Static Response Assessment of the Entire Suspension Bridge under Horizontal Transverse Live Load: An Analytical Calculation Method

Acknowledgments

Notation

A_c

cross-sectional area of the main cable;

A_h

cross-sectional area of the hanger;

a_i

catenary equation parameter of the ith segment in the main cable in the main span;

a_L

catenary equation parameter of the left-side span;

b_h

transverse distance from each hanger to the longitudinal centerline of the deck;

b_s

transverse distance from the vertical support at the deck end to the longitudinal centerline of the deck;

b_t

horizontal distance from each tower column to the central axis;

C_m,1 and C_m,2

postintegration constant terms of the deck’s bending moment;

D_m,1

constant term of indefinite integration;

d_m

length of the mth segment of the deck;

E_b

elastic modulus of the deck;

E_c

elastic modulus of the main cable;

E_h

elastic modulus of the hanger;

ΔF_L,y

horizontal reaction force of the left antiwind support;

ΔF_L,z,d

vertical reaction force increment on the downstream side of the left end;

ΔF_L,z,u

vertical reaction force increment on the upstream sides of the left end;

G

shear modulus of the deck;

H_i

horizontal component of the force in the ith segment of the main cable under the combined action of the dead and live loads;

H_L,u

horizontal force component in the main cable upstream of the left-side span;

H_L,d

horizontal force component in the main cable downstream of the left-side span;

H_1,u

horizontal force component in the first catenary segment of the main cable upstream of the main span;

H_1,d

horizontal force components in the first catenary segment of the main cable downstream of the main span;

I_p

polar moment of inertia of the deck;

I_y

bending moment of inertia of the deck about the z-axis;

I_z

bending moment of inertia of the deck in the vertical direction;

L₁

horizontal projected length of the main cable in the left-side span;

l_i

horizontal distance between the two endpoints of the ith catenary segment of the main cable in the bridge-axis direction;

P_i,x

component of the hanger force P_i in the x-direction;

P_i,y

components of the hanger force P_i in the y-direction;

P_i,z

components of the hanger force P_i in the z-direction;

q

self-weight of the main cable per unit length;

$S_{\mathrm{c},i}^{\mathrm{\prime }}$

unstrained length of the ith catenary segment of the main cable in the main span in the initial state;

$S_{\mathrm{c},\mathrm{L}}^{\mathrm{\prime }}$

unstrained length of the main cable in the left-side span in the initial state;

$S_{\mathrm{c},\mathrm{R}}^{\mathrm{\prime }}$

unstrained length of the main cable in the right-side span in the initial state;

$S_{\mathrm{h},i}^{\mathrm{\prime }}$

unstrained length of the ith hanger in the initial state;

X_b,i

X-coordinate of the ith lower hanging point in the global coordinate system;

X_c,i

X-coordinate of the ith upper hanging point in the global coordinate system;

Y_b,i

Y-coordinate of the ith lower hanging point in the global coordinate system;

Y_c,i

Y-coordinate of the ith upper hanging point in the global coordinate system;

Z_b,i

Z-coordinate of the ith lower hanging point in the global coordinate system;

Z_c,i

Z-coordinate of the ith upper hanging point in the global coordinate system;

α_i

included angle between the plane of the ith catenary location and the xoz plane;

η(x)

function produced by indefinite integration $\int \lambda (x)\mathrm{d}x$, with the constant term excluded;

ϕ_i

included angle between the ith catenary at point O_i and the xoy plane;

φ_i

included angle between the projection of the hanger force P_i on the xoz plane and the z-axis (the vertical inclination angle);

ΔP_i,y,d

increment of the horizontal component of the hanger force downstream at the location of x_i;

ΔP_i,y,u

increment of the horizontal component of the hanger force upstream at the location of x_i;

ΔP_i,z,d

vertical force increment in the ith hanger on the downstream;

ΔP_i,z,u

vertical force increment in the ith hanger on the upstream;

δ_B

flexibility coefficient of the left tower in lateral bending;

δ_i+1

included angle between the i + 1st catenary at point O_i and the xoy plane;

ζ_B

flexibility coefficient of the left tower in torsion;

θ_i

included angle between the projection of the hanger force P_i on the yoz plane and the z-axis (the transverse inclination angle); and

v

longitudinal rigid body displacement of the deck.

References