Compressive Yield Stress by Straight-Line Formula Calculator

Compressive Yield Stress by Straight-Line Formula for Columns and Struts Calculator

Compressive Stress Formula:

\[ \sigma_c = \frac{P}{A} + n \times \left(\frac{L_{eff}}{r_{least}}\right) \]

Crippling Load (P):

Cross Sectional Area (A):

m²

Straight Line Constant (n):

Effective Length (L_eff):

Least Radius of Gyration (r_least):

Compressive Stress (σ_c): Pa

1. What is Compressive Yield Stress by Straight-Line Formula?

Definition: This calculator determines the compressive yield stress in columns and struts using the straight-line formula, which accounts for both direct compression and buckling effects.

Purpose: It helps structural engineers evaluate the load-bearing capacity of columns under compressive loads, considering both material strength and geometric slenderness.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_c = \frac{P}{A} + n \times \left(\frac{L_{eff}}{r_{least}}\right) \]

Where:

\( \sigma_c \) — Compressive stress (Pa)
\( P \) — Crippling load (N)
\( A \) — Cross-sectional area (m²)
\( n \) — Straight-line formula constant (material-dependent, ±5%)
\( L_{eff} \) — Effective length of column (m)
\( r_{least} \) — Least radius of gyration (m)

Explanation: The first term calculates direct compressive stress, while the second term accounts for buckling effects based on column slenderness.

3. Importance of Compressive Stress Calculation

Details: Proper calculation ensures structural stability, prevents buckling failures, and helps in designing efficient column sections.

4. Using the Calculator

Tips: Enter all required parameters. The straight-line constant (n) typically ranges from 1 to 10 depending on material (default is 4 with ±5% variation).

5. Frequently Asked Questions (FAQ)

Q1: What is the straight-line formula constant (n)?
A: It's a material-dependent constant that accounts for the relationship between slenderness ratio and compressive strength.

Q2: How do I determine the effective length?
A: Effective length depends on end conditions: pinned-pinned = actual length, fixed-fixed = 0.5×length, fixed-free = 2×length, etc.

Q3: What's the least radius of gyration?
A: It's the minimum value of √(I/A) where I is the moment of inertia and A is cross-sectional area.

Q4: When is this formula most accurate?
A: For intermediate slenderness ratios (neither very short nor very long columns).

Q5: What are typical values for constant n?
A: For steel: 1-5, for concrete: 3-8, for timber: 2-6 (exact values depend on specific material properties).