Allowable Compressive Stress when Slenderness Ratio is Less than Cc Calculator

Allowable Compression Stress Formula:

\[ F_a = \frac{\left(1 - \frac{\left(\frac{k \cdot l}{r}\right)^2}{2 \cdot C_c^2}\right) \cdot F_y}{F_s} \]

Effective Length Factor:

Effective Column Length:

Radius of Gyration:

Factor for Allowable Stress Design:

Yield Stress of Steel:

Safety Factor:

Allowable Compression Stress (Pa):

1. What is Allowable Compressive Stress when Slenderness Ratio is Less than Cc?

Definition: This calculator determines the allowable compressive stress for steel columns when the slenderness ratio is less than the critical value Cc.

Purpose: It helps structural engineers ensure columns can safely carry compressive loads without buckling.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ F_a = \frac{\left(1 - \frac{\left(\frac{k \cdot l}{r}\right)^2}{2 \cdot C_c^2}\right) \cdot F_y}{F_s} \]

Where:

\( F_a \) — Allowable compression stress (Pa)
\( k \) — Effective length factor
\( l \) — Effective column length (m)
\( r \) — Radius of gyration (m)
\( C_c \) — Factor for allowable stress design
\( F_y \) — Yield stress of steel (Pa)
\( F_s \) — Safety factor

Explanation: The formula accounts for column geometry, material properties, and safety factors to determine safe stress levels.

3. Importance of Allowable Stress Calculation

Details: Proper calculation prevents structural failure, ensures code compliance, and optimizes material usage in construction projects.

4. Using the Calculator

Tips: Enter all required parameters. Default values are provided for common steel properties. All values must be > 0. Results are in Pascals (Pa).

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for effective length factor (k)?
A: k typically ranges from 0.5 (fixed-fixed) to 2.0 (free-fixed), with 0.65-1.2 being common for practical cases.

Q2: How do I determine the radius of gyration?
A: The radius of gyration (r) is calculated as √(I/A), where I is the moment of inertia and A is the cross-sectional area.

Q3: What's a typical value for Cc in steel design?
A: For structural steel, Cc is typically around 125.66 (for Fy = 250 MPa and E = 200 GPa).

Q4: When is this formula applicable?
A: Only when the slenderness ratio (k·l/r) is less than Cc. For higher ratios, a different formula applies.

Q5: Why include a safety factor?
A: The safety factor accounts for material variability, load uncertainties, and consequences of failure.