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To make sure the tension adjustment in the cables of concrete cable-stayed bridges is conducted successfully, a new adjustment technique for the tension adjustment is presented, with the cable-girder temperature difference taken into account. The tensions are measured via frequency method. Prior to the tension adjustment, tensions and temperatures of all cables and girders are measured when the ambient temperature is stable, and this set of tensions is taken as reference tensions. During the tension adjustment, the relative variable quantities of the tensions are regarded as the control values, while the vertical displacement in the mid-span section of the main span is regarded as the verification value. After each pair of cables is adjusted, it is required to measure the temperatures of cables and girders as well as the vertical displacement variation in the mid-span section of the main span. To guarantee the structural behavior of entire bridge is controlled, at one-third cable points, two-third cable points and the farthest cable points, the frequencies of each pair of cables as well as the temperatures of each pair of cables and girders should be measured so as to recalculate the cable tensions. After that, these cable tensions are compared with the theoretical ones to ensure the structural behavior of entire bridge in control. Finally, Furong bridge, a concrete cable-stayed bridge with double inclined pylons, is taken as a sample application of this proposed technique. The results of cable tensions in this bridge illustrate the new adjustment technique is both accurate and efficient.

Purpose Stiffened plates have been widely used in civil, marine, aerospace engineering. As a kind of thin-walled structure operating in complex environment, stiffened plates mostly undergo a variety of dynamic loads, which may sometimes result in large-amplitude vibration. Additionally, initial stresses and geometric imperfections are widespread in this type of structure. Furthermore, it is universally known that initial stresses and geometric imperfections may affect mechanical behavior of structures severely, particularly in dynamic analysis. Thus, the purpose of this paper is to study the stress variation rule of a stiffened plate during large-amplitude vibration considering initial stresses and geometric imperfections. Design/methodology/approach The initial stresses are represented in the form of initial bending moments applying to the stiffened plate, while the initial geometric imperfections are considered by means of trigonometric series, and they are assumed existing in the plate along the z-direction exclusively. Then, the dynamic equilibrium equations of the stiffened plate are established using Lagrange’s equation as well as aforementioned conditions. The nonlinear differential equations of motion are simplified as a two-degree-of-freedom system by considering 1:2 and 1:3 internal resonances, respectively, and the multiscale method is applied to solve the equations. Findings The influence of initial stresses on the plate, stresses during internal resonance is remarkable, while that is moderate for initial geometric imperfections. (Upon considering the existence of initial stresses or geometric imperfections, the stresses of motivated modes are less than the primary mode for both and internal resonances). The influence of bidirectional initial stresses on the plate’s stresses during internal resonance is more remarkable than that of unidirectional initial stresses. The coupled vibration in 1%3A2 internal resonance is fiercer than that in internal resonance. Originality/value Stiffened plates are widely used in engineering structures. However, as a type of thin-walled structure, stiffened plates vibrate with large amplitude in most cases owning to their complicated operation circumstance. In addition, stiffened plates usually contain initial stresses and geometric imperfections, which may result in the variation of their mechanical behavior, especially dynamical behavior. Based on the above consideration, this paper studies the nonlinear dynamical behavior of stiffened plates with initial stresses and geometrical imperfections under different internal resonances, which is the originality of this work. Furthermore, the research findings can provide references for engineering design and application.

This paper presents a study on the nonlinear dynamic behavior of a stiffened plate with the existence of initial stresses. A stiffened plate is assumed to be composed of a plate and some stiffeners, which are treated separately. The plate is analyzed based on Thin Plate Theory, while the stiffeners are considered as geometrically nonlinear Euler-Bernoulli beams. The equations of both kinetic energies and strain energies of the plate and stiffeners are established. After that, the dynamic equilibrium equations for the stiffened plate are derived according to Lagrange equation. The nonlinear frequency for single-mode result is obtained through Elliptic function, and the accuracy of the analytical solution is verified through comparison with Ansys finite element method. In addition, homotopy analysis method is used to solve 3:1 internal resonance of the stiffened plate. With parametric analysis being conducted, the investigation on how initial stresses influence the nonlinear dynamic properties is carried out. Some useful nonlinear dynamic properties and conclusions are obtained, and thees can provide references for engineering application.

This paper deals with the nonlinear dynamic response of elastically supported stiffened plates with initial stresses under impact loads. A stiffened plate is assumed to be composed of a plate with some stiffeners, which are treated separately. The plate is modeled by the thin plate theory, whereas the stiffeners are considered as geometrically nonlinear Euler–Bernoulli beams. First, the equations of both the kinetic energies and strain energies of the plate and stiffeners are established. Then, the dynamic equilibrium equations for the stiffened plate are derived as the Lagrange’s equation of the functional. A parametric analysis is performed to evaluate how initial stresses, initial geometric imperfections, elastic supports, impact loads and configuration of stiffeners affect the time-history responses of the stiffened plates. Some useful nonlinear dynamic properties are obtained, which serve as references for engineering design and application.

An approach is presented to investigate the nonlinear vibration of stiffened plates. A stiffened plate is divided into one plate and some stiffeners, with the plate considered to be geometrically nonlinear, and the stiffeners taken as geometrically nonlinear Euler beams. Lagrange equation and modal superposition method are used to derive the dynamic equilibrium equations of the stiffened plate according to the energy of the system. Besides, the effect caused by boundary movement is transformed into equivalent excitations. The primary parametric resonance–primary resonance of the stiffened plate is studied by using homotopy analysis method. Numerical examples for stiffened plates with different thicknesses of the plates are presented to discuss the amplitude–frequency and amplitude–excitation relationship of the primary parametric resonance–primary resonance. In addition, the analysis on how the damping coefficients and the transverse excitations influence amplitude–frequency curves is also carried out. Some nonlinear vibration characteristics of stiffened plates are obtained, which are useful for engineering design.

According to the common girder with side main rib section of PC cable-stayed bridge with double cable planes, a computational model of two-dimension temperature field is presented. Temperature gradient of main rib, small longitudinal rib, top plate and flange plate was computed respectively, and then the stress and strain of each section are derived through plane cross-section assumption. For the cable-stayed bridge, member structure FEM is applied to compute node equivalent load and displacement, which resulted from both sunshine and seasonal thermal difference. Finally, a case study is analyzed, the results showed: computed and measured deflection of girder that result from thermal effect are very close, therefore, this method is feasible.

To ensure that the cable force tuning of Banfu No.2 bridge was carried out successfully, an incremental method for cable force tuning was presented, which took into account the cable-girder temperature difference. The cable forces were measured through frequency method. Before cable force tuning, all cable forces and temperatures of cables and girders were measured when the ambient temperature was stable, and these cable forces were taken as reference cable forces. During cable force tuning, the increment of cable force was regarded as the control quantity, while the displacement in the middle of main span was regarded as the verification quantity. After each stage, it was necessary to measure the temperatures of cables and girders and the displacement variation in the middle of the main span. To ensure the mechanical state of bridge was in control, all cable forces were measured after the 5th, 10th pairs of cables and all cables were tuned. In addition, the temperature-corrected cable forces were compared with the calculated ones, which showed the incremental method was not only accurate but also efficient.

An approach is presented to study the nonlinear forced vibration of a stiffened plate. The stiffened plate is divided into one plate and some stiffeners, with the plate considered to be geometrically nonlinear, and the stiffeners taken as geometrically nonlinear Euler beams. Assuming the displacement of the stiffened plate, Lagrange equation and modal superposition method are used to derive the dynamic equilibrium equations of the stiffened plate according to energy of the system. A stiffened plate with four clamped edges subjected to harmonic excitation is studied by means of the method of multiple scales; the first approximation solutions of the double-modal motion of the system are obtained. Numerical examples for different stiffened plates are presented to discuss the steady response of the primary resonance and the amplitude–frequency relationship; and some nonlinear forced vibration characteristics of the stiffened plate are obtained, which are useful for engineering design.