In earthquake engineering, the ductility demand mu of a structure is defined as the ratio of the maximum displacement Delta_ max to the yield displacement Delta_y. For a structure with a force reduction factor R = 6 designed using the equal energy principle (applicable for intermediate period structures), the relationship between R and mu is approximately:

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Architecture Engineering QUESTION #2362

Question 1

In earthquake engineering, the ductility demand \(\mu\) of a structure is defined as the ratio of the maximum displacement \(\Delta_{max}\) to the yield displacement \(\Delta_y\). For a structure with a force reduction factor \(R = 6\) designed using the equal energy principle (applicable for intermediate period structures), the relationship between \(R\) and \(\mu\) is approximately:

\(R = \mu\)
\(R = \sqrt{2\mu - 1}\)✔️
\(R = \mu^2\)
\(R = 2\mu\)

Correct Answer Explanation

The equal energy principle (Newmark-Hall approach for intermediate periods \(0.1\,\text{s} < T < T_s\)) gives \(R = \sqrt{2\mu - 1}\). For long-period structures (equal displacement principle): \(R = \mu\). For short-period structures (equal acceleration): \(R = 1\) regardless of ductility. Understanding which principle applies determines the inelastic displacement demand in seismic design.

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