ABSTRACT
Assume the displacements along the main girder are u, vertical displacements are v, displacements in the transverse direction are w, twisted angles are θ, displacements along the direction of the main girder, in the vertical direction, and transverse direction of the left side cables of the main girder are ul, vl, wl, displacements along the direction of the main girder, in the vertical direction, and transverse direction of the right side cables of the main girder are ur, vr, wr, Hl(t), Hr(t) represent the left and right side increment horizontal forces instigated by the vibration inertial force, Ec, Acl are the cross-sectional areas and the elastic modulus of the main cables, q represents total load density, q = qs + qc, qs is the statical load density of the main girder, qc is the statical load density of the main cables, Hq is the horizontal force of the two main cables under statical load conditions, Lc is the length of each span, λl, λr are the Lagrange Multipliers, fl, fr are the forces constraining the extension of the left and right hangers, g is gravity acceleration, h’ is the cable length along the x-axis, As, Iy, Iz are the crosssectional area, lateral, and vertical flexural inertial moments of the main girder, respectively, E is the elastic modulus of the main girder, μ is the shearing influence coefficient, βElJw is the main girder’s warping rigidity, β = Jp/(Jp – Jt), El = E/(1 – ν2), Jp is the pole moment inertia of the cross section, Jt is St. Venant’s torsional constant.
