Building Height for other Buildings given Fundamental Period Calculator

Building Height Formula:

\[ h_n = \left(\frac{T}{0.02}\right)^{\frac{4}{3}} \]

Building Height (hn):

Height Range (5% tolerance):

1. What is Building Height Calculator given Fundamental Period?

Definition: This calculator estimates the height of a building based on its fundamental period of oscillation.

Purpose: It helps structural engineers and architects determine approximate building height when only the fundamental period is known.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h_n = \left(\frac{T}{0.02}\right)^{\frac{4}{3}} \]

Where:

\( h_n \) — Height of building (meters)
\( T \) — Fundamental period (seconds)
0.02 — Empirical coefficient

Explanation: The formula relates a building's natural period of vibration to its height through an empirical relationship.

3. Importance of Building Height Estimation

Details: Accurate height estimation helps in structural analysis, wind load calculations, and seismic design considerations.

4. Using the Calculator

Tips: Enter the fundamental period in seconds and tolerance percentage (default ±5%). The calculator provides both the exact height and tolerance range.

5. Frequently Asked Questions (FAQ)

Q1: What is fundamental period?
A: The time taken for one complete oscillation (back-and-forth) by the building under free vibration.

Q2: Why include a tolerance percentage?
A: The formula provides an estimate; actual height may vary due to structural system, mass distribution, and other factors.

Q3: What's a typical fundamental period for buildings?
A: For a 10-story building: ~1 second, 20-story: ~2 seconds, but varies significantly with structural system.

Q4: Is this formula applicable to all building types?
A: It works best for regular moment-resisting frame buildings. Special structures may require different formulas.

Q5: How accurate is this estimation?
A: Typically within ±20% of actual height, hence the inclusion of tolerance adjustment.