# 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:

1. Define Moment-Curvature Reports for column sections.
2. Create Hinge Properties and assign them to columns.
3. Set up a Pushover Analysis case.
4. Configure a Response Spectrum Analysis case.
5. Run the analyses and generate the pushover capacity curve.

## Prerequisites

{% hint style="info" %}
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.
  {% endhint %}

## 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.

1. 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](/templates/steel-i-girder-bridge-workflow/properties-sig/pushover-sig/moment-curvature-report-sig.md).)

   ![](/files/Q3qfSpnVVVANb4GHTdh7)
2. 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.

   ![](/files/B3Zs2hz6CleElZC07HCW)
3. 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.

   ![](/files/oDPVxiGrYAECzpjNCwnA)
4. 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.

   ![](/files/oq38p6lutoAoYl6NOo6E)

{% hint style="warning" %}
The Moment-Curvature Report **must be computed** before it can be assigned to a Hinge Property — otherwise the hinge has no valid stiffness data.
{% endhint %}

## Step 2: Create a Hinge Property

Hinge Properties define the nonlinear behavior at potential plastic-hinge locations during pushover analysis.

1. 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](/templates/steel-i-girder-bridge-workflow/properties-sig/pushover-sig/hinge-property-sig.md).)

   ![](/files/vYutAbPPFo9qq1gUuxDB)

{% hint style="info" %}
**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.
{% endhint %}

## Step 3: Assign Hinge Properties to the Column

Now assign the Hinge Property to the pier column to enable nonlinear pushover analysis.

1. 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](/templates/steel-i-girder-bridge-workflow/substructure-sig/pier-sig/pier-column-sig.md) for parameter details.)

   ![](/files/d4FPVKmSaynUaRZlkhVX)

{% hint style="info" %}
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.
{% endhint %}

## Step 4: Define the Pushover Analysis Case

Create a Pushover Analysis case that incrementally applies lateral load until failure.

1. 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**.

   ![](/files/5g1nlKDl746ZNqAtz4JE)

   ![](/files/aCFXRYCPGQO4lrcCX7UU)
2. 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](/templates/steel-i-girder-bridge-workflow/loading-sig/loads-sig/pushover-load-sig/pushover-case-sig.md).)

   ![](/files/TvDgxxmV6y3C36iOHtEe)
3. 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](/templates/steel-i-girder-bridge-workflow/loading-sig/loads-sig/pushover-load-sig/pushover-load-sig.md).)

   ![](/files/RTOLY7QswJvFG89HUZmu)

{% hint style="warning" %}
Make sure the pushover direction matches the expected direction of seismic forces.
{% endhint %}

## Step 5: Define the Response Spectrum Analysis Case

Create a Response Spectrum Analysis (RSA) case to determine the elastic seismic demand on the structure.

1. 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).

   ![](/files/q0DlzDFF589CAl51Rht8)
2. 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](/templates/steel-i-girder-bridge-workflow/properties-sig/pushover-sig/moment-curvature-report-sig.md).

   ![](/files/garw4o672M8NhgJPSujz)
3. 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](/templates/steel-i-girder-bridge-workflow/loading-sig/loads-sig/dynamic-loads-sig/response-spectrum-curve-sig.md).)

   ![](/files/f87GEMSELNjHDBzj8dtb)
4. 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](/templates/steel-i-girder-bridge-workflow/loading-sig/loads-sig/dynamic-loads-sig/eigenvalue-and-rsa-case-sig.md).)

   ![](/files/RMR5ccaA5uKvs7bEcR3P)

   ![](/files/QsWWX2oMZz7S8MNMUN3C)

## Step 6: Run the Analysis

Run both the Pushover Analysis and the Response Spectrum Analysis.

1. 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.

   ![](/files/mVB5bqFKWy6BOnziJjWd)

   ![](/files/p2Qkz23g6ggeSZJErC18)

{% hint style="info" %}
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.
{% endhint %}

## Step 7: Generate the Pushover Graph Report

Create a Static Pushover Graph to visualize the capacity curve and compare it with the RSA demand.

1. 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](/templates/steel-i-girder-bridge-workflow/reports-sig/static-pushover-graph-sig.md).)

   ![](/files/6fBCxidpHDkU2hjFppqP)
2. 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.

   ![](/files/Dhu64xzF6YhQngJozzDJ)

{% hint style="success" %}
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.
{% endhint %}

## 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.

![](/files/LxANLCNWUANlUngDHFR7)

## Additional Tips

{% hint style="info" %}
**Tips for Successful Pushover Analysis**

1. **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.
2. **Hinge length:** plastic hinge length significantly affects results. Consult design codes or research literature for appropriate values.
3. **Coordinate consistency:** verify that the column rotation angle, the section orientation in the Moment-Curvature Report, and the pushover direction are all aligned.
4. **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.
5. **Result interpretation:**
   * Steep initial slope → high initial stiffness.
   * Yield plateau → ductile behavior with hinge formation.
     {% endhint %}

{% hint style="warning" %}
**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).
  {% endhint %}

## Related Documentation

For more detail on individual components, see:

* [Moment-Curvature Report](/templates/steel-i-girder-bridge-workflow/properties-sig/pushover-sig/moment-curvature-report-sig.md) — parameter descriptions
* [Hinge Property](/templates/steel-i-girder-bridge-workflow/properties-sig/pushover-sig/hinge-property-sig.md) — hinge definition and assignment
* [Pier Column](/templates/steel-i-girder-bridge-workflow/substructure-sig/pier-sig/pier-column-sig.md) — column object including the Pushover section
* [Pushover Case](/templates/steel-i-girder-bridge-workflow/loading-sig/loads-sig/pushover-load-sig/pushover-case-sig.md) — pushover case configuration
* [Response Spectrum Curve](/templates/steel-i-girder-bridge-workflow/loading-sig/loads-sig/dynamic-loads-sig/response-spectrum-curve-sig.md) — response spectrum function definition
* [Eigenvalue and RSA Case](/templates/steel-i-girder-bridge-workflow/loading-sig/loads-sig/dynamic-loads-sig/eigenvalue-and-rsa-case-sig.md) — RSA case setup
* [Static Pushover Graph](/templates/steel-i-girder-bridge-workflow/reports-sig/static-pushover-graph-sig.md) — report generation and interpretation


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