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Earthquake frame time history

A reinforced concrete frame shaken at its base, integrated step by step with Newmark’s average acceleration method.

Parameters

3
3.5
m
5
m
30
t
0.2
g
0.5
s
5
%
Open in editor ↗

The editor opens the frame, its sections and supports. The floor masses and the ground motion are not carried over.

Results

First period 0.73166 s
Peak roof displacement 57.924 mm
Peak interstorey drift 0.67719 %
Peak elastic base shear 273.7 kN

Base shear from the column stiffness forces K·u, the same quantity as the engine’s peak reactions. Damping forces and the columns’ own inertia are not included.

Certified (time integration)· largest relative residual of the discrete equations ≤ 5.5 × 10−13. This certifies the time-stepping scheme and its equations, not the error against the continuous motion.

Roof displacement (mm)

mm−75−50−25025507502468t (s)

Ground acceleration (g)

g−0.2−0.10.00.10.20.302468t (s)

A one-bay concrete frame (columns 35 × 35 cm, beams 25 × 55 cm, E = 30 GPa) carries a lumped mass at every floor. The ground follows a sine acceleration for four cycles and then stops; the engine integrates 8 s at Δt = 0.01 s with Rayleigh damping on the first two modes. The ground motion is a synthetic pulse, not a recorded earthquake.

Verified by: Newmark 1959 benchmark

A teaching example, not a design check. SI units: m, kN, MPa. Published by Ergodic Group.