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GATE 2019 CE (CE1) – Question 41

Solid Mechanics · Simple bending theory, flexural and shear stresses, shear centre · 2 marks · Multiple choice

The built-up wood beam section shown is symmetric about its neutral axis and carries vertical shear 8 kN. Its second moment about that axis is $1.5\times10^9\ \mathrm{mm^4}$. Nails at P have longitudinal spacing 60 mm. Find shear force on each nail at P.

Diagram for GATE 2019 CE (CE1) question 41
  1. 60 N
  2. 120 N
  3. 240 N
  4. 480 N

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Show answer and explanation

Correct answer: (C) 240 N

Explanation

For the outer block fastened at P, area is $50(100)=5000$ mm² and its centroid lies 150 mm from the neutral axis. First moment is $Q=750000$ mm³. Shear flow is $VQ/I=8000(750000)/(1.5\times10^9)=4$ N/mm. Each nail carries 60 mm of flow: **4 × 60 = 240 N, C**.