SAP2000 Seismic Analysis: Response Spectrum, Time History, and Pushover

SAP2000 Seismic Analysis: Response Spectrum, Time History, and Pushover

Seismic analysis is something I take very seriously — I've seen what happens when it's done wrong. SAP2000 gives you three levels of seismic analysis, and I've used all of them on different projects. Response spectrum is my go-to for most buildings, time history is essential for critical structures with site-specific ground motion, and pushover is what I use for performance-based assessment. Let me walk you through each method and when to use them.

Modal Analysis (Prerequisite)

Mass Model

1. Define > Mass Source
2. Select load patterns contributing to seismic mass:
   • Dead Load: 100% (self-weight + superimposed dead)
   • Live Load: 25% (reduced per ASCE 12.7.2)
3. SAP2000 assembles the mass matrix from specified load patterns

Running Modal Analysis

1. Define > Analysis Cases > Add New Case
2. Set case type: Modal
3. Set:
   • Number of modes: 15-30 (enough for 90% mass participation)
   • Maximum frequency: Optional cut-off
4. Analyze > Run Analysis
5. Results:
   • Natural periods (T): For each mode
   • Frequencies (f): f = 1/T
   • Mode shapes: Displacement pattern per mode
   • Mass participation: Per mode and cumulative

Mass Participation Check

1. Display > Show Tables > Modal Information
2. Check cumulative mass participation:

| Mode | Period (s) | UX (%) | UY (%) | RX (%) | RY (%) | RZ (%) | |------|-----------|--------|--------|--------|--------|--------| | 1 | 1.234 | 0.1 | 72.5 | 0.0 | 0.0 | 15.2 | | 2 | 1.087 | 68.3 | 0.2 | 0.0 | 0.0 | 5.1 | | 3 | 0.892 | 5.1 | 8.7 | 0.0 | 0.0 | 45.3 | | 4 | 0.456 | 12.4 | 0.5 | 0.0 | 0.0 | 3.2 | | 5 | 0.321 | 8.2 | 15.3 | 0.0 | 0.0 | 8.7 | | Cum. | - | 94.1 | 97.2 | 0.0 | 0.0 | 77.5 |

3. Requirement: Cumulative ≥ 90% in each horizontal direction (UX, UY)
4. If not met: increase number of modes

Response Spectrum Analysis

Defining the Response Spectrum

1. Define > Functions > Response Spectrum
2. Add new function:
   • ASCE 7-22: Built-in spectrum per ASCE 7
   • IS 1893: Indian standard spectrum
   • EN 1998-1: Eurocode 8 spectrum
   • User-defined: Custom spectrum from text file
3. Set ASCE 7 parameters:
   • SDS: Short-period spectral acceleration (e.g., 0.6g)
   • SD1: 1-second spectral acceleration (e.g., 0.3g)
   • TL: Long-period transition (e.g., 8 seconds)
   • Site class: A through F
4. SAP2000 generates the spectrum curve (Sa vs. T)

Creating Response Spectrum Load Case

1. Define > Load Cases > Add New Case
2. Set:
   • Case type: Response Spectrum
   • Initial case: Modal (uses modal results)
   • Damping: 5% (concrete), 3% (steel), 2% (welded steel)
3. Set direction:
   • U1 (X): Acceleration in X direction
   • U2 (Y): Acceleration in Y direction
   • Scale factor: Convert g to actual acceleration (e.g., 9.81 m/s²)
4. Set modal combination:
   • CQC (Complete Quadratic Combination): Recommended (accounts for closely-spaced modes)
   • SRSS (Square Root of Sum of Squares): Simple, conservative
5. Set directional combination:
   • SRSS: √(Rx² + Ry²) for combined X+Y
   • Absolute: |Rx| + |Ry| (conservative)
   • Percentage: 100% one direction + 30% perpendicular

Running Response Spectrum

1. Analyze > Run Analysis
2. SAP2000 performs:
   • Modal analysis (if not already done)
   • For each mode: calculate spectral acceleration from spectrum
   • Calculate modal forces: F = m × Sa × mode shape
   • Combine modal forces using CQC or SRSS
3. Results are absolute (positive) — no sign information

Directional Combinations

Per ASCE 7, combine orthogonal directions:

1. Create two response spectrum cases: RS-X and RS-Y
2. Create load combinations:
   • Combo 1: 1.2D + 1.0RS-X + 0.3RS-Y + 0.5L
   • Combo 2: 1.2D + 0.3RS-X + 1.0RS-Y + 0.5L
   • Combo 3: 0.9D + 1.0RS-X + 0.3RS-Y
   • Combo 4: 0.9D + 0.3RS-X + 1.0RS-Y
3. These combinations capture the worst-case directional scenario

Base Shear Scaling

Per ASCE 12.9, compare dynamic base shear to static:

1. Calculate static base shear: V_static = Cs × W
2. Calculate dynamic base shear: V_dynamic = √(Vx² + Vy²) or from CQC
3. If V_dynamic < 0.85 × V_static:
   • Scale factor = 0.85 × V_static / V_dynamic
   • Apply scale factor to response spectrum case
   • Re-run analysis
4. If V_dynamic ≥ 0.85 × V_static: acceptable as-is

Time History Analysis

When to Use Time History

• Near-fault sites (within 10km of active fault)
• Structures with seismic isolation or dampers
• Irregular structures where response spectrum is inadequate
• Equipment vibration analysis
• Blast loading

Defining Time History Function

1. Define > Functions > Time History
2. Add new function:
   • From file: Import ground motion record (AT2, CSV, TXT)
   • Built-in: El Centro, Northridge, Loma Prieta, Kobe
   • User-defined: Enter acceleration values manually
3. Format: Time (sec), Acceleration (g) — one pair per line
4. Set:
   • Number of points: Typically 1000-5000
   • Time step: 0.005-0.02 seconds
   • Duration: 10-60 seconds

Creating Time History Load Case

1. Define > Load Cases > Add New Case
2. Set:
   • Case type: Time History
   • Initial case: Modal or None (direct integration)
3. Set analysis method:
   • Modal: Uses modal superposition (faster, good for linear)
   • Direct Integration: Newmark-β or Hilber-Hughes-Taylor (slower, for nonlinear)
4. Set:
   • Time step: 0.005-0.02 seconds (match ground motion)
   • Number of steps: Match ground motion duration
   • Damping: 5% (concrete), 3% (steel)
5. Add load application:
   • Acceleration: U1 (X), U2 (Y), or U3 (vertical)
   • Function: Select the time history function
   • Scale factor: Convert g to m/s² (multiply by 9.81)

Running Time History

1. Analyze > Run Analysis
2. SAP2000 performs:
   • At each time step: calculate displacements, velocities, accelerations
   • At each time step: calculate member forces
   • Store results at every time step (or at specified intervals)
3. Analysis time: minutes to hours depending on model size and time steps

Reviewing Time History Results

1. Display > Show Plot Functions
2. Select joints and components:
   • Displacement vs. time: For any joint
   • Velocity vs. time: For any joint
   • Acceleration vs. time: For any joint
   • Force vs. time: For any frame element
3. Identify peak values:
   • Maximum displacement: Over entire time history
   • Maximum force: Over entire time history
   • Time of peak: When maximum occurs
4. Export time history data to CSV for further analysis

Maximum and Minimum Envelope

1. Create a "Modal History" load combination
2. SAP2000 creates envelopes:
   • Max: Maximum value at each location over all time steps
   • Min: Minimum value at each location over all time steps
   • Abs Max: Maximum absolute value
3. Use envelopes for design:
   • Design for the maximum force at each location
   • Envelopes capture the worst case over the entire earthquake

Pushover Analysis

What Pushover Does

Pushover analysis applies a gradually increasing lateral load to the structure until it collapses. It evaluates the structure's performance under seismic loading beyond the elastic range.

Defining Hinge Properties

1. Define > Section Properties > Hinge Properties
2. Create hinges for:
   • Beams: Moment hinges (M3) at ends
   • Columns: Axial-moment hinges (P-M3) at ends
   • Braces: Axial hinge (P) at midpoint
3. Set hinge moment-rotation curve:
   • Yield point: My = fy × Z (plastic section modulus)
   • Ultimate: Rotation capacity per ASCE 41
   • Acceptance criteria: IO (Immediate Occupancy), LS (Life Safety), CP (Collapse Prevention)

Creating Pushover Load Case

1. Define > Load Cases > Add New Case
2. Set:
   • Case type: Nonlinear Static
   • Load application: Gravity (dead + live) first, then lateral push
3. Set lateral load pattern:
   • Uniform: Force proportional to mass (uniform acceleration)
   • Modal: Force proportional to first mode shape (triangular for buildings)
   • Custom: User-defined force distribution
4. Set:
   • Load control: Push to a target displacement
   • Displacement control: Push to a target displacement at a control joint
   • Target displacement: Per ASCE 41 equation

Running Pushover

1. Analyze > Run Analysis
2. SAP2000 performs:
   • Apply gravity loads (linear)
   • Incrementally apply lateral loads
   • At each step: check for hinge formation
   • When a hinge forms: redistribute forces
   • Continue until target displacement or collapse
3. Results:
   • Capacity curve: Base shear vs. roof displacement (pushover curve)
   • Hinge formation sequence: Which hinges form and in what order
   • Performance point: Where demand meets capacity (per ASCE 41)

Interpreting Pushover Results

1. Display > Show Hinge Results
2. View:
   • Hinge state: A-B (elastic), B-C (yielded), C-D (strength loss), D-E (collapsed)
   • Acceptance level: IO, LS, or CP for each hinge
3. Check performance objective:
   • IO: Structure is operational after earthquake
   • LS: Structure is safe but may need major repairs
   • CP: Structure is near collapse — life safety only
4. If performance is not met:
   • Increase member sizes (delay hinge formation)
   • Add bracing or walls (reduce demand)
   • Add seismic isolation or dampers

Wrapping Up

For most of my projects, response spectrum analysis is all I need. It's fast, code-accepted, and gives you the forces and drifts you need for design. Time history is for those special cases where the site-specific ground motion tells you something the code spectrum doesn't. Pushover is for when you need to demonstrate performance beyond elastic limits. My recommendation: master response spectrum first, then add time history and pushover to your toolkit as project demands require them.