Critical Buckling Stress when Slenderness Parameter is Less than 2.25 Calculator

Critical Buckling Stress Formula:

\[ F_{cr} = 0.658^{\lambda_c} \times F_y \]

Critical Buckling Stress (MPa):

Allowable Range (MPa):

1. What is Critical Buckling Stress?

Definition: Critical Buckling Stress is the maximum stress that can be taken by the section without failure. Any stress surpassing the critical stress makes the section (e.g., column) fail.

Purpose: This calculator determines the critical buckling stress for steel members when the slenderness parameter is ≤ 2.25.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ F_{cr} = 0.658^{\lambda_c} \times F_y \]

Where:

\( F_{cr} \) — Critical Buckling Stress (MPa)
\( \lambda_c \) — Slenderness Parameter (must be ≤ 2.25)
\( F_y \) — Yield Stress of Steel (MPa)

Explanation: The formula calculates the inelastic buckling stress for members with low to moderate slenderness.

3. Importance of Critical Buckling Stress

Details: Proper calculation ensures structural stability and prevents premature failure of compression members.

4. Using the Calculator

Tips: Enter the slenderness parameter (≤ 2.25), yield stress of steel, and tolerance percentage (default ±5%). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What happens if λ_c > 2.25?
A: This calculator is only valid for λ_c ≤ 2.25. For higher values, elastic buckling formulas should be used.

Q2: What's a typical yield stress for structural steel?
A: Common values range from 250 MPa to 690 MPa depending on the steel grade.

Q3: Why include a tolerance value?
A: The tolerance (±5% by default) accounts for material variations and safety factors.

Q4: How is slenderness parameter calculated?
A: λ_c = (KL/rπ)√(F_y/E), where KL/r is the slenderness ratio and E is modulus of elasticity.

Q5: Does this consider residual stresses?
A: The formula implicitly accounts for typical residual stress patterns in rolled sections.