GATE CE 2024 Set 2 — Question 49
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Question
For the 6 m long horizontal cantilever beam PQR shown in the figure, Q is the mid-point. Segment PQ of the beam has flexural rigidity whereas the segment QR has infinite flexural rigidity. Segment QR is subjected to uniformly distributed, vertically downward load of 5 kN/m.
(Figure NOT to scale)The magnitude of the vertical displacement (in mm) at point Q is ________ (rounded off to 3 decimal places).
Correct answer
1.176 to 1.186
Solution
The segment QR is rigid (), so it does not bend. The load on QR acts as a concentrated force and a moment at point Q.
1.Total vertical force at Q due to UDL on QR: .
2.Moment at Q due to UDL on QR: .
The vertical displacement at Q () is the deflection of the cantilever segment PQ (length ) under the action of point load and moment at its free end Q:Substituting the values:Converting to mm:Rounding off to 3 decimal places, the magnitude is .Continue learning with Success Tracker
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