Seismic Design for Steel Structures — Part 1: Theoretical Foundations & Design Philosophy

1. Lessons from Northridge 1994

On 17 January 1994 the Northridge earthquake (M 6.7) in Los Angeles shattered the profession's confidence in welded steel moment frames (WSMF).

Before Northridge

Welded steel moment frames were regarded as the gold standard for seismic resistance.
Beam-to-column connections used CJP welds at the beam flanges.
Engineers believed the system had excellent ductile deformation capacity.

After Northridge — the shock

Hundreds of beam-to-column connections suffered brittle fracture at the welds.
Cracks initiated at the CJP weld of the bottom flange and propagated into the column flange.
Many structures were damaged with no sign of ductile deformation — the very thing the design relied on.

#	Root cause	Explanation
1	Low-toughness weld metal	E70T-4 electrodes had very low Charpy V-Notch toughness
2	Weld backing bars	Created root defects that became crack initiation points
3	Stress concentration	Plastic deformation occurred right at the column face — the peak-stress location
4	Actual strength above design	A36 steel had Fy well above nominal, raising the force delivered into the connection
5	Poor quality control	Weld inspection failed to catch latent defects

Why this matters in low-seismicity regions

Vietnam sits in a low to moderate seismic zone under TCVN 9386.
Yet many industrial projects — plants, pipe racks — are designed to US codes (AISC/ASCE).
Understanding this lets you pick a system that is appropriate and economical, avoiding both over-design and unsafe detailing.

2. The capacity design philosophy

Figure 1. Capacity design — separating the yielding elements from the protected ones. — **Figure 1.** Capacity design — separating the yielding elements from the protected ones.

Group	Role	Examples	Requirement
Fuse	Yields and dissipates energy	Beam plastic hinges, EBF link beams, CBF braces	Large, stable inelastic deformation
Protected	Stays elastic	Columns, connections, welds, gusset plates	Strength above the ultimate capacity of the fuse

Strong column — weak beam

This is the single most important rule in seismic frame design. Plastic hinges must form in the beams first. If the columns yield first you get a soft-storey collapse mechanism — total failure.

ΣM*pc  ≥  ΣM*pb

ΣM*pc = sum of COLUMN moment capacities at the joint (allowing for axial load)
ΣM*pb = sum of BEAM plastic-hinge moments (using expected strength)

Expected strength and the plastic hinge moment

Real steel always yields above its nominal Fy. When designing a protected element you must use the expected strength of the fuse — otherwise the protected element is not genuinely stronger than the fuse.

Fye = Ry × Fy        (expected yield strength)
Fue = Rt × Fu        (expected tensile strength)

Plastic hinge moment:
  Mpr = Cpr × Ry × Fy × Ze

Cpr = strain-hardening factor, AISC recommends 1.1
Ze  = plastic section modulus at the hinge location

3. The seven seismic systems and their design coefficients

Figure 2. Design coefficients compared across the seismic force-resisting systems. — **Figure 2.** Design coefficients compared across the seismic force-resisting systems.

System	R	Ω₀	Cd	Fuse element
SMF — special moment frame	8	3	5.5	Beam plastic hinge
IMF — intermediate moment frame	4.5	3	4	Beam plastic hinge
OMF — ordinary moment frame	3.5	3	3	Beam plastic hinge
SCBF — special concentrically braced	6	2	5	Braces in tension/compression
OCBF — ordinary concentrically braced	3.25	2	3.25	Braces
EBF — eccentrically braced	8	2	4	Link beam
BRBF — buckling-restrained braced	8	2	5	BRB core

What the three coefficients mean

R — response modification: lets you reduce the design force in exchange for ductility. A higher R means smaller design forces but far stricter detailing. It is a trade, not a gift.
Ω₀ — overstrength: amplifies the design force for particular elements (columns, connections, collectors) so they do not fail before the fuse reaches its ultimate capacity.
Cd — deflection amplification: elastic analysis gives δxe; the real drift is δx = Cd × δxe / Ie. This is what the drift check uses.

Moment frames — three tiers

	SMF	IMF	OMF
Drift capacity	0.04 rad	0.02 rad	0.02 rad
Strong column – weak beam	Required	Required	Not required
b/t limits	λhd	λmd	λp
Connections	Prequalified (AISC 358)	Tested / qualified	Flexible
Height limit	None	Yes	Tight
Suitable SDC	D, E, F	C, D	A, B, C

Braced frames — concentric, eccentric and BRBF

CBF (concentric): brace axes pass through the joint; energy is dissipated by tension yielding and compression buckling. K-braces are prohibited in both SCBF and OCBF.
EBF (eccentric): the brace axis deliberately misses the joint, creating a short link beam. The link yields while the brace and outer beam stay elastic. R = 8 like an SMF but far stiffer.
BRBF: the brace is encased so it cannot buckle in compression — it yields symmetrically both ways, dissipating energy very efficiently. Detailing is simpler than SCBF.

Link type (EBF)	Length	Mechanism	Rotation capacity
Short link (shear)	e ≤ 1.6·Mp/Vp	Shear yielding	γp = 0.08 rad
Intermediate	1.6 < e/(Mp/Vp) < 2.6	Combined	Interpolate
Long link (flexural)	e ≥ 2.6·Mp/Vp	Flexural yielding	γp = 0.02 rad

4. Determining the design seismic force

The six ASCE 7 steps

1. Read the seismic maps → Ss (0.2s period) and S1 (1.0s period)

2. Site coefficients for Site Class A→F:
     SMS = Fa × Ss          SM1 = Fv × S1

3. Design spectral accelerations:
     SDS = 2/3 × SMS        SD1 = 2/3 × SM1

4. Seismic Design Category (SDC) from SDS, SD1 and Risk Category

5. Seismic response coefficient:
     Cs = SDS / (R / Ie)
     not more than  SD1 / [ T × (R / Ie) ]     when T ≤ TL
     not less than  0.044 × SDS × Ie  ≥  0.01

6. Base shear:
     V = Cs × W            W = total effective seismic weight

ASCE 7 versus TCVN 9386

Feature	ASCE 7 (US)	TCVN 9386 / EC8
Primary parameter	Ss, S1 (spectral acceleration)	agR (peak ground acceleration)
Design spectrum	From SDS, SD1	Elastic spectrum × 1/q
Force reduction	R	q (behaviour factor)
Return period	2,475 years (MCE) then ×2/3	475 years
Zoning	USGS maps	Province-level maps

The Vietnamese context

agR ranges from 0.0432g in the quietest zones to 0.1086g in Điện Biên and Lai Châu.
Most of the country sits below agR = 0.08g — low to very low seismicity.
Foreign-invested projects usually demand US codes, so a PGA-to-ASCE conversion is needed.

Rough conversion:  SDS ≈ 2/3 × Fa × (2.5 × agR)

  agR = 0.08g, Site Class D  →  SDS ≈ 0.21g  →  SDC B
                                 OMF or OCBF is acceptable

  agR > 0.10g, Site Class D  →  SDS ≈ 0.27g  →  SDC C
                                 IMF or SCBF and above required

The drift check

δx = Cd × δxe / Ie

Limits by Risk Category:
  I, II  →  0.020 × hsx
  III    →  0.015 × hsx
  IV     →  0.010 × hsx      (hsx = storey height)

Figure 3. Drift angle and the formation of the plastic hinge. — **Figure 3.** Drift angle and the formation of the plastic hinge.

5. Material requirements — why A36 is the wrong steel

Mass-produced steel typically yields 20–50% above its nominal value. A36 is nominally Fy = 248 MPa but routinely tests at 300–380 MPa.

Steel grade	Fy (MPa)	Ry	Rt
ASTM A36	248	1.5	1.2
ASTM A572 Gr.50	345	1.1	1.1
ASTM A992	345	1.1	1.1
ASTM A500 Gr.B (HSS)	317	1.4	1.3
ASTM A500 Gr.C (HSS)	345	1.3	1.2
ASTM A913 Gr.50/S75	345	1.1	1.1

When to use Ry × Fy and when to use nominal Fy

Use expected strength Ry × Fy	Use nominal Fy
Computing the plastic hinge moment Mpr	Designing the fuse element itself
Designing connections that receive fuse forces	Ordinary capacity-ratio checks
The strong column – weak beam check	—
Designing CBF gusset plates	—

CVN toughness

Demand-critical welds must achieve CVN ≥ 27J at −29°C.
Use high-toughness filler metal — low-toughness electrodes were what caused Northridge.
Remove the backing bar after CJP welding at the bottom beam flange.

6. Width-to-thickness limits

Under large inelastic strains the flange or web can buckle locally. Early buckling means losing capacity before any energy is absorbed — precisely what seismic design depends on. Hence seismic elements need tighter b/t ratios than ordinary design.

Level	Symbol	Applies to
Highly ductile	λhd	SMF beams, SCBF braces, EBF links
Moderately ductile	λmd	IMF beams, SCBF columns
Compact	λp	OMF and ordinary design

FLANGE (unstiffened element)
  I-shape:   λhd = 0.32·√(E/Fy)    λmd = 0.40·√(E/Fy)    λp = 0.38·√(E/Fy)
  HSS    :   λhd = 0.65·√(E/Fy)    λmd = 0.76·√(E/Fy)    λp = 1.12·√(E/Fy)

WEB (stiffened element)
  Flexure  :  λhd = 2.57·√(E/Fy)   λmd = 3.76·√(E/Fy)
  Combined :  λhd = 1.57·√(E/Fy)
  HSS wall :  λhd = 0.65·√(E/Fy)   λmd = 0.76·√(E/Fy)

Actual numbers for Fy = 345 MPa

Element	λhd	λmd	λp
I-shape flange (bf/2tf)	7.70	9.63	9.15
Web in flexure (h/tw)	61.8	90.5	—

Two sections checked

W21×62  (Fy = 345 MPa)
  bf/2tf = 7.53   ≤  λhd = 7.70   →  OK for SMF
  h/tw   = 46.9   ≤  λhd = 61.8   →  OK for SMF

W14×48  (Fy = 345 MPa)
  bf/2tf = 6.75   ≤  λhd = 7.70   →  OK for SMF
  h/tw   = 33.6   ≤  λhd = 61.8   →  OK for SMF

7. Part 1 summary

Topic	Key point
Northridge	Brittle weld fracture rewrote the entire design philosophy
Capacity design	Pre-select the fuse, then make everything else stronger than it
Strong column – weak beam	ΣMpc ≥ ΣMpb, using Ry × Fy
R, Ω₀, Cd	R cuts force, Ω₀ amplifies locally, Cd amplifies drift
Systems	SMF/EBF/BRBF at R = 8, SCBF at 6, OMF at 3.5
Material	Use A992 (Ry = 1.1), avoid A36 (Ry = 1.5)
b/t	λhd for SMF/SCBF/EBF, λmd for IMF, λp for OMF
Vietnam	Mostly agR < 0.08g → SDC B–C → OMF/OCBF usually suffices

References: FEMA 350 · AISC 341-22 · ASCE 7-22 · AISC 358-22 · TCVN 9386:2012. Part of the “Industrial structural design guide” series by Roberto Structural. The content is technical guidance only; the engineer remains responsible for verifying and adapting it to each project and the governing code.