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The ratio of the maximum deflection between a simply supported beam carrying a point load at its midspan and the same beam carrying the seem load as total load of uniformly distributed load will be
  • a)
     5/3
  • b)
     7/5
  • c)
     8/5
  • d)
     3/5
Correct answer is option 'C'. Can you explain this answer?
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Solution:

Given, a simply supported beam carrying a point load at its midspan and the same beam carrying the same load as total load of uniformly distributed load.

Let, the point load be W and the length of the beam be L.

Maximum deflection for a simply supported beam carrying a point load at its midspan is given by:

δmax = (WL^3)/(48EI)

Maximum deflection for a simply supported beam carrying a total load of uniformly distributed load is given by:

δmax = (5WL^4)/(384EI)

Ratio of maximum deflection between the two cases is:

(δmax for point load)/(δmax for uniformly distributed load)

= ((WL^3)/(48EI))/((5WL^4)/(384EI))

= 8/5

Therefore, the correct option is C) 8/5.
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The ratio of the maximum deflection between a simply supported beam carrying a point load at its midspan and the same beam carrying the seem load as total load of uniformly distributed load will bea)5/3b)7/5c)8/5d)3/5Correct answer is option 'C'. Can you explain this answer?
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