Question

Beam $GHI$ is supported by three pontoons as shown in the figure below. The horizontal cross-sectional area of each pontoon is $8m^2,$ the flexural rigidity of the beam is $10000kN-m^2$ and the unit weight of water is $10kN/m^3.$



When the middle pontoon is removed, the deflection at H will be

• A. $0.2m$
• B. $0.4m$
• C. $0.6m$
• D. $0.8m$

Answer 1

The correct option is B $0.4m$



$C$ and $D$ are internal hinge
So, $\sum M_C=0$
$R_A\times x=0$
$\Rightarrow R_A=0$
Similarly, $R_B=0$
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 $\left(h\right)$.
$\therefore$ Reaction at support $=wt.$ of displaced liquid by pontoon
$24=$ Volume $\times$ unit $wt.$ of water
$24=Ah{\gamma }_w$
$=8\times h\times 10$
$\Rightarrow h=\frac{24}{80}=0.3m$
Elastic deflection at $H$ due to load
$=\frac{P{L}^3}{48EI}=\frac{48\times {10}^3}{48\times 10000}=0.1m$
Total deflection at
$H=0.3+0.1=0.4m$