Buckling Research

General Buckling Equation

The critical buckling load Pcr is given by:

• Pcr = (π^2)(E)(I) / (KL)^2

  Where:

  • Pcr​: Critical buckling load

  • E: Elastic modulus of the material

  • I: Area moment of inertia of the cross-section

  • K: Effective length factor (depends on the boundary conditions)

  • L: Length of the rod

Carbon Fiber-Specific Considerations

Carbon fiber is an anisotropic material, meaning its properties vary depending on the fiber orientation. This affects EEE and III.

1. Elastic Modulus (E):

   • For carbon fiber, use the modulus in the longitudinal direction of the fibers (E∥E_{\parallel}E∥​).

   • For unidirectional carbon fiber, E∥E_{\parallel}E∥​ is high, typically ranging from 150–250 GPa.

   • For woven or multidirectional composites, use an effective modulus depending on the layup.

2. Area Moment of Inertia (I):

   • For circular cross-sections: I = (π/4)((router^4) - (rinner^4))

3. Boundary Conditions (Effective Length Factor K):

   • Fixed-fixed: K=0.5

   • Pinned-pinned: K=1

   • Fixed-free (cantilever): K=2

   • Fixed-pinned: K≈0.7

Additional Considerations

Material Failure:

• Carbon fiber might fail before buckling if the applied load exceeds the material's compressive strength. Check the compressive strength (σcomp​) of the composite:

  • σcomp= Pcr/A

    • A is the cross-sectional area