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Question

Beam GHI is supported by three pontoons as shown in the figure below. The horizontal cross-sectional area of each pontoon is 8m2, the flexural rigidity of the beam is 10000kN−m2 and the unit weight of water is 10kN/m3. When the middle pontoon is removed, the deflection at H will be

A
0.2m
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B
0.4m
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C
0.6m
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D
0.8m
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Solution

The correct option is B 0.4m C and D are internal hinge So, ∑MC=0 RA×x=0 ⇒RA=0 Similarly, RB=0 When middle pontoon is removed, force P will be resisted by pontoon at G and I hence beam GHI will act as a simply supported beam Deflection of H will be due to the load at H as well as due to the displacement of pontoon at G and I in water since the loading is symmetrical, both the pontoons will be immersed to the same depth (h). ∴ Reaction at support =wt. of displaced liquid by pontoon 24= Volume × unit wt. of water 24=Ahγw =8×h×10 ⇒h=2480=0.3m Elastic deflection at H due to load =PL348EI=48×10348×10000=0.1m Total deflection at H=0.3+0.1=0.4m

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