The GATE Grind

GATE 2017 CE (CE2) – Question 41

Structural Analysis · Deflections of determinate beams, frames and trusses · 2 marks · Multiple choice

The two prismatic beams shown have the same flexural rigidity 1000 kN m². If their midspan deflections are $\delta_1,\delta_2$, the correct comparison is ______.

Diagram for GATE 2017 CE (CE2) question 41
  1. $\delta_1=\delta_2$
  2. $\delta_1<\delta_2$
  3. $\delta_1>\delta_2$
  4. $\delta_1\gg\delta_2$

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Show answer and explanation

Correct answer: (A) $\delta_1=\delta_2$

Explanation

For the upper simply supported UDL beam, $\delta_1=5wL^4/(384EI)=5(6)(4^4)/(384\times1000)=0.020$ m. For the lower centrally loaded beam, $\delta_2=PL^3/(48EI)=120(2^3)/(48\times1000)=0.020$ m. Both deflect 20 mm, hence A.