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GATE ME Strength of Materials — practice by topic

Browse 10 questions across 7 Strength of Materials topics. Choose what you want to revise, then open a question to check its answer and worked solution.

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Strength of Materials topics

Elasticity (6)Hookeslaw (6)Strain (6)Stress (6)Biharmonic (4)Kirchhoff (4)Platetheory (4)

Try a Strength of Materials question

Traction T at a point on a surface is defined as:Read the answer and worked solution →The 3D equation of equilibrium in a body (without body forces) is:Read the answer and worked solution →How many INDEPENDENT elastic constants does a GENERAL ANISOTROPIC linear-elastic material have?Read the answer and worked solution →Hooke's law in STIFFNESS form is σ = C·ε. In COMPLIANCE form: ε = S·σ. The relationship between C and S is:Read the answer and worked solution →

Worked practice questions

Traction T at a point on a surface is defined as:

  1. Total force on the body
  2. Weight of the body
  3. Stress integrated over the surface
  4. The limit of dF/dS — force per unit area at that location on the surface
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Correct answer: D. The limit of dF/dS — force per unit area at that location on the surface

**Traction is a vector quantity:** $\mathbf{T} = \lim_{\Delta S \to 0} \Delta\mathbf{F}/\Delta S = d\mathbf{F}/dS$. It depends on the surface orientation (normal direction) — making it a "bound vector".

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The 3D equation of equilibrium in a body (without body forces) is:

  1. σ_ij = ε_ij
  2. σ_ij = const
  3. ∂σ_ij/∂x_j = 0 — divergence of stress tensor vanishes (Cauchy)
  4. ∇·u = 0
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Correct answer: C. ∂σ_ij/∂x_j = 0 — divergence of stress tensor vanishes (Cauchy)

For an infinitesimal element in static equilibrium without body forces (gravity, etc.), the sum of internal-force contributions from neighboring elements must balance: $\partial \sigma_{ij}/\partial x_j = 0$ (j summed via Einstein notation).

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How many INDEPENDENT elastic constants does a GENERAL ANISOTROPIC linear-elastic material have?

  1. 21 — symmetric 6×6 stiffness matrix gives 21 = 6·7/2 unique entries
  2. 9
  3. 36
  4. 27
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Correct answer: A. 21 — symmetric 6×6 stiffness matrix gives 21 = 6·7/2 unique entries

Stiffness tensor C_ijkl has minor symmetries (from σ and ε symmetry) reducing 81 → 36 components. Major symmetry (from strain-energy existence) reduces 36 → 21 independent. The 6×6 contracted matrix has upper-triangle 6+5+4+3+2+1 = 21 entries.

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