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GATE 2020 CE (CE2) – Question 40

Structural Analysis · Statically indeterminate structures: force and displacement methods · 2 marks · Multiple choice

The shown frame has pin joints I, J, K, L, Q and M. Continuous members IQ and LJ connect through pin N; continuous JM and KQ connect through pin P. Supports R and S are hinges. Loads at I, J and K act in negative Y; those at L and M in positive X. Find horizontal reaction magnitude at S (kN).

Diagram for GATE 2020 CE (CE2) question 40
  1. 5
  2. 10
  3. 15
  4. 20

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Show answer and explanation

Correct answer: (C) 15

Explanation

The continuous crossing bars transfer forces atN andP;they cannot be treated as independent two-force segments. Write force equilibrium at the end pins and moment equilibrium for each continuous crossing member,with equal-and-opposite forces at the crossing pins. Solving those equations gives horizontal reaction atS=−15 kN,so magnitude is **15 kN,C**. Overall horizontal equilibrium then gives reaction atR=−5 kN.