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GATE 2018 CE (CE2) – Question 40

Steel Structures · Connections: simple, eccentric, beam-column · 2 marks · Multiple choice

Four equal-diameter bolts P, Q, R and S hold a bracket carrying 130 kN as shown. The force in bolt P is ______.

Diagram for GATE 2018 CE (CE2) question 40
  1. 32.50 kN
  2. 69.32 kN
  3. 82.50 kN
  4. 119.32 kN

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Show answer and explanation

Correct answer: (B) 69.32 kN

Explanation

Direct shear per bolt is $130/4=32.5$ kN. At P, centroid coordinates are (50,120) mm, and $\sum r^2=4(50^2+120^2)=67600$ mm². Moment is $130(200)=26000$ kN mm. Its vertical and horizontal components at P are $26000(50)/67600=19.2308$ and $26000(120)/67600=46.1538$ kN. Resultant is $\sqrt{(32.5+19.2308)^2+46.1538^2}=69.32$ kN (B).