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📈 Pushover & Target Displacement

Force-based design asks whether the structure is strong enough. Performance-based design asks a harder question: how far will it actually move, and can it survive moving that far? Push the building over, idealize the capacity curve, and find where the demand and the capacity meet.

Capacity

Yield strength F_y* 2.00 MN

Yield displacement D_y* 0.050 m

Ultimate displacement D_u* 0.250 m

Demand

Equivalent mass m* 500 t

Spectral plateau S_DS 1.00 g

Corner period T_B = S_D1/S_DS (TBDY; T_C in EC8) 0.60 s

Live Result

—

Equivalent SDOF period T*—

Elastic displacement demand D_e*—

Reduction factor q_u—

Target displacement D_t*—

Ductility demand μ—

N2 branch applied—

Powered by the N2 method (engine/pushover.js). Verified before publishing: the equivalent SDOF period matches an independent 2π√(m*/k*) evaluation exactly, the equal-displacement rule is confirmed to hold to machine precision in the long-period branch, the short-period branch is confirmed never to fall below the elastic demand, and the equal-energy bilinear idealization is verified to recover the true yield point of an elastic–perfectly-plastic curve exactly. A perfectly linear (never-yielding) capacity curve is rejected rather than idealized into a degenerate zero-ductility result.

Method

Fajfar (2000)N2 method — equal-displacement rule for T* ≥ T_C, amplification for T* < T_C.

EN 1998-1 Annex BEquivalent SDOF conversion and equal-energy bilinear idealization; reflected in TBDY 2018 Chapter 5.

Scope: first-mode-dominated response only — the N2 method does not capture higher-mode effects, which matter for tall or irregular buildings. Assumes a monotonic, non-degrading capacity curve with no cyclic strength or stiffness degradation.

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Visual explanation

Pushover analysis: capacity curve and yield sequence. Event-to-event incremental solution; each kink marks a storey yielding — **Figure 35.** Pushover analysis: capacity curve and yield sequenceSource: FEMA 440 (2005) principles; TBDY 2018 Ch. 5. Simplified shear-building example.