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Theory of Structures - Engineering

Q1:

A masonry dam (density = 20, 000 N/m3) 6 m high, one metre wide at the top and 4 m wide at the base, has vertical water face. The minimum stress at the base of the dam when the reservoir is full, will be

A 75 N/m2

B 750 N/m2

C 7500 N/m2

D 75000 N/m2

ANS:C - 7500 N/m2

Assume length is equal to 1m.

W = Density x Volume.
a=1, b=4, h=6.
W = 20000 x [1/2 x (a+b) x h x 1m],
W = 300000.

For, minimum stress = W/b (1 - 6e/b),
for stability e = b/6 = 4/6 = 0.6.
Stress = 300000/4 (1 - 6x0.6/4).
Stress 7500 N/m^2.