Seismic Design Basics for Structural Engineers

During an earthquake, the ground accelerates horizontally (and vertically). A structure attached to the ground is dragged along; its mass resists the motion through inertia, generating inertial forces F = ma. The peak ground acceleration (PGA) is measured in units of g (9.81 m/s²). The intensity and frequency content of the ground shaking depend on:

• Source magnitude and distance: A M7.5 earthquake near a city generates much stronger shaking than a M6.0 at the same distance.
• Site soil conditions: Soft soils amplify long-period ground motion significantly. A building on soft clay in a seismic zone can experience 3–5× more acceleration than the same building on rock.
• Directivity and path effects: Rupture propagating toward a site produces stronger pulse-like ground motion (near-fault effects).

ASCE 7-22 uses probabilistic seismic hazard maps to define design-basis ground motion: the risk-targeted maximum considered earthquake (MCER) has a 2% probability of exceedance in 50 years (approximately a 2,475-year return period). The design earthquake (DE) is ⅔ of MCER.

A response spectrum is a plot of the maximum acceleration experienced by a single-degree-of-freedom (SDOF) oscillator as a function of its natural period T. Engineers use it to characterize ground motion intensity at the building's natural period rather than using raw time-history records.

ASCE 7-22 defines the design spectral acceleration at two reference periods:

The design response spectrum has three zones:

• Short-period plateau (T ≤ T_s): S_a = S_DS. Short, stiff buildings experience constant peak acceleration.
• Constant-velocity descending region (T_s < T ≤ T_L): S_a = S_D1/T. Taller buildings with longer periods experience lower spectral acceleration.
• Long-period region (T > T_L): S_a = S_D1·T_L/T². Applies to very tall or soft structures (T_L = 4–16 s depending on region).

ASCE 7-22 §11.6 assigns every structure an SDC (A through F) based on ground motion intensity and occupancy. The SDC determines what structural system is permitted, what detailing is required, and what analysis procedures apply:

Key consequence of SDC: in SDC A and B, ordinary concrete and steel frames are permitted. In SDC D–F, only special moment frames (SMF), special concentrically braced frames (SCBF), or special structural walls are permitted for buildings above certain heights. The special detailing requirements are what allow the R factor economy.

The ELF procedure (ASCE 7-22 §12.8) converts dynamic seismic demand into a set of static lateral forces applied at each floor. It is permitted for most regular structures with T ≤ 3.5T_s and for all SDC B/C structures.

Step 1 — Seismic Base Shear V

Where W_s is the effective seismic weight (dead load + 25% of floor live load in storage, plus snow where ≥ 30 psf). The seismic response coefficient:

Step 2 — Approximate Fundamental Period T_a

For steel moment frames: C_t=0.0724, x=0.8. For concrete moment frames: C_t=0.0466, x=0.9. For all other systems: C_t=0.0488, x=0.75. h_n is the height above grade to the highest level in meters.

Step 3 — Vertical Distribution of Forces

k = 1.0 for T ≤ 0.5 s (linear distribution); k = 2.0 for T ≥ 2.5 s (parabolic — more force in upper floors); interpolated between 0.5 s and 2.5 s. This vertical distribution concentrates forces at upper floors for taller buildings, reflecting the whipping effect of higher modes.

The R factor reduces elastic seismic forces to design-level forces by assuming the structure will undergo controlled ductile yielding rather than remaining elastic. A structure designed for the full elastic demand would require 3–8× more steel or concrete than one designed with ductile detailing.

C_d (deflection amplification factor) scales elastic displacements back to actual inelastic displacements: δ_actual = C_d × δ_elastic / I_e. This is used for drift checks.

Ω_o (overstrength factor) amplifies design forces for force-controlled components (columns, connections) that must remain elastic: Ω_o×E is applied to column axial demands and anchor bolt forces.

Story drift Δ is the relative lateral displacement between the top and bottom of a story. Excessive drift damages non-structural elements (partitions, facades, mechanical/electrical systems) and can trigger P-Δ instability in tall frames.

ASCE 7-22 Table 12.12-1 allowable story drift limits (Δ_a) as a fraction of story height h_sx:

P-Δ Stability Check (§12.8.7)

When the stability coefficient θ exceeds 0.10, P-Δ effects must be explicitly included in the analysis:

Where P_x = total vertical design load at and above story x. When θ > 0.10, drifts and member forces must be amplified by 1/(1-θ). When θ > θ_max (Eq. 12.8-17), the structural system must be redesigned — the story is unstable.

The R factor economy is "paid for" by detailing requirements that ensure ductile behaviour. ACI 318-25 Chapter 18 specifies these for RC structures in SDC C–F:

Special Moment Frame Beams (SMF — ACI §18.6)

• Clear span ≥ 4× effective depth (to prevent deep-beam shear mode)
• Width ≥ min(b_w/2 of column, 250 mm)
• Hoops with 135° seismic hooks at plastic hinge zones (2d from column face)
• Min 2 bars continuous top AND bottom throughout span
• Max stirrup spacing in plastic hinge zone: min(d/4, 6d_b, 150 mm)

Special Moment Frame Columns (SMF — ACI §18.7)

• Strong-column weak-beam: ΣM_nc ≥ 1.2ΣM_nb (column moments exceed beam moments at joint)
• Spiral or rectangular confinement hoops throughout column height
• Confinement zone length: max(h_col/6, 450 mm, h_col) at top and bottom
• Confinement hoop spacing: min(b/4, 6d_b, s_o=100–150 mm)
• Minimum A_s=1%, Maximum A_s=6% (reduced from 8% for constructability)

Special Structural Walls (ACI §18.10)

• Distributed reinforcement (vertical and horizontal) ≥ 0.0025b_wh in each direction
• Boundary elements required when compressive strain demand ε_c ≥ 0.003 (strain-based trigger)
• Boundary element confinement: similar requirements to column confinement zones