🏗️ Understanding Pushover Analysis and Capacity Spectrum Method (CSM)

Adisorn O.
Apr 24
2 min read

by alpsdev · April 2025

🔎 What is Pushover Analysis?

Pushover analysis is a nonlinear static method used to evaluate structural performance under seismic loads. It simulates how a building behaves as lateral loads increase — allowing us to track yielding, strength loss, and deformation capacity.

🔄 What is the Capacity Spectrum Method (CSM)?

The Capacity Spectrum Method (CSM) overlays:1. The structure’s pushover-derived capacity curve2. The ASCE 7 demand spectrum (converted to spectral coordinates)The intersection of both in Sa–Sd space gives the performance point, predicting the maximum seismic response.

🧭 Step-by-Step Procedure

🔹 1. Run a Nonlinear Pushover Analysis

Apply lateral loads in a mode-shape pattern (1st mode or ELF-like). Record:- Base shear (V)- Roof displacement (Δ)You now have a capacity curve: V–Δ

🔹 2. Convert to Capacity Spectrum (Sa–Sd)

Use modal properties (effective mass and participation factor) to convert V–Δ to Sa–Sd:

Sa = Vb / Me

Sd = Δr / Γ1Alternatively, normalize displacement using participation factor and plot:

Sd = Δ × Γ / Φ_roof

Sa = ω² × Sd

🔹 3. Generate ASCE 7 Demand Spectrum in Sa–Sd Space

Get design values:

Sds = 1.0; Sd1 = 0.6;

T = linspace(0.1, 4, 100);

Ts = Sd1 / Sds;%

Build ASCE 7 design spectrum (5% damping)

Sa(T <= Ts) = Sds;

Sa(T > Ts) = Sd1 ./ T (T > Ts);

% Convert to spectral displacement (Sd)

Sd = (Sa .* T.^2) / (4 * pi^2);

🔹 4. Overlay Capacity Spectrum and Find Performance Point

Assume you have a capacity curve from pushover (Sa_cap, Sd_cap):

plot(Sd_cap, Sa_cap, 'r--', 'LineWidth', 1.5);

legend('ASCE 7 Demand', 'Capacity Spectrum');

pushover

Where the curves intersect = performance point → This is the expected maximum displacement and acceleration for the given seismic demand.

🎯 Interpretation

Once you locate the performance point:- You can estimate dama

ge level (IO, LS, CP)- Check drift limits and hinge rotations- Compare against ASCE 7 performance objectives

📌 Summary Shortcut

Step	What You Do	Purpose
1	Run pushover analysis	Get capacity curve (V–Δ)
2	Convert to spectral coordinates	Get Sa–Sd curve (capacity)
3	Convert ASCE 7 spectrum to Sa–Sd	Get demand in same space
4	Overlay both and find intersection	Identify performance point

🚀 Conclusion

The Capacity Spectrum Method helps shift your seismic design toward performance-based engineering. ETABS automates this — but with MATLAB, you can see the full picture and validate the results independently.This method empowers you to assess whether your building meets Immediate Occupancy, Life Safety, or Collapse Prevention goals, all without needing time history analysis.

🚀 ETABS Watch & Learn (CSM, FEMA 440) ETABS - 28 Nonlinear Static Procedures - Pushover Analysis: Watch & Learn

Input design spectrum Sda vs T
Assign Hinge properties
Set gravity load cases
Apply lateral load case
Check for capacity chart and performance point