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

Sheikh Manan 2 years ago

Finding area of the trapizum = (4+1)×1/2 ×6= 15m³
Weight of Dam/m = density × area = 20000×15 = 300000 N/m
Min stress = w/b = 300000/4 = 75000 N/m

Shubhash Chandra 3 years ago

Weight of dam: W1=1*6*1*20=120kN/m3; W2=0.5*3*6*1*20=180KN/m3
Hydrostatic force: F=0.5*60*6=180KN/m3.
Taking a moment at the toe of the dam: Mr= 120*3.5+180*2=780KNm; Mo=180*2=360KNm.
find X=(Mr-Mo)/ Total Vertical force=1.4m
Find, e=B/2-X=2-1.4=0.6.
Now, Min stress at base= Total vertical force/B(1-6e/B)=7.5KN/m2=7500N/m2.

Ranjeet Kumar 3 years ago

Option "D" shall be correct answer as calculation reflect the answer 75,000 N/M2 [ =20,000x(LxBxH)] / [ LxB ]
So,
= [20,000x(1x{(1+4)/2}x6] / [ 1x4]
=20,000x(1x2.5x6) / 4
=3,00,000 / 4
=75,000 N/M2

Ashwin Aryan 4 years ago

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.

Asad Ullah 5 years ago

Thank you

YOGESH SHELKE 5 years ago

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/m2

Mehfuz Hathila 6 years ago

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/m2

Shahbaz Ali 6 years ago

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/m2

Ketul Patel 6 years ago

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/m2

Santanu Sarder 6 years ago

Please discuss the method

Madhav Sharma 6 years ago

Atul Kaushik,
but right ans is7500...??

Kaushik Bakshi 7 years ago

How?? Please explain..

Rsm Man 7 years ago

what will be correct ans?

Al Amin 7 years ago

pressure calculated only for rectangular portion

Atul Kaushik 8 years ago

Option D is correct answer.
Density*volume/area=stress at base
(20000*(1/2*(1+4)*6))/(4*1)=75000 N/sq.m

Sanjay Chandrawal 8 years ago

give the solution

KRISHNA SINGH 8 years ago

Solution of these question.