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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. 7,500 N/m2

D. 75,000 N/m2

Answer: Option C


This Question Belongs to Civil Engineering >> Theory Of Structures

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Comments ( 16 )

  1. Shubhash Chandra
    Shubhash Chandra :
    6 months 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.

  2. Ranjeet Kumar
    Ranjeet Kumar :
    7 months 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

  3. Ashwin Aryan
    Ashwin Aryan :
    2 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.

  4. Asad Ullah
    Asad Ullah :
    3 years ago

    Thank you

  5. YOGESH SHELKE
    YOGESH SHELKE :
    3 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

  6. Mehfuz Hathila
    Mehfuz Hathila :
    3 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

  7. Shahbaz Ali
    Shahbaz Ali :
    3 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

  8. Ketul Patel
    Ketul Patel :
    3 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

  9. Santanu Sarder
    Santanu Sarder :
    4 years ago

    Please discuss the method

  10. Madhav Sharma
    Madhav Sharma :
    4 years ago

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

  11. Kaushik Bakshi
    Kaushik Bakshi :
    4 years ago

    How?? Please explain..

  12. Rsm Man
    Rsm Man :
    4 years ago

    what will be correct ans?

  13. Al Amin
    Al Amin :
    4 years ago

    pressure calculated only for rectangular portion

  14. Atul Kaushik
    Atul Kaushik :
    5 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

  15. Sanjay Chandrawal
    Sanjay Chandrawal :
    6 years ago

    give the solution

  16. KRISHNA SINGH
    KRISHNA SINGH :
    6 years ago

    Solution of these question.

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