SSC JE Civil Engineering 29-Oct-2020 Shift 1 Paper

Question : 132 of 200

Marks: +1, -0

For safety of a concrete dam against overturning, what must be width of the dam of rectangular cross section of height 10 m, if the height of water storage on one side of it is 9 m? Take unit weight of water as 10 kN/m

^3

and unit weight of concrete as 25 kN/m

^3

.
(Ignore effect of uplift, friction and any other force)

${4√{3}}/{5} \m$
${3√{3}}/{5} \m$
${9√{3}}/{5} \m$
0.6 m

Validate

Solution:

r_{c}=25 {\kN} \/ {\m}^{3}

\γ_{{\W}}=10 {\kW} \/ {\m}^{3}

let length of Dam is

{\pm}

\B

is width of Dam
Hydrostatic force on dam,

P_{w}={1}/{2} \γ_{w} H ×H

={1}/{2} ×10 × 9 × 9=405 {\kN}

Force due to weight of Dam,

{\W}={\Y}_{{\c}} × {\A} × {\L}

=25 × {\B} ×10 × 1=250 {\B} {\kN}

\P_{\w}

' force try to overturn the dam about the and '

w

' force try to script it.
To safety against overturning,

{\N}_{{\OT}} ≤ {\N}_{{\R}}

{\P}_{{\W}}× 3 ≤{\W} × {\B} / 2

405 × 3 ≤ 250 \B × {\B}/{2}

⇒ B ≥ √{{405 × 2 ×3}/{250}}

⇒B ≥ {9}/{5} √{3} \m

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