Slenderness Parameter Calculator

Slenderness Parameter Formula:

\[ \lambda_c = \left(\frac{k \cdot l}{r}\right)^2 \cdot \left(\frac{F_y}{286220}\right) \]

Effective Length Factor:

Effective Column Length:

Radius of Gyration:

Yield Stress of Steel:

MPa

Slenderness Parameter:

1. What is Slenderness Parameter?

Definition: The Slenderness Parameter is a value that distinguishes between elastic and inelastic behavior of structural members under compression.

Purpose: It helps engineers determine whether a column will fail by buckling (elastic) or yielding (inelastic).

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \lambda_c = \left(\frac{k \cdot l}{r}\right)^2 \cdot \left(\frac{F_y}{286220}\right) \]

Where:

\( \lambda_c \) — Slenderness Parameter
\( k \) — Effective Length Factor
\( l \) — Effective Column Length (m)
\( r \) — Radius of Gyration (m)
\( F_y \) — Yield Stress of Steel (MPa)

Explanation: The formula combines geometric properties and material properties to evaluate column stability.

3. Importance of Slenderness Parameter

Details: This parameter is crucial in structural design to ensure columns can safely support their intended loads without buckling or yielding prematurely.

4. Using the Calculator

Tips: Enter all required values with ±5% accuracy. The effective length factor depends on end conditions (typically 0.5-2.0).

5. Frequently Asked Questions (FAQ)

Q1: What does λc < 1.5 indicate?
A: The column will likely fail by yielding (inelastic buckling).

Q2: What's a typical effective length factor?
A: For pinned-pinned ends k=1.0; fixed-fixed k=0.5; fixed-pinned k=0.7; fixed-free k=2.0.

Q3: How is radius of gyration determined?
A: \( r = \sqrt{I/A} \), where I is moment of inertia and A is cross-sectional area.

Q4: What steel yield stress should I use?
A: Common values are 250 MPa for mild steel, 350 MPa for high-strength steel.

Q5: Why is 286220 in the denominator?
A: This constant comes from \( \pi^2 \cdot E \) where E is Young's modulus for steel (≈200 GPa).