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Buckling

Calculate Young's modulus, Von Mises yield stress, Poisson's ratio, Mohr's circle principal stresses, and hardness conversions for buckling.

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Input Material Parameters

Enter tensile force, cross-sectional area, or strain ratio.

Calculated Mechanical Stress (σ)

300.00 MPa
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Hooke's Law of Elasticity

In the elastic deformation regime, stress is directly proportional to strain: σ = E × ε, where E is Young's Modulus (1 GPa = 1000 MPa = 10⁹ N/m²).

Calculation Methodology & Details

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Formula

Normal Stress: σ = F / A Poisson's Ratio: ν = -ε_transverse / ε_axial Young's & Shear Relation: E = 2G(1 + ν) Von Mises Stress: σ_vm = √[½((σ₁-σ₂)² + (σ₂-σ₃)² + (σ₃-σ₁)²)]

Applies continuum mechanical stress tensors, Mohr's circle transformation, Euler column buckling, and Brinell/Rockwell hardness conversions.

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Important Disclaimer

Calculations assume linear isotropic elastic solid properties under static loading unless plastic yield limits or fatigue S-N curves are selected.

How to Calculate Step-by-Step

Follow these steps to complete the calculation:

1

Step 1

Enter applied force F (kN) or torque moment T (N·m).

2

Step 2

Specify material Young's modulus E (GPa), Poisson's ratio ν (0.25–0.35 for metals), or section area A.

3

Step 3

View normal stress (MPa), shear strain, Von Mises yield criteria, or Brinell/Rockwell hardness value (BHN/HRC).

Detailed Insights & Expert Guide

ℹ️ About this Calculation

The Buckling solves solid continuum mechanics problems, Young's / Bulk / Shear elastic moduli, Mohr's circle principal stresses, hoop stress in pressure vessels, and metal hardness scale conversions.

Variable Glossary

Input

Young's Modulus (E)

Material tensile stiffness measuring stress per unit elastic strain (Structural Steel E ≈ 200 GPa).

Parameter

Von Mises Stress (σ_vm)

Equivalent scalar stress criterion used to predict yielding in ductile materials under multi-axial loading.

FAQ

What is Poisson's ratio (ν)?
Poisson's ratio is the negative ratio of transverse contraction strain to longitudinal extension strain. Most structural engineering metals have ν between 0.27 and 0.33 (incompressible materials ν = 0.50).
What is thin-walled pressure vessel hoop stress?
Hoop (circumferential) stress σ_h = (P × d) / (2t). It acts tangentially along the cylinder wall and is exactly twice as large as axial longitudinal stress σ_a = (P × d) / (4t).
How is Euler column buckling load calculated?
Critical buckling load P_cr = (π² × E × I) / (K × L)², where E is Young's modulus, I is area moment of inertia, L is column length, and K is end-fixity factor (pinned-pinned K=1, fixed-fixed K=0.5).