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GATE ME Kirchhoff — practice questions

Explore 4 free Kirchhoff questions in GATE ME Mechanical Engineering. Open each question or exercise to read its content, reference answers and available explanation.

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Kirchhoff questions and exercises with answers

Showing questions 1–4 of 4.

The KIRCHHOFF hypothesis specifically excludes which physical effect?Read the answer and worked solution →Boundary conditions on a CLAMPED edge of a thin plate (Kirchhoff) at x = 0 are:Read the answer and worked solution →Boundary conditions on a SIMPLY SUPPORTED edge of a thin plate at x = 0 are:Read the answer and worked solution →For a thin plate, increasing thickness t by 2× changes flexural rigidity D by what factor?Read the answer and worked solution →

Worked practice questions

The KIRCHHOFF hypothesis specifically excludes which physical effect?

  1. Stretching
  2. Twisting
  3. TRANSVERSE SHEAR deformation — strains γ_xz and γ_yz are zero
  4. Bending
Show answer and solution

Correct answer: C. TRANSVERSE SHEAR deformation — strains γ_xz and γ_yz are zero

**Kirchhoff:** γ_xz = γ_yz = 0 by assumption. This is fine for thin plates where shear deformation is negligible, but underpredicts deflection for thick plates (t/L > ~1/20). Mindlin-Reissner relaxes this assumption.

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Boundary conditions on a CLAMPED edge of a thin plate (Kirchhoff) at x = 0 are:

  1. w = ∞
  2. w = 0 only
  3. w = 0 AND ∂w/∂x = 0 (no deflection, no slope into the support)
  4. w_xx = 0
Show answer and solution

Correct answer: C. w = 0 AND ∂w/∂x = 0 (no deflection, no slope into the support)

**Clamped edge:** zero deflection (w = 0) and zero rotation (∂w/∂x = 0 along the edge normal). Compare to simply-supported (w = 0, M_x = 0) and free (M_x = 0, V_x + ∂M_xy/∂y = 0 — the "effective" shear).

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Boundary conditions on a SIMPLY SUPPORTED edge of a thin plate at x = 0 are:

  1. w = 0 and M_x = 0 (no deflection, no moment along the edge)
  2. M_x = 0 only
  3. V_x = 0
  4. w = 0 and w_x = 0
Show answer and solution

Correct answer: A. w = 0 and M_x = 0 (no deflection, no moment along the edge)

SS edge resists transverse deflection (w = 0) but offers no moment resistance (M_x = 0). Since M_x = −D(w_xx + νw_yy) and w_yy = 0 along x = const where w = 0, equivalent BC is often w = w_xx = 0.

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