Pushover and Response Spectrum Analysis
This guide covers Pushover Analysis and Response Spectrum Analysis (RSA) for the seismic design of bridge substructures. It assumes you are already familiar with creating Column objects.
You will:
Define Moment-Curvature Reports for column sections.
Create Hinge Properties and assign them to columns.
Set up a Pushover Analysis case.
Configure a Response Spectrum Analysis case.
Run the analyses and generate the pushover capacity curve.
Prerequisites
Before starting, make sure you have:
A bridge model with defined pier columns.
Column sections properly defined.
A working understanding of OpenBrIM's workflow structure.
Step 1: Define the Moment-Curvature Report
The Moment-Curvature Report computes the nonlinear behavior of a reinforced concrete section under a range of axial loads. It provides the hinge stiffness data required for pushover analysis.
Navigate to Properties > Pushover and create a new Moment-Curvature Report object. On the Section tab, define the column section: Section Type (Circle, Oblong, or Rectangle), dimensions, Cover Thickness, Longitudinal Bar Size, Transverse Bar Size, and reinforcement layout. (See Moment-Curvature Report.)
Define material properties on the Concrete Material, Rebar Material, and Circular Hoop-Spiral Confinement Details tabs: concrete strength, elastic modulus, rebar yield/fracture stress, steel grade, transverse reinforcement type, spacing, and strain limits.
On the Axial Forces tab, define axial-force values covering the expected load range. Include both tension (positive) and compression (negative) values. Example: for a column with −750 kip dead load, enter 250, 0, −50, −100, −200, −400, −600, −750, −1000 kips, with intervals of about 50 kips near the maximum load.
On the Output tab, click the three-dot menu (⋮) next to Report Output and choose Compute. The system computes the moment-curvature curves and populates the output field.
The Moment-Curvature Report must be computed before it can be assigned to a Hinge Property — otherwise the hinge has no valid stiffness data.
Step 2: Create a Hinge Property
Hinge Properties define the nonlinear behavior at potential plastic-hinge locations during pushover analysis.
Navigate to Properties > Pushover and create a new Hinge Property object. On the Nonlinear tab, set Hinge Stiffness Option to From Report and choose the Moment-Curvature Report computed in Step 1 — Ry and Rz are extracted automatically. On the Linear tab, set Tx, Ty, Tz, and Rx to Fixed for typical pier columns. (See Hinge Property.)
Ry and Rz are the rotational stiffnesses governed by the nonlinear moment-curvature behavior; they are not specified on the Linear tab. These are the primary bending directions where plastic hinges form during pushover analysis.
Step 3: Assign Hinge Properties to the Column
Now assign the Hinge Property to the pier column to enable nonlinear pushover analysis.
Open your Column object under Substructure > Pier. In the Pushover section, set Generate Top Hinge to YES, choose the Hinge Property from Step 2 in Top Hinge Property, and specify Top Hinge Length. Repeat for Generate Bottom Hinge, Bottom Hinge Property, and Bottom Hinge Length as needed. (See Pier Column for parameter details.)
The hinge coordinate system (Ry and Rz axes) must be consistent with the Column Rotation Angle and the section orientation in the Moment-Curvature Report. Make sure these are aligned for accurate results.
Step 4: Define the Pushover Analysis Case
Create a Pushover Analysis case that incrementally applies lateral load until failure.
Navigate to Construction > Construction Stage. Create a new construction stage and assign the Prior Stage that identifies the structural state at which Pushover Analysis runs. Set Nonlinear to Yes.
Navigate to Loading > Loads > Pushover Load > Pushover Case and create a new Pushover Analysis Case. Specify the Pushover Direction (e.g. Ty for transverse seismic) and the Stopping Criteria. (See Pushover Case.)
Navigate to Loading > Loads > Pushover Load and create Pushover Load objects. Specify the Point where the load is applied, the Pushover Case (the case created above), the initial force values Fx, Fy, Fz (which will be incrementally increased during analysis), and the Element type the load is applied to. (See Pushover Load.)
Make sure the pushover direction matches the expected direction of seismic forces.
Step 5: Define the Response Spectrum Analysis Case
Create a Response Spectrum Analysis (RSA) case to determine the elastic seismic demand on the structure.
Navigate to Construction > Construction Stage. Create a new construction stage and assign the Prior Stage that identifies the structural state at which Eigenvalue Analysis runs. Loads other than self-weight must be specified in the Eigenvalue and RSA Case (covered in the next steps).
Navigate to Construction > Changes > Pier Section Property Override and assign the Cracked Moment of Inertia modifier for the columns. The Cracked Moment of Inertia represents reduced stiffness once concrete cracks under bending; the appropriate modify factor is reported in Moment-Curvature Report.
Navigate to Loading > Loads > Dynamic Loads > Response Spectrum Curve and create a new Response Spectrum Curve. Specify the data points for the Response Spectrum Function. (See Response Spectrum Curve.)
Navigate to Loading > Loads > Dynamic Loads > Eigenvalue and RSA Case and create a new Eigenvalue and RSA Case. Specify the Response Spectrum Curve, then the parameters for the case: Direction of seismic excitation, Damping Ratio, Number of Modes, Modal Combination Method, and Directional Combination Method. (See Eigenvalue and RSA Case.)
Step 6: Run the Analysis
Run both the Pushover Analysis and the Response Spectrum Analysis.
Make sure the FEM button is active to compile the model and wait for the Analysis button to appear. Click Analysis, ensure the stages for both the Pushover Analysis Case and the RSA Case are active, and click Run Analysis. Monitor the run until it completes.
Pushover analysis typically takes longer than linear analysis because of the iterative nonlinear solution. Run time depends on model size, number of hinges, and target displacement.
Step 7: Generate the Pushover Graph Report
Create a Static Pushover Graph to visualize the capacity curve and compare it with the RSA demand.
Navigate to Reports > Static Pushover Graph and create a new Static Pushover Graph. On the General tab, choose the Pushover Case and RSA Case from Steps 4 and 5. On the Advanced tab, set Result Coord. System to Alignment or Global. (See Static Pushover Graph.)
Click Design to compute the pushover graph. When it completes, click Report to view the capacity curve — base shear vs. displacement, with the RSA demand point overlaid.
The pushover capacity curve shows the structure's nonlinear force-displacement relationship. The RSA demand point should fall below the capacity curve, indicating adequate seismic capacity.
Understanding the Results
The pushover graph plots base shear vs. control node displacement. The curve shows elastic behavior initially, then yielding as hinges form, and finally a plateau or drop-off at ultimate capacity. The RSA displacement demand should fall within the acceptable range of the capacity curve.
Additional Tips
Tips for Successful Pushover Analysis
Axial-force range: the Moment-Curvature Report should cover the expected dead-load range. Include both tension and compression values, with finer intervals (~50 kips) near the maximum load.
Hinge length: plastic hinge length significantly affects results. Consult design codes or research literature for appropriate values.
Coordinate consistency: verify that the column rotation angle, the section orientation in the Moment-Curvature Report, and the pushover direction are all aligned.
Convergence issues: if pushover analysis fails to converge:
Reduce the target-displacement increment.
Add more axial-force data points in the Moment-Curvature Report.
Re-check hinge property definitions for errors.
Verify hinges are properly assigned to columns.
Result interpretation:
Steep initial slope → high initial stiffness.
Yield plateau → ductile behavior with hinge formation.
Common Issues and Solutions
Hinge not forming: verify that Generate Top Hinge / Generate Bottom Hinge is YES and the correct Hinge Property is assigned.
Report Output empty: ensure the Moment-Curvature Report was computed (via Compute) before assignment.
RSA demand not showing: check that both the Pushover Case and the RSA Case are properly defined and analyzed.
Coordinate mismatch: confirm the Result Coord. System setting matches your expected output (Alignment vs. Global).
Related Documentation
For more detail on individual components, see:
Moment-Curvature Report — parameter descriptions
Hinge Property — hinge definition and assignment
Pier Column — column object including the Pushover section
Pushover Case — pushover case configuration
Response Spectrum Curve — response spectrum function definition
Eigenvalue and RSA Case — RSA case setup
Static Pushover Graph — report generation and interpretation
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