Earthquake Engineering MCQ with answer and solution

Concept

Empirical fundamental natural period of RC frame

Formula

T_a = 0.075 × h^0.75

Step-by-step solution

1. IS 1893:2016 provides empirical formulas for fundamental natural period Ta of buildings. 2. For a bare RC moment-resisting frame building without masonry infills, Ta = 0.075 × h^0.75. 3. Given height of the building h = 30 m. 4. Evaluating (30)^0.75 = (30³)^0.25 = (27,000)^0.25 = 12.818. 5. Ta = 0.075 × 12.818 = 0.961 seconds approx 1.0 s. Answer: B

Explanation

As per IS 1893 (Part 1): 2016 Clause 7.6.2, the approximate fundamental natural period of an RC moment-resisting frame building without masonry infills is given by Ta = 0.075 × h^0.75. For height h = 30 m, Ta = 0.075 × (30)^0.75 = 0.075 × 12.82 = 0.96 s, which is approximately 1.0 s.

Why the other options are wrong

A) 0.75 s underestimates the flexible period of a 30 m bare frame. C) 1.5 s corresponds to a much taller structure of roughly 55 m. D) 2.0 s corresponds to a tall high-rise building of over 80 m.

Shortcut

T_a = 0.075 × h^0.75 ≈ 0.075 × 12.82 ≈ 0.96 s ≈ 1.0 s.

Common mistake

Using Ta = 0.09 × h / √(d), which applies to buildings with masonry infill panels.