Allowable Compressive Stress when Slenderness Ratio is Greater than Cc Calculator

Allowable Compression Stress Formula:

\[ F_a = \frac{12 \pi^2 E_s}{23 \left(\frac{k l}{r}\right)^2} \]

Modulus of Elasticity of Steel (E_s):

MPa

Effective Length Factor (k):

Effective Column Length (l):

Radius of Gyration (r):

Allowable Compressive Stress (F_a): MPa

1. What is Allowable Compressive Stress?

Definition: Allowable compressive stress is the maximum stress (compressive) that is allowed to be applied on a structural material when the slenderness ratio is greater than C_c.

Purpose: It helps structural engineers determine the safe load capacity of columns and compression members.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ F_a = \frac{12 \pi^2 E_s}{23 \left(\frac{k l}{r}\right)^2} \]

Where:

\( F_a \) — Allowable compressive stress (MPa)
\( E_s \) — Modulus of elasticity of steel (MPa)
\( k \) — Effective length factor (±5%)
\( l \) — Effective column length (m)
\( r \) — Radius of gyration (m)

Explanation: This formula accounts for Euler buckling when the slenderness ratio exceeds the critical value C_c.

3. Importance of This Calculation

Details: Proper calculation ensures structural stability and prevents buckling failure in long columns under compressive loads.

4. Using the Calculator

Tips: Enter the modulus of elasticity (default 200,000 MPa for steel), effective length factor (default 0.75), column length, and radius of gyration. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: When is this formula applicable?
A: Only when the slenderness ratio (kL/r) is greater than the column constant C_c.

Q2: What's a typical modulus of elasticity for steel?
A: Most structural steel has E ≈ 200,000 MPa, but check material specifications for exact values.

Q3: How do I determine the effective length factor?
A: It depends on end conditions (0.5 for fixed-fixed, 0.7 for fixed-pinned, 1.0 for pinned-pinned, 2.0 for fixed-free).

Q4: What units should I use?
A: Use consistent units (MPa for stress, meters for length). The calculator handles conversions internally.

Q5: Does this include safety factors?
A: Yes, the formula already incorporates appropriate safety factors for structural design.