Value Obtained from Secant given Axial Compression Stress Slenderness Ratio Greater than 160 Calculator

Secant Formula:

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

Value obtained from Secant Formula:

1. What is Value Obtained from Secant Formula?

Definition: This calculator determines the stress value on mild steel columns using the secant formula when the slenderness ratio is greater than 160.

Purpose: It helps structural engineers calculate the allowable stress for long columns where buckling is a primary concern.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula accounts for the additional bending stress caused by initial imperfections in long columns.

3. Importance of Secant Formula Calculation

Details: Proper calculation ensures structural stability for slender columns where Euler's formula alone is insufficient.

4. Using the Calculator

Tips: Enter the allowable compression stress, effective column length, and least radius of gyration. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: When should I use the secant formula?
A: Use it for columns with slenderness ratio > 160 where buckling is the primary failure mode.

Q2: What does the ±5% tolerance mean?
A: It accounts for typical variations in material properties and measurements.

Q3: How is effective length determined?
A: It depends on end conditions - pinned, fixed, or free.

Q4: What's the least radius of gyration?
A: The smallest value of radius of gyration about any principal axis.

Q5: Can this be used for other materials?
A: The formula is specific to mild steel; other materials require different coefficients.