Rectangular Tube Load Calculator

Buckling Load Formula:

\[ P_{cr} = \frac{\pi^2 E I}{(K L)^2} \]

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Effective Length Factor (K):

factor

Length (L):

Critical Buckling Load (P_cr):

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1. What is the Buckling Load Formula?

The Euler buckling formula calculates the critical axial load at which a slender column will buckle. This formula is essential for structural engineering design to ensure columns can support intended loads without buckling failure.

2. How Does the Calculator Work?

The calculator uses the Euler buckling formula:

\[ P_{cr} = \frac{\pi^2 E I}{(K L)^2} \]

Where:

\( P_{cr} \) — Critical buckling load (N)
\( E \) — Modulus of elasticity of the material (Pa)
\( I \) — Moment of inertia of the cross-section (m⁴)
\( K \) — Effective length factor (dimensionless)
\( L \) — Actual length of the column (m)

Explanation: The formula determines the maximum load a column can carry before buckling occurs, considering material properties, cross-sectional geometry, and end conditions.

3. Importance of Buckling Load Calculation

Details: Accurate buckling load calculation is crucial for structural safety, preventing catastrophic failures in buildings, bridges, and other structures with slender compression members.

4. Using the Calculator

Tips: Enter modulus of elasticity in Pascals, moment of inertia in meters to the fourth power, effective length factor, and column length in meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the effective length factor (K)?
A: K depends on end conditions: 1.0 for pinned-pinned, 0.5 for fixed-fixed, 0.7 for fixed-pinned, and 2.0 for fixed-free ends.

Q2: When is Euler's formula applicable?
A: Euler's formula applies to long, slender columns where buckling occurs before material yielding (slenderness ratio > critical slenderness ratio).

Q3: What are typical modulus of elasticity values?
A: Steel: ~200 GPa, Aluminum: ~69 GPa, Wood: ~10 GPa (varies by species and direction).

Q4: How to calculate moment of inertia for rectangular tubes?
A: For a rectangular tube: I = (b*h³ - (b-2t)*(h-2t)³)/12, where b=width, h=height, t=wall thickness.

Q5: What safety factors are typically used?
A: Safety factors vary by application and material, but typically range from 1.5 to 3.0 for building structures.