The Lugeon Test: Methodology, Interpretation, and Applications in Geotechnical Engineering

1. What is stress, and what are its types?

Stress is the internal resistance per unit area induced in a material when subjected to external force.
Types:

• Normal stress (σ): due to axial load (tensile or compressive).

• Shear stress (τ): due to tangential load.

• Bending stress: due to bending moment.

• Torsional stress: due to twisting.

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2. Define strain and its types.

Strain is the deformation per unit length caused by stress.
Types:

• Linear strain: ΔL/L.

• Lateral strain: change in lateral dimension/original lateral dimension.

• Volumetric strain: ΔV/V.

• Shear strain: angular distortion.

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3. What is Hooke’s Law?

Within the elastic limit, stress is directly proportional to strain:

$$σ = E \cdot ε$$

where E is Young’s modulus.

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4. Explain Young’s Modulus.

It is the ratio of normal stress to longitudinal strain. It represents material stiffness. Higher E means less deformation under load.

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5. What is Poisson’s Ratio?

The ratio of lateral strain to longitudinal strain under axial loading.

$$ν = \frac{\text{Lateral Strain}}{\text{Longitudinal Strain}}$$

For most materials, 0.25 ≤ ν ≤ 0.35.

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6. Define bulk modulus and shear modulus.

• Bulk modulus (K): ratio of volumetric stress to volumetric strain.

• Shear modulus (G): ratio of shear stress to shear strain.
  They are related to E and ν:

$$E = 2G(1+ν), \quad E = 3K(1-2ν)$$

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7. State the difference between ductile and brittle materials.

• Ductile: undergo large plastic deformation before failure (e.g., steel, aluminum).

• Brittle: fail suddenly with little deformation (e.g., cast iron, glass).

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8. What is the factor of safety (FoS)?

It is the ratio of ultimate strength to allowable working stress.

$$FoS = \frac{σ_{ultimate}}{σ_{working}}$$

It ensures safety against material failure.

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9. What is the difference between elastic limit and yield point?

• Elastic limit: maximum stress up to which a material returns to original shape after unloading.

• Yield point: stress at which material starts plastic deformation.

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10. Explain bending moment and shear force.

• Bending moment: algebraic sum of moments about a section.

• Shear force: algebraic sum of vertical forces on one side of a section.
  Diagrams (BMD & SFD) help in structural analysis.

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11. What is the bending equation?

$$\frac{M}{I} = \frac{σ}{y} = \frac{E}{R}$$

Where:

• M = bending moment

• I = moment of inertia

• σ = bending stress

• y = distance from neutral axis

• R = radius of curvature

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12. Define torsional equation.

$$\frac{T}{J} = \frac{τ}{r} = \frac{Gθ}{L}$$

Where:

• T = torque

• J = polar moment of inertia

• τ = shear stress

• r = radius

• θ = angle of twist

• L = length

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13. What is slenderness ratio, and why is it important?

$$\lambda = \frac{L_{effective}}{r}$$

Where r = radius of gyration.
It indicates column’s tendency to buckle. Higher ratio → more prone to buckling.

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14. Differentiate between short and long columns.

• Short column: fails by crushing (low slenderness ratio).

• Long column: fails by buckling (high slenderness ratio).

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15. What is Euler’s buckling load formula?

$$P_{cr} = \frac{\pi^2EI}{(L_{eff})^2}$$

Where E = Young’s modulus, I = moment of inertia, L_eff = effective length.

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16. Explain strain energy.

The energy stored in a body due to deformation under load.

$$U = \frac{σ^2}{2E} \cdot V$$

where V = volume.

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17. What is Castigliano’s theorem?

It states that partial derivative of strain energy with respect to a load gives the deflection in the direction of that load.

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18. Define stress concentration.

Localized increase in stress due to sudden change in geometry (holes, notches, sharp corners). It can cause premature failure.

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19. What is fatigue failure?

Failure under repeated cyclic loading at stresses below yield strength. It is characterized by crack initiation and propagation.

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20. What is creep?

Time-dependent deformation of materials under constant load and high temperature. Common in turbines, boilers, concrete under long-term load.

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