Seismic Design of Steel Structures — Engineering Reference

Seismic design of steel structures requires selecting an appropriate seismic force-resisting system (SFRS), proportioning members for amplified seismic forces, and detailing connections to sustain inelastic deformations. The governing standards are AISC 341-22 (Seismic Provisions) and ASCE 7-22 (Minimum Design Loads), with parallel requirements in NZS 3404, EN 1998, and CSA S16.

Seismic force-resisting systems

Steel buildings resist earthquake forces through one or more lateral systems. Each system is assigned response modification (R), overstrength (Omega_0), and deflection amplification (Cd) factors that reflect its expected ductility.

System	R	Omega_0	Cd	Height Limit (SDC D)
SMF (Special Moment Frame)	8	3	5.5	No limit
IMF (Intermediate Moment Frame)	4.5	3	4	No limit
SCBF (Special Concentrically Braced)	6	2	5	No limit
OCBF (Ordinary Concentrically Braced)	3.25	2	3.25	35 ft (SDC D-F)
EBF (Eccentrically Braced)	8	2	4	No limit
BRBF (Buckling-Restrained Braced)	8	2.5	5	No limit

The selection of system type depends on the Seismic Design Category (SDC), building height, architectural constraints, and cost. Higher R values reduce design base shear but demand more stringent detailing.

Equivalent lateral force procedure — worked example

Given: 5-story steel office building, SDC D, SCBF system. Site class D. SDS = 1.0 g, S_D1 = 0.60 g. Seismic weight W = 4,500 kips. Building period T = 0.65 s (per ASCE 7 Eq. 12.8-7: T_a = C_t * hn^x = 0.02 * 65^0.75 = 0.45 s, use computed T = 0.65 s with Cu = 1.4 upper limit check: C_u * Ta = 1.4 * 0.45 = 0.63 s, so use T = 0.63 s).

Step 1 — Seismic response coefficient (ASCE 7 Eq. 12.8-2):

C_s = S_DS / (R / I_e) = 1.0 / (6 / 1.0) = 0.167

Step 2 — Check upper limit (ASCE 7 Eq. 12.8-3):

C_s <= S_D1 / [T * (R / I_e)] = 0.60 / [0.63 * 6] = 0.159

C_s = 0.159 (governs)

Step 3 — Check minimum (ASCE 7 Eq. 12.8-5):

Cs >= 0.044 * SDS * I*e = 0.044 * 1.0 _ 1.0 = 0.044 (OK, 0.159 > 0.044)

Step 4 — Base shear:

V = C*s * W = 0.159 _ 4,500 = 716 kips

This base shear is distributed vertically to each floor using the exponent k (ASCE 7 Eq. 12.8-12), where k = 1.0 for T <= 0.5 s and k = 2.0 for T >= 2.5 s; interpolate for T = 0.63 s giving k approximately 1.07.

Capacity design philosophy

Seismic provisions use capacity design to ensure that yielding occurs in designated ductile elements while non-ductile elements remain elastic. For an SCBF:

Braces are the designated yielding members — they must satisfy width-to-thickness limits of AISC 341 Table D1.1 (e.g., round HSS: D/t <= 0.053 E/Fy).
Beams and columns must resist the maximum force that the braces can deliver, calculated using the expected yield strength Ry * Fy (not the nominal F_y). For A992 steel, R_y = 1.1, so the expected strength is 1.1 * 50 = 55 ksi.
Connections must develop the expected tensile strength of the brace: Ry * Fy * A_g.
Gusset plates in SCBF must accommodate brace buckling through a linear clearance of 2t_p from the end of the brace to the gusset fold line (Thornton method).

Code comparison across standards

Requirement	AISC 341-22	EN 1998-1	CSA S16-19	AS 4100 (NZS 3404)
Overstrength factor	R_y * F_y (material)	gamma_ov = 1.25 (typical)	R_y * F_y (same as AISC)	phi_o dependent on system
Brace slenderness	KL/r <= 200 (SCBF)	lambda_bar <= 2.0 (DCH)	KL/r <= 200	lambda_n <= 200
Column splice location	Middle third of story	Middle third	Middle third	Middle third
Strong-column weak-beam	Sum(M_pc) >= Sum(1.0 M_pb)	Sum(M_Rc) >= 1.3 Sum(M_Rb)	Sum(M_rc) >= 1.1 Sum(M_rpb)	Capacity design check
Protected zones	Within hinge region	Dissipative zones	Protected zones	Designated yielding regions

EN 1998 uses behavior factor q (analogous to R) and ductility classes DCL/DCM/DCH. CSA S16 follows AISC closely but uses Canadian seismic hazard maps (2% in 50 years, site class F factors). NZS 3404 (used with AS 1170.5 in New Zealand) has very detailed capacity design procedures due to high seismicity.

Key clause references

ASCE 7-22 Section 12.8 — Equivalent lateral force procedure, C_s calculation, vertical distribution
AISC 341-22 Chapter D — Member ductility requirements, width-to-thickness limits
AISC 341-22 Chapter E — Moment frame provisions (SMF, IMF, OMF)
AISC 341-22 Chapter F — Braced frame provisions (SCBF, OCBF, EBF, BRBF)
AISC 341-22 Section A3.2 — Expected material strength (R_y, R_t values)
AISC 358-22 — Prequalified connections for SMF and IMF

Common pitfalls in seismic steel design

Using nominal Fy instead of expected strength R_y * Fy when checking capacity-protected elements — this underestimates the force demand on columns and connections by roughly 10-20%.
Neglecting the strong-column weak-beam check at every beam-column joint — AISC 341 Section E3.4a requires Sum(M*_pc) / Sum(M*_pb) >= 1.0, and the column moment must include axial load reduction via P_uc / A_g.
Omitting the 2t_p gusset clearance for SCBF brace buckling — without this clearance the gusset cannot form a plastic hinge, and the connection may fracture.
Applying drift limits to elastic analysis only — code drift limits (typically 0.020 h_sx for SDC D) apply to the amplified drift delta_x = C_d * delta_xe / I_e, not the raw elastic displacement.

Run this calculation

Related references

Disclaimer

This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against the applicable standard and project specification before use. The site operator disclaims liability for any loss arising from the use of this information.