133.NA July 2021 Q.7(b)

 A triangular bulkhead is 7 m wide at the top and has a vertical depth of 8 m. Calculate the load on the bulkhead and position of centre of pressure if the water is i) to the top edge ii) 4 m head to the top edge.

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Solution

 

We know that bulkhead is in triangular shape.

Area of triangle A = (B x D) / 2 = (7 x 8) / 2 = 28 m2

Centroid from  Top surface H = D / 3 = 8 / 3 = 2.67 m

Load on the bulkhead = Density x g x Area x Centroid

Centre of pressure from surface = (Ina / AH) + H

 Ina = Second moment about centroid. Fo triangle Ina = BD3/ 36 = (7 x 83) /36 = 99.55 m4

 

i) In case 1 

Load on the bulkhead = 1.025 x 9.81 x  28 x 2.67
                                    = 751.73 kN

 

Centre of pressure fro the top = (Ina / AH) + H

                                                = (99.55 / (28 x 2.67)) + 2.67

                                                = 4.0 m

 

ii) In case 2  it is given that 4 m head to top edge. We can not substitute this formula directly because these formulas are based on the plane with edge in the surface.

So Load on bulkhead the centroid will be H + 4 (As 4 m is the head)

So New H = 2.67 + 4 = 6.67 m

 Load on the bulkhead = 1.025 x 9.81 x  28 x 6.67

                                     = 1877.9 kN

 

Centre of pressure  from the surface = (Ina / AH) + H

                                                           = (99.55 / (28 x 6.67)) + 6.67

                                                           =  7.20 m

Centre of pressure from the top of the bulkhead = 7.20 - 4.0 = 3.2 m