Stress-free-state based structural analysis and construction control theory for staged construction bridges

Structural analysis and construction control of staged construction process is a major subject for modern long-span bridges. This paper introduces the concept of stress-free-state variable of structural elements and deduces the mechanical equilibrium equations and geometric shape governing equations for staged construction structures utilizing the minimum potential energy theorem. As the core of stress-free-state theory, the two aforementioned equations demonstrate following principles, 1) when the stress-free-state variable of a structural element is set, the internal force and deformation of the element are unique at the completion state of the structure regardless of its construction process; 2) the stress-free length of a cable is independent of its external loads, change in stress-free length of the cable corresponds to a unique variation of the cable force when load is constant; and 3) the internal force of a structural element can be independent from its geometric shape within the completion state of a staged construction structure through an active manipulation of stress-free-state variables of the element. Stress-free-state theory establishes the stage-to-stage and stage-to-completion relationships for staged construction bridges, provides a direct and efficient method for theoretical calculations and a flexible and convenient approach for the control of staged construction, and makes parallel construction and auto-filtering of thermal and temporary loading effect possible.