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Evaluation of requirements for global analysis in EC3 for the structural analysis of the simple-span under-deck cable-stayed bridge
Transcript of Evaluation of requirements for global analysis in EC3 for the structural analysis of the simple-span under-deck cable-stayed bridge
Variations of relative restraint stiffness Non-linear Behavior (deformation response)
Variations of relative restraint stiffness Non-linear Behavior (deformation response) Variations of the displacement with slenderness parameter Numerical Example
Errors determined Structural model Non-linear Behavior
(flexural response) I. Misiunaite and A. Juozapaitis Evaluation of requirements for global analysis in EC3 for the structural analysis of the simple-span under-deck cable-stayed bridge Governing Equations for the Generalized problem Boundary Problems Restraint stiffness N.S. Trahair and etc. “The Behaviour and Design of Steel Structures to EC3 (Fourth edition)”, Taylor & Francis Press, NY, 2008. Slenderness parameters N.S. Trahair Governing parameters First boundary problem
Governing Equations Influence of the restraint stiffness Analysis was performed varying: Numerical Example Second boundary problem
Governing Equations substituting: equation reduces to: General solution: Boundary conditions: and Deflection response: Flexural response: With constant EI and substituting: the equation reduces to: The solution of equation: Boundary conditions: at the end of support is satisfied when and at the intermediate restraint is satisfied when: Deformation response: Displacement at the intermediate restraint: Restoring force: Boundary conditions: and Deformation response: Restoring force: Possibility of superposition Central deflection: Relationship between restoring force and restraint stiffness: Flexural response: Calculation model: kl +0.25 0.5 q 2.5 20 +2.5 2.5 20 +variable Conclusions Computational method for additionally elastically restrained steel beam-column presented Calculation model for the considering element formed Governing equations derived to obtain deformation and flexural response of the considering element Two of known non-linear buckling problems presented and set as boundary problems for the generalization of the scope Using known boundary problems the possibility of the appropriate superposition procedure presented The governing parameters defined and appropriate relationships presented The influence of the additional restraint was discussed giving the limiting value of it 6.28 and and axial compression intermediate restraint, with variable stiffness distributed load restrained intermediate displacement displacement at any point of the element restoring force acting on the restraint and thus free movement of the member is restricted to greater or lesser extend Consider the simple supported continuous beam of the length l with constant flexural rigidity EI subjected simultaneously to a distributed load q and axial compression Nc An additional lateral restraint at the midspan is provided to prevent it from deflection. First boundary problem: Simply supported continuous beam with inelastic intermediate restraint under interaction of bending and compression Secondary boundary problem: Simply supported continuous beam with elastic intermediate restraint under compression Approach to the considering buckling problem Restoring force: By considering the relative stiffness of the intermediate restraint equal to Variable kl Constant distributed load q=10N/mm The value of the displacements ratio equal to 1,0 was assumed as the limiting value for the significant changes of the deflected shape of the element. When the ration of the displacements is grater then 1,0 the restrained shape of the element approaches the unrestrained deflection shape When the relative displacement exceeds 1,0 and decreases the deflection of the element approaches restrained deflection shape. Constant distributed lateral load q=10 N/mm The ratio bending moment at the restraint bending moment at the center of the midspan when the ration of the restraint stiffness exceeds 1,0 the bending moment changes the sign disturbing restoring extreme values of bending moment shifting from hogging to sagging 11th International Conference "Modern Building Materials, Structures and Techniques" Vilnius Gediminas Technical University, May 16, 2013 – May 17, 2013