ρ

length of the stud rod after rust removal;

M

relative molecular mass or relative atomic mass of the metal;

M_u

ultimate flexural capacity of composite beams;

M_ρ

quality of studs after rust removal;

m

amount of substance that changes chemically;

n_l

number of columns arranged longitudinally for the studs;

N_c

fatigue life of concrete;

N_s

fatigue life of the steel beam;

N_st

fatigue life of the stud;

n

fatigue loading cycles;

n_E

elastic modulus ratio of steel to concrete;

n_f

number of studs required for a complete shear connection of the composite beams after corrosion time t and n fatigue cycles;

n_s

actual number of studs in a shear span zone of a simply supported beam;

n₁

valence number of iron;

P

vertical load at the midspan of a simply supported composite beam;

P_max

upper limit of the fatigue load;

P_min

lower limit of the fatigue load;

P_u

measured static ultimate load of the test beam;

Q

electric quantity passing through the specified electrode;

R

ratio of σ_min to σ_max;

S_max

maximum compressive fatigue strength of concrete;

S₀

area moment of the concrete plate to the neutral axis of the composite section;

t

rust time;

t_f

thickness of the wing plate on the steel beam;

t_w

web thickness of the steel beam;

V_sf

shear flow per unit length at the interface between the steel and the concrete;

W_s(t)

crack width of concrete rust expansion after t time;

w

average mass loss rate of iron per unit area in the anode area, in g/s;

X_c

compression range of concrete;

x_c

height of the concrete compression zone;

y

distance between the stress point and the neutral axis of the conversion section;

α

material constant;

σ_n

residual strength of the test specimen;

σ_max

stress value corresponding to maximum load;

σ_c,max

upper limit of the stress amplitude for concrete during fatigue loading;

σ_s,max

peak stress of the steel beam during fatigue loading;

σ₀

initial strength of the test specimen;

τ_st,max

upper limit value of the shear stress amplitude of the fatigue load;

Δl

longitudinal spacing of the stud;

Δm

mass loss of the stud within the energized time;

Δτ_st

fatigue shear stress amplitude of the stud;

Δσ

fatigue strength corresponding to two million cycles;

Δσ_s

fatigue stress amplitude of the steel beam;

ξ(n,t)

shear connection degree of the composite beams after corrosion time t and n fatigue cycles; and

ρ

corrosion rate of the stud.

References