| name | seismic-design |
| description | Seismic design — ASCE 7 seismic provisions, design response spectrum, equivalent lateral force (ELF), response spectrum analysis (RSA), R/Cd factors, drift limits, base isolation, AISC 341. |
| metadata | {"priority":7,"promptSignals":{"phrases":["seismic","earthquake","seismic design","ASCE 7","response spectrum","base shear","lateral force","base isolation","drift","Seismic Design Category"],"minScore":3}} |
Seismic Design — Complete Skill
Seismic Hazard (ASCE 7-22)
Spectral Acceleration
S_s = mapped MCER short-period spectral acceleration [g] (0.2s period)
S₁ = mapped MCER 1-second spectral acceleration [g]
Obtained from: USGS Seismic Hazard Tool or ASCE 7 maps (2% probability of exceedance in 50 years = 2475-yr return)
Site-adjusted accelerations:
S_MS = F_a × S_s (short-period, adjusted for site class)
S_M1 = F_v × S₁ (1-second, adjusted for site class)
Design spectral accelerations (2/3 of MCER):
S_DS = (2/3) S_MS
S_D1 = (2/3) S_M1
Site class (ASCE 7 Table 20.3-1):
A: hard rock (V_s > 1500 m/s), B: rock, C: very dense soil, D: stiff soil (most common default)
E: soft clay (V_s < 180 m/s); special design required
V_s,30 = weighted average shear wave velocity top 30m
Seismic Design Category (SDC)
Determined from S_DS, S_D1, and Risk Category (I-IV)
SDC A-F: A/B = low hazard; C = moderate; D/E/F = high hazard
SDC D-F: AISC 341 seismic provisions apply (SMF, SCBF, etc.)
Risk Category and Importance Factor
RC I: nonessential = I_e = 1.0
RC II: ordinary buildings = I_e = 1.0
RC III: substantial hazard (school, assembly) = I_e = 1.25
RC IV: essential facilities (hospital, emergency) = I_e = 1.5
Design Response Spectrum
ASCE 7 Spectrum
T_s = S_D1 / S_DS (transition from flat to descending)
T_L = long-period transition period (mapped, typically 6-16 s)
T_0 = 0.2 × T_s
S_a values:
T < T_0: S_a = S_DS × (0.4 + 0.6T/T_0) [ascending]
T_0 ≤ T ≤ T_s: S_a = S_DS [constant acceleration, short period]
T_s < T ≤ T_L: S_a = S_D1 / T [descending, constant velocity]
T > T_L: S_a = S_D1 × T_L / T² [long period]
Equivalent Lateral Force (ELF) Method
Seismic Base Shear
V = C_s × W [kN]
C_s = S_DS / (R/I_e) (but C_s need not exceed S_D1/(T×R/I_e) for T ≤ T_L)
C_s minimum = 0.044 × S_DS × I_e (≥ 0.01)
C_s minimum = 0.5 × S₁/(R/I_e) when S₁ ≥ 0.6g
W = effective seismic weight (dead load + partitions + applicable live)
R = response modification factor (ductility/overstrength reduction)
I_e = importance factor
T = fundamental period [s]
R and Cd Factors (ASCE 7 Table 12.2-1)
| System | R | Cd | Ω₀ | Notes |
|---|
| OMRF (ordinary steel frame) | 3.5 | 3 | 3 | Low seismic only |
| IMRF (intermediate steel frame) | 4.5 | 4 | 3 | SDC C max |
| SMRF (special steel frame) | 8 | 5.5 | 3 | High seismic |
| SCBF (special concentric BF) | 6 | 5 | 2 | Good for stiff bldgs |
| OCBF | 3.25 | 3.25 | 2 | Low seismic |
| ECBF (eccentric) | 8 | 4 | 2.5 | High ductility |
| Shear wall (CIP concrete) | 5 | 5 | 2.5 | — |
| Bearing wall (masonry) | 2 | 1.75 | 2.5 | — |
R > 1: structure expected to yield — amplified ductility demands in connections
Vertical Distribution of Forces
F_x = C_vx × V
C_vx = w_x × h_x^k / Σ(w_i × h_i^k)
k = 1 (T ≤ 0.5s); k = 2 (T ≥ 2.5s); linear interpolation between
Fundamental Period (Approximate)
T_a = C_t × h_n^x
Steel MRF: C_t=0.0724, x=0.8
Steel braced frame: C_t=0.0488, x=0.75
Concrete shear wall: C_t depends on A_b
Upper limit: T ≤ C_u × T_a (C_u = 1.4 for S_D1 ≥ 0.4, 1.7 for S_D1 ≤ 0.1)
Eigenvalue analysis gives exact T (use for RSA)
Response Spectrum Analysis (RSA)
Modal Analysis Procedure
- Compute mode shapes and periods: [K - ω_n² M]{Φ_n} = 0
- Modal participation factor: Γ_n = {Φ_n}ᵀ [M]{1} / {Φ_n}ᵀ [M]{Φ_n}
- Modal base shear: V_n = Γ_n × M_n × S_a(T_n)
- Combine modes: SRSS or CQC (preferred)
CQC combination:
Σ² = Σ_i Σ_j ρ_ij × r_i × r_j
ρ_ij = 8ζ²(1+β)β^(3/2) / ((1-β²)² + 4ζ²β(1+β)²)
β = ω_i/ω_j (frequency ratio)
Number of modes: include enough to capture 90% mass participation (ASCE 7)
Scaling RSA Results
Scale so V_RSA ≥ 0.85 × V_ELF (minimum base shear check)
If RSA base shear < 0.85 V_ELF: scale up all forces and drifts
Drift Limits
Story Drift
δ_x = C_d × δ_xe / I_e [amplified drift using inelastic amplifier C_d]
δ_xe = elastic drift from ELF or RSA
Story drift ratio: Δ/h_sx ≤ Δ_a
Allowable drift Δ_a (ASCE 7 Table 12.12-1):
RC I, II, III: 0.025 h_sx (2.5%) for steel/concrete frame
RC IV (essential): 0.015 h_sx
Masonry: 0.007 h_sx
P-Delta Effects
θ = P_x × Δ / (V_x × h_sx × C_d) (stability coefficient)
θ ≤ θ_max = 0.5/(β×C_d) ≤ 0.25
If θ > 0.10: amplify forces by 1/(1-θ); if θ > θ_max: redesign required
AISC 341 — Seismic Provisions for Steel
Special Moment Frame (SMF)
Beam-to-column connections: must achieve 0.04 rad plastic rotation (tested)
Prequalified: RBS (Reduced Beam Section), BFP (Bolted Flange Plate), WUF-W
Panel zone check: balance shear yielding in panel zone vs. beam yielding
Column splice: above mid-height; complete joint penetration (CJP) if required
Special Concentrically Braced Frame (SCBF)
Brace expected tension capacity: R_y × F_y × A_g (R_y = actual/nominal yield ratio)
Brace expected compression capacity: lower of 1.14 F_cre A_g or P_n
Connections designed for maximum brace force (max tension or compression)
Gusset plate: clear distance from brace end 2t gusset (buckling accommodation)
Eccentrically Braced Frame (EBF)
Link element (short beam segment): ductile shear yielding
Short link (e ≤ 1.6 M_p/V_p): shear yielding (most ductile)
Long link (e ≥ 2.6 M_p/V_p): moment yielding
Design rest of frame elastically for link maximum forces
Base Isolation
Isolation System
Concept: decouple structure from ground; lengthen period to avoid resonance
T_iso ≈ 2-4 sec (above typical ground motion content)
Effective stiffness: k_eff = W × (2π/T_iso)²/g
Isolator types:
Lead Rubber Bearing (LRB): flexibility + damping (15-25%); most common
Friction Pendulum System (FPS): concave dish; T = 2π√(R/g) (R = radius)
Triple FPS: variable stiffness with displacement
Design spectral acceleration at T_iso: S_a(T_iso) ≪ S_a(T_fixed) → much less force on structure
Peak displacement:
D_D = g S_D1 T_D / (4π² B_D) [at design level]
D_M = g S_M1 T_M / (4π² B_M) [at maximum level]
B = damping reduction factor (B=1.0 at 5%; B=1.5 at 20% damping)
Output
Provide: S_DS and S_D1 [g], SDC classification, R and Cd values selected, T_a [s], C_s and V [kN], vertical force distribution F_x, story drift Δ/h [%] vs. allowable, P-delta check θ, base isolation target period T_iso [s] if applicable.
