Ultimate Crushing Stress Calculator by Tons of Concrete

Ultimate Crushing Stress given Crippling Load and Rankine's Constant Calculator

Ultimate Crushing Stress Formula:

\[ \sigma_c = \frac{P \times (1 + \alpha \times (\frac{L_{eff}}{r_{least}})^2)}{A} \]

Crippling Load (P):

Rankine's Constant (α):

Effective Column Length (L_eff):

Least Radius of Gyration (r_least):

Column Cross Sectional Area (A):

m²

Ultimate Crushing Stress (σ_c): Pa

1. What is Ultimate Crushing Stress?

Definition: Column Crushing stress is a special type of localized compressive stress which occurs at the surface of contact of two members that are relatively at rest.

Purpose: This calculator helps determine the ultimate stress a column can withstand before crushing, considering Rankine's formula.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_c = \frac{P \times (1 + \alpha \times (\frac{L_{eff}}{r_{least}})^2)}{A} \]

Where:

\( \sigma_c \) — Column Crushing stress (Pascal)
\( P \) — Crippling Load (Newton)
\( \alpha \) — Rankine's Constant (±5%)
\( L_{eff} \) — Effective Column Length (meters)
\( r_{least} \) — Least Radius of Gyration (meters)
\( A \) — Column Cross Sectional Area (m²)

Explanation: The formula accounts for both direct compressive stress and additional stress due to column buckling.

3. Importance of Ultimate Crushing Stress Calculation

Details: Proper calculation ensures structural integrity and safety of columns under compressive loads.

4. Using the Calculator

Tips: Enter all required values with appropriate units. Rankine's Constant typically has ±5% variation.

5. Frequently Asked Questions (FAQ)

Q1: What is Rankine's Constant?
A: It's an empirical constant that depends on the column material (0.00038 for mild steel).

Q2: How to find Least Radius of Gyration?
A: It's calculated as \( r = \sqrt{I/A} \), where I is the smallest moment of inertia.

Q3: What's a typical value for Rankine's Constant?
A: For mild steel it's about 0.00038 with ±5% variation.

Q4: How does Effective Length affect the result?
A: Longer columns have higher buckling tendency, increasing crushing stress.

Q5: What units should I use?
A: Use consistent SI units: Newtons for load, meters for dimensions.