Special features of MIDAS/Civil for cable stayed bridge analysis Special features for cable stayed bridge analysis MIDAS/Civil provides superb pre- and post-processors in conjunction with Cable Stayed Bridge Wizard, which readily creates a cable stayed bridge model. Initial tension forces in cables can be also calculated through the Unknown Load Factor function. MIDAS/Civil enables us to carry out construction stage analysis, which is a prerequisite for cable stayed bridge analysis. And such analysis allows us to examine structural displacements, forces, stresses, etc. during construction. MIDAS/Civil is also capable of carrying out analyses for traffic moving loads, response spectrum, time history, buckling, etc, that are applicable for a completed structure all within the same program. It contains a true cable element, which is used to reflect geometric nonlinearity of a cable stayed bridge for both stage analysis and analysis for a completed structure. Cable Stayed Bridge Wizard Cable Stayed Bridge Wizard automatically generates a symmetrical or unsymmetrical cable stayed bridge model including, truss or box girders with a specified profile. The quick modeling capability permits more time for engineering and reduces potential errors. The following outlines a process of analysis:

Cable replacement checks

Buckling analysis

(Girders & Towers)

Stability checks

Seismic analysis

(3-D analysis including

substructure)

Wind analysis

(Eigenvalue analysis)

Wind tunnel test

Dynamic analysis

Moving load analysis

(Influence line/surface analysis)

Dead load analysis

(Temperature, Settlement,

Fabrication & Erection errors)

Static analysis

Define construction stages

Define construction loads

Construction stage analysis

(Backward stage analysis)

Construction stage analysis

Summary of design forces, reactions and displacements

Initial state configuration(Completed state)

Modeling & Boundary condition assignment

Selection of design standards

Figure 1. Completed cable stayed bridge model created by Cable Stayed Bridge Wizard

Calculation of Initial cable tension forces MIDAS/Civil calculates initial tension forces in cables while satisfying the design conditions specified by the engineer. Optimum initial tension forces are found through Unknown Load Factor, which minimizes trial and error. The Unknown Load Factor function calculates initial cable tension forces while satisfying the specified constraint conditions of zero and the range of maximum and minimum values for displacements, reactions, member forces, etc. Figure 2. Analysis result of an initial equality condition of a completed cable stayed bridge after calculating initial tension forces in the cables by Unknown Load Factor

Dynamic analysis reflecting geometric nonlinearity In order to examine the dynamic characteristics of a cable stayed bridge more accurately, geometric stiffness due to cable tensions is reflected in the analysis. MIDAS/Civil accounts for geometric stiffness of cables by the Initial Force for Geometric Stiffness function for eigenvalue analysis. Figure 3. Eigenvalue analysis of a cable stayed bridge based on the geometric stiffness reflecting the initial forces in cables entered in Initial Force for Geometric Stiffness

Nonlinear analysis using cable elements A cable stayed bridge generally contains linear materials; nevertheless, it exhibits nonlinear behavior of overall loaddisplacement relationship. In a long span cable stayed bridge, cable sag may need to be reflected to account for a decrease in its stiffness. MIDAS/Civil includes a cable element that can reflect the geometric nonlinear behavior of cables for the analysis of a completed structure and construction stage analysis. The cable element in MIDAS/Civil performs as an equivalent truss element for linear analysis, but it automatically transforms into a catenary cable element for nonlinear analysis.

Figure 4. Nonlinear analysis result of a completed cable stayed bridge using cable element

Construction stage analysis In order to determine the tension forces for cable erection in a cable stayed bridge, an initial equality condition is established under the dead load and then construction stage analysis is carried out. Generally, structural members and cable sections and tensions are determined from the overall analysis of a completed state. And the stage tension forces in cables and fabrication/erection cambers for girders are determined in the construction stage analysis. Construction stage analysis can be classified into backward analysis and forward analysis. Backward analysis entails a method by which the completed structure determined under the initial equality state is staged in the reverse order of construction by eliminating structural members and loadings pertaining to each construction stage. Forward analysis is performed in the order of true construction sequence. For construction stage analysis, capabilities for activating and deactivating elements, loads and boundary conditions are necessary to represent each stage. MIDAS/Civil provides group definitions to represent such variation of any combination for any construction stage. Backward analysis is performed first to determine reasonable tension forces in cables for erection. Using the erection tensioning forces, forward analysis is repeated and true erection tensioning forces are obtained. MIDAS/Civil allows easy verification of construction stage analysis results in windows by means of graphics and tables.

Figure 5. Stage models of backward analysis

Figure 6. Stage models of forward analysis

Rendering window

Modeling window

Figure 7. Construction stage analysis model defined by stages using the Construction Stage function