ETABS Seismic Analysis: Modal, Response Spectrum, and Story Drift Evaluation

ETABS Seismic Analysis: Modal, Response Spectrum, and Story Drift Evaluation

I've performed seismic analysis on buildings from 3-story concrete structures to 50-story steel towers in ETABS. Seismic analysis is one of the most critical aspects of building design in earthquake-prone regions. ETABS provides comprehensive tools for modal analysis, response spectrum analysis, and story drift evaluation — all essential for verifying that a building meets seismic code requirements.

Seismic Analysis Overview

ETABS supports several seismic analysis methods:

• Equivalent Lateral Force (ELF): Simplified static method per ASCE 7
• Response Spectrum Analysis (RSA): Dynamic method using the design spectrum
• Time History Analysis: Step-by-step dynamic analysis with ground motion records
• Pushover Analysis: Nonlinear static analysis for performance-based design

Modal Analysis

Why Modal Analysis First?

Modal analysis is the foundation of all dynamic analysis:

• Calculates natural frequencies and mode shapes
• Determines the building's fundamental period
• Provides the basis for response spectrum analysis
• Identifies the mass participation in each direction

Setting Up Modal Analysis

1. Go to Define → Load Cases
2. Find the MODAL case (auto-created by ETABS)
3. Set parameters:
   • Number of modes: 12-20 minimum (enough for 90% mass participation)
   • Maximum frequency: Optional (e.g., 100 Hz) to limit modes
   • Mass source: Verify the correct mass source is selected
4. Click OK

Running Modal Analysis

1. Go to Analyze → Run Analysis
2. Select the MODAL case
3. Click Run
4. After analysis, check results:
   • Table: Display → Show Tables → Modal Results
   • Frequencies and periods: Each mode's frequency (Hz) and period (s)
   • Mass participation: X, Y, and Z participation for each mode

Interpreting Modal Results

Natural Periods

• Fundamental period (T1): The period of the first mode in each direction
  • Compare with the approximate period Ta = Ct × hn (ASCE 7 formula)
  • Ct: 0.016 (steel moment frame), 0.020 (RC moment frame), 0.030 (RC shear wall)
  • h: Building height in meters
  • If the ETABS period is much larger than Ta, the model may be too flexible
  • ASCE 7 limits the period used for design: T ≤ Cu × Ta

Mass Participation

• Check mass participation for each direction:
  • X direction: Sum of participation should be > 90%
  • Y direction: Sum of participation should be > 90%
  • Z direction: Usually low (vertical modes are higher frequency)
• If participation is < 90%, increase the number of modes
• The first 2-3 modes typically capture 80-90% of the mass

Mode Shapes

1. Display → Show Mode Shape
2. Select a mode number
3. The mode shape is displayed as a deformed shape
4. Interpret:
   • Mode 1: Usually first X or Y translation (fundamental mode)
   • Mode 2: Usually the other horizontal direction
   • Mode 3: Usually torsion
   • Mode 4+: Higher modes (less mass participation)
5. Check for:
   • Torsional modes: If torsion is the first or second mode, the building has a torsional irregularity
   • Coupled modes: If translation and torsion are coupled, the building has an irregularity

Response Spectrum Analysis

Setting Up Response Spectrum

1. Define a response spectrum function (see Load Definition guide)
2. Go to Define → Load Cases
3. Click Add New Load Case
4. Set:
   • Name: "RSX" (response spectrum X)
   • Type: Response Spectrum
   • Direction: X
   • Function: Select the response spectrum function
   • Scale factor:
     • If spectrum is in g: Scale = g (9.81 m/s² or 386 in/s²)
     • If spectrum is in m/s²: Scale = 1.0
   • Modal combination: CQC (recommended) or SRSS
   • Directional combination:
     • SRSS: √(Rx² + Ry²) — for combining X and Y
     • 100/30/30: 100% in one direction + 30% in perpendicular
5. Damping:
   • 5%: Typical for concrete buildings
   • 3%: Typical for steel buildings
   • 2%: For lightly damped structures
6. Click OK
7. Repeat for Y direction ("RSY")

Running Response Spectrum Analysis

1. Go to Analyze → Run Analysis
2. Select MODAL, RSX, and RSY
3. Click Run
4. ETABS runs modal analysis first, then applies the response spectrum

Scaling Response Spectrum Results

The response spectrum base shear must be scaled to match the ELF base shear per ASCE 7:

1. Calculate the ELF base shear (Velf):
   • V = Cs × W
   • Cs = SDS / (R / Ie)
   • W = Seismic weight of the building
2. Calculate the RSA base shear (Vrs):
   • Display → Show Tables → Base Reactions → RSX
   • Read the total base shear in the X direction
3. Scale factor = Velf / Vrs
4. If Vrs < Velf × 0.85 (ASCE 7-16) or Vrs < Velf (ASCE 7-22):
   • Scale up the response spectrum by the scale factor
   • Update the scale factor in the load case
5. Re-run the analysis with the updated scale factor

Interpreting Response Spectrum Results

Story Forces

1. Display → Show Tables → Story Forces
2. Select the response spectrum load case
3. Check:
   • Story shear: Force at each story level
   • Story moment: Overturning moment at each story
   • Story drift: Lateral displacement between stories

Displacement

1. Display → Show Deformed Shape
2. Select the response spectrum load case
3. The deformed shape shows the building's response to the spectrum
4. Check:
   • Maximum displacement: At the roof
   • Displacement profile: Should be smooth (no kinks)
   • Torsional displacement: Check for asymmetric displacement

Story Drift Evaluation

Calculating Story Drift

1. Display → Show Tables → Story Drifts
2. Select the load case (RSX, RSY, or wind)
3. The table shows:
   • Story: Story name
   • Displacement: Lateral displacement at each story
   • Drift: Difference in displacement between adjacent stories
   • Drift ratio: Drift / story height
4. ASCE 7 drift limits:
   • Risk Category I/II: Δ ≤ 0.020 × story height (1/50)
   • Risk Category III: Δ ≤ 0.015 × story height (1/67)
   • Risk Category IV: Δ ≤ 0.010 × story height (1/100)
5. The drift must be multiplied by the deflection amplification factor Cd:
   • Δ × Cd: Design story drift
   • Compare Δ × Cd to the code limits

Drift Check Example

For a 4-story office building (Risk Category II):

• Story height: 3.5m
• ASCE 7 limit: 0.020 × 3500mm = 70mm
• Cd = 5.5 (special RC moment frame)
• ETABS drift (from RSA): 8mm at Story 3
• Design drift: 8mm × 5.5 = 44mm
• 44mm < 70mm → OK

Torsional Irregularity Check

1. Check the displacement at each edge of the building:
   • Maximum displacement: At one edge
   • Average displacement: At the center
2. Torsional irregularity exists if:
   • Max / Avg > 1.2: Torsional irregularity (Type 1)
   • Max / Avg > 1.4: Extreme torsional irregularity (Type 1a)
3. If torsional irregularity exists:
   • Amplify the accidental torsion by Ax = (δmax / δavg)²
   • Increase the design forces
   • Consider repositioning walls or adjusting stiffness

P-Delta Analysis

Setting Up P-Delta

1. Go to Analyze → Set Analysis Options
2. Set P-Delta:
   • P-Delta with Large Delta: Nonlinear geometric (most accurate)
   • P-Delta with Small Delta: Linearized (faster, less accurate)
3. P-Delta load case:
   • Load combination: Typically 1.0 × DEAD + 0.5 × LIVE
   • This represents the gravity load that causes second-order effects
4. Run the analysis with P-Delta enabled
5. P-Delta effects increase drift and forces in slender buildings

When P-Delta Matters

• Slender buildings: Height/width > 3
• Flexible structures: Long periods
• Heavy gravity loads: High axial forces in columns
• Seismic design: ASCE 7 requires P-Delta for stability coefficient check
• Stability coefficient (θ): θ = P × Δ / (V × hs × Cd)
  • If θ > 0.25: Structure is unstable — redesign
  • If θ > 0.10: P-Delta effects must be included
  • If θ < 0.10: P-Delta effects are negligible

Seismic Design Checks

Base Shear Distribution

1. Check the story shear distribution:
   • ELF: Fx = Cvx × V (triangular distribution)
   • RSA: From modal combination
2. Compare ELF and RSA base shears
3. If RSA < 0.85 × ELF (ASCE 7-16), scale up RSA

Overturning Moment

1. Check the overturning moment at the base
2. Compare with the resisting moment (dead load × building width/2)
3. Safety factor = Resisting / Overturning > 1.5 (typical)

Diaphragm Forces

1. Check diaphragm forces at each floor
2. Fpx = Fnx × (Wpx / Wx) — ASCE 7 diaphragm force
3. Verify the diaphragm can transfer the force to the vertical elements

Common Issues

Mass Participation Is Low

• Increase the number of modes (12 → 20 → 30)
• Check the mass source (ensure dead load is included)
• Verify that all elements have mass (check material density)
• Look for disconnected elements (they add mass but don't participate)

Period Is Much Different from Approximate

• If ETABS period > Cu × Ta: The model may be too flexible
  • Check section properties (too small?)
  • Check boundary conditions (supports fixed?)
  • Check stiffness modifiers (too low?)
• If ETABS period < Ta: The model may be too stiff
  • Check for rigid diaphragm constraints
  • Verify section sizes (too large?)

Drift Exceeds Code Limits

• Increase member sizes (beams, columns, walls)
• Add shear walls or braced frames
• Reduce the building height (if possible)
• Change the structural system (higher R value)
• Check P-Delta effects (may be amplifying drift)

Torsional Irregularity

• Reposition shear walls or braced frames for better symmetry
• Increase the stiffness of one side to balance torsion
• Add accidental torsion (5% eccentricity per ASCE 7)
• Consider a torsionally stiff structural system

Summary

ETABS seismic analysis evaluates building response to earthquake loads. Run modal analysis first to determine natural periods and mass participation (target > 90% in each direction). Set up response spectrum analysis with the design spectrum, CQC modal combination, and appropriate damping (5% concrete, 3% steel). Scale the RSA base shear to match the ELF base shear per ASCE 7. Calculate story drift and multiply by Cd for the design drift — compare to ASCE 7 limits (0.020h for Risk Category II). Check for torsional irregularity (max/avg displacement > 1.2). Enable P-Delta analysis for slender buildings and check the stability coefficient. The most common issues — low mass participation, period mismatch, excessive drift, and torsional irregularity — are addressed by increasing modes, checking section properties and stiffness, increasing member sizes, and repositioning lateral force-resisting elements. Seismic analysis in ETABS ensures the building meets code requirements and performs safely under earthquake loading.