Pushover Analysis - Bridge Piers#

Introduction#

Welcome to the Pushover Analysis - Bridge Piers tutorial.

In this tutorial we are assesing the seismic behaviour of a two-column concrete bridge pier modelled in SOFiPLUS, and analysed in the SOFiSTiK Structural Desktop. We perform a pushover analyis by incrementally increasing a predefined load pattern to meet a specified structural demand. The nonlinear structural behaviour is modelled using concentrated plasticity models, i.e., concrete plastic hinges.

We divide the Pushover Workflow into 4 distinct steps:

1. Modelling of Concrete Plastic Hinge

2. Determination of Structural Demand

3. Determination of Structural Capacity

4. Assessing the Structural Performance

By the end of the tutorial, you should be able to:

• Define Concrete Plastic Hinges based on a cross-sectional analysis and assigning them to a model in SOFiPLUS.

• Conduct a seismic Response Spectrum Analysis (RSA) for this model to determine the Structural Demand.

• Setup and perform a nonlinear Pushover Analysis to determine the inelastic structural behaviour.

• Perform checks of the structural performance by looking at the performance levels of plastic hinges and internal forces of structural elements.

Project Description#

The example a two-column reinforced concrete pier with a header beam. The structure is 13 m high with 8 m space between the columns. The cross-section of the column is circular with radius of 1.6 m, reinforced by approximately 150 cm2 steel. The header is rectangular beam with dimensions of 1.6 m x 1.8 m. We use the standard concrete C 35/45 and standard reinforcement B 500 as materials. In addition to the self-weight of the pier bridge structure, there is a dead load of 3000 kN applied at three locations of the pier to simulate the permanent loading transferred by the main girders of the superstructure.

Plastic Hinges#

A plastic hinge is a family of idealised plastic Moment-Rotation worklaws, possibly at various normal force levels. These worklaws are obtained based on a cross-sectional analysis and subsequent idealisation through bilinearisation. We use the Concrete Plastic Hinge Task to determine the plastic hinges for the present example.

Note

Polygonal cross sections (e.g., rectangular) it must be defined through SOFiPLUS or SECT in AQUA with the reinforcement specified as “minimum reinforcement”. Otherwise, the reinforcement will not be taken into account in the cross sectional analysis.

Demand#

We perform Response Spectrum Analysis based on a given site seismicity to specify the structural demand in terms of target displacement. The structure is modelled to take into account the cracking of the concrete by reducing the stiffness of the columns. The stiffness reduction factor is based on the cross sectional analysis of the plastic hinge at the normal force levels due to (quasi-)permanent loading.

Capacity#

We determine the structural capacity by increasing a particular seismic load pattern. Here, the seismic load pattern is based on the first mode-shape. The structure is modelled with reduced elastic stiffness (based on cross sectional analysis). Starting from the system state under permanent loads (preceding load case), the structure is pushed by incrementally increasing the seismic loads in the scope of a nonlinear static analysis until the target displacements at the selected nodes are reached.

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