seismic-design

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

1. Compute mode shapes and periods: [K - ω_n² M]{Φ_n} = 0
2. Modal participation factor: Γ_n = {Φ_n}ᵀ [M]{1} / {Φ_n}ᵀ [M]{Φ_n}
3. Modal base shear: V_n = Γ_n × M_n × S_a(T_n)
4. 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.