Discussion
The Newmark-beta method is unconditionally stable provided
Answer: D
Correct answer: \( \gamma \ge 1/2 \) and \( \beta \ge \gamma/2 \)
These conditions make the scheme unconditionally stable, so the solution does not diverge however large the time step. The average acceleration method, with \( \gamma = 1/2 \) and \( \beta = 1/4 \), satisfies them exactly.
Stability is not accuracy: a stable scheme with too large a step gives a bounded but wrong answer, which is why a step of about a tenth of the shortest period of interest is still recommended. Elastic behaviour is not required, and that is precisely why the method suits inelastic analysis.
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