Moment of Inertia of Secondary Member given Capacity Spectrum Calculator

Formula:

\[ I_s = \frac{32 \times S \times L_s^4}{10^7 \times C_s} \]

Moment of Inertia of Secondary Member (m⁴/m):

1. What is Moment of Inertia of Secondary Member given Capacity Spectrum?

Definition: This calculator computes the moment of inertia for secondary structural members based on their spacing, length, and the system's capacity spectrum.

Purpose: It helps structural engineers determine the appropriate moment of inertia for secondary members in seismic design applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ I_s = \frac{32 \times S \times L_s^4}{10^7 \times C_s} \]

Where:

\( I_s \) — Moment of inertia of secondary member (m⁴/m)
\( S \) — Spacing of secondary members (m)
\( L_s \) — Length of secondary member (m)
\( C_s \) — Capacity spectrum

Explanation: The formula relates the geometric properties of secondary members to the system's seismic capacity spectrum.

3. Importance of Moment of Inertia Calculation

Details: Proper calculation ensures structural integrity, appropriate stiffness distribution, and compliance with seismic design requirements.

4. Using the Calculator

Tips: Enter the spacing of secondary members, their length, and the capacity spectrum. All values must be > 0. Results are accurate within ±5%.

5. Frequently Asked Questions (FAQ)

Q1: What is the capacity spectrum in structural engineering?
A: The capacity spectrum represents a structure's seismic capacity transformed from force-displacement to spectral coordinates.

Q2: Why is the length raised to the 4th power?
A: The moment of inertia depends strongly on member length, with the 4th power relationship reflecting beam deflection physics.

Q3: What are typical values for secondary member spacing?
A: Spacing typically ranges from 0.5m to 3m depending on structural system and design requirements.

Q4: How accurate is this calculation?
A: Results are theoretical estimates with ±5% accuracy; always verify with detailed analysis.

Q5: Can this be used for primary structural members?
A: No, this formula is specifically calibrated for secondary members in seismic systems.