Allowable Axial Compression Stress for Slenderness Ratio 0 to 160 Calculator

Formula:

\[ F_a = \frac{F_{yw}/f_s}{1 + 0.20 \times \left(\frac{EAR}{r_{least}} \times \sqrt{\frac{f_s \times P_{compressive}}{4 \times \varepsilon_{column}}}\right)} \]

Specified minimum yield stress for column:

Factor of Safety:

Effective Interest Rate:

Least Radius of Gyration Column:

Column Compressive load:

Modulus of Elasticity Column:

Allowable compression stress: Pa

1. What is Allowable Axial Compression Stress?

Definition: This calculator determines the maximum allowable compressive stress for columns with slenderness ratios between 0 and 160.

Purpose: It helps structural engineers ensure column designs meet safety requirements under compressive loads.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ F_a = \frac{F_{yw}/f_s}{1 + 0.20 \times \left(\frac{EAR}{r_{least}} \times \sqrt{\frac{f_s \times P_{compressive}}{4 \times \varepsilon_{column}}}\right)} \]

Where:

\( F_a \) — Allowable compression stress (Pa)
\( F_{yw} \) — Specified minimum yield stress for column (Pa)
\( f_s \) — Factor of Safety
\( EAR \) — Effective Interest Rate (%)
\( r_{least} \) — Least Radius of Gyration Column (m)
\( P_{compressive} \) — Column Compressive load (N)
\( \varepsilon_{column} \) — Modulus of Elasticity Column (Pa)

3. Importance of Calculation

Details: Proper calculation ensures structural stability and prevents column buckling under compressive loads.

4. Using the Calculator

Tips: Enter all required parameters. Default values are provided for common steel columns. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical Factor of Safety for columns?
A: Common values range from 2.5 to 3.0, with 2.8 being a typical default.

Q2: How is Effective Interest Rate related to column design?
A: EAR accounts for the time value of money in long-term structural projects, affecting material choices.

Q3: What's a typical Modulus of Elasticity for steel columns?
A: About 200 GPa (200,000,000 Pa) for structural steel, but varies by alloy.

Q4: Why is the least radius of gyration used?
A: It represents the most critical (smallest) value that governs buckling resistance.

Q5: What if my slenderness ratio exceeds 160?
A: Different formulas apply for more slender columns; consult structural engineering references.