Effective Column Length given Allowable Axial Compression Stress, SL Ratio Greater than 160 Calculator

Effective Column Length Formula (SL Ratio > 160):

\[ L_{eff} = 1.2 - \left(\frac{F_a}{\sigma_c'}\right) \times (800 \times r_{least}) \]

Allowable Compression Stress (F_a):

Value from Secant Formula (σ_c'):

Least Radius of Gyration (r_least):

Tolerance:

Effective Column Length (L_eff):

1. What is Effective Column Length?

Definition: Effective column length is the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.

Purpose: It helps structural engineers determine the buckling capacity of columns, especially those with slenderness ratio (SL) greater than 160.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L_{eff} = 1.2 - \left(\frac{F_a}{\sigma_c'}\right) \times (800 \times r_{least}) \]

Where:

\( L_{eff} \) — Effective column length (meters)
\( F_a \) — Allowable compression stress (Pascals)
\( \sigma_c' \) — Value obtained from secant formula (Pascals)
\( r_{least} \) — Least radius of gyration (meters)

Explanation: The formula accounts for the relationship between allowable stress, material properties, and geometric properties of the column.

3. Importance of Effective Length Calculation

Details: Accurate calculation is crucial for determining column stability, preventing buckling failures, and ensuring structural safety.

4. Using the Calculator

Tips:

Enter allowable compression stress in Pascals
Enter value from secant formula in Pascals
Enter least radius of gyration in meters
Default tolerance is ±5% but can be adjusted

5. Frequently Asked Questions (FAQ)

Q1: When is this formula applicable?
A: Specifically for columns with slenderness ratio (SL) greater than 160.

Q2: What is the secant formula?
A: A formula that describes the stress distribution in a column considering eccentric loading and initial imperfections.

Q3: How to determine least radius of gyration?
A: It's the smallest value of √(I/A) where I is moment of inertia and A is cross-sectional area.

Q4: Why include tolerance?
A: To account for material variations, construction tolerances, and safety factors.

Q5: What units should be used?
A: Consistent SI units - Pascals for stress, meters for length dimensions.