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UPSC Civil Service Exam Questions - Engineering

Q1:

A cantilever has rectangular cross-section and supports concentrated load at its free end initially. If depth and width of the beam sections are doubled, the deflection, at free end of the cantilever will reduce to what percentage of the initial deflection ?

A 20%

B 15.72%

C 9.37%

D 6.25%

ANS:C - 9.37%

Here defl: =1/MOI, Keeping all thing constant.

Let us B=1UNIT and D = 2UNIT.
When we have only BandD then MOI=1/12 SO deflection is = 12units.
When B=2b=2UNITS and D=2d= 4UNITS then MOI= 32/3 SO defelction = 3/32,
Hence 3/32 =0.09375 or 9.375%.