#601 The concrete specific weight 150 lb/ft3 seawall

The concrete specific weight of 150 lb/ft3 seawall - Mechanical Engineering

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Free Chegg Question

The concrete (specific weight 150 lb/ft3 ) seawall of Fig. P2.123 has a curved surface and restrains seawater at a depth of 24 ft. The trace of the surface is a parabola as illustrated. Determine the moment of the fluid force (per unit length) with respect to an axis through the toe (point A).

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Free Chegg Answer

General guidance

Concepts and reason

When the surface is submerged in a fluid, the forces developed on the surface due to the fluid.

Calculation of these forces is an important role in design of tanks, dams, and hydraulic structures.

Force must be perpendicular to the surface for static fluids since no shear stresses are involved.

Fundamentals

Write the formula for hydrostatic force.

Here, the specific weight of fluid is , area of the dam is A and centroidal distance of dam is h_c.

Write the formula for weight of the dam.

Here, the volume of the fluid is .

Write the formula for a moment.

Step 1 of 6

Draw the free-body diagram of the system when it has turned through an angle.

Explanation | Hint for next step

Hydrostatic force is F₁ and weight is W.

Step 2 of 6

Compute the horizontal component of fluid force acting on the wall.

Here,  is the weight density of the fluid,  is the height at which the horizontal component acts and  is the projected vertical area on which the force acts h the height of the sea wall and l the length of the sea wall.

Substitute for, for, for  (since unit length).

Explanation | Hint for next step

Use hydrostatic force formula to find horizontal components of fluid force.

Step 3 of 6

Draw the curved section of the concrete wall.

Explanation | Hint for next step

Use a strip diagram to find the area of the wall.

Step 4 of 6

Calculate the value of using the curve equation.

 …… (1)

Substitute, 24 ft for y.

Determine the area of BCD.

 …… (2)

Substitute equation (1) in equation (2).

Substitute  for .

Explanation | Hint for next step

Use integration relation of the curve to find the area of the wall.

Step 5 of 6

Calculate the vertical force acting on the concrete wall.

Substitute for,  for A, and for l (since unit length).

Calculate the centroid of the area.

Here, the distance of the centroid from the y-axis is and the area of the section is A.

Substitute  for  and  for .

Substitute for  and for A.

Explanation | Hint for next step

Use the weight of dam relation and centroid relation to finding the vertical force on the dam and distance of the centroid from the y-axis.

Step 6 of 6

Calculate the moment of the fluid about point A.

Here, the distance of centroid of the parabolic section from the x-axis is 

Substitute  for , for,  for W, and for .

Therefore, the moment about point A is .

Explanation

Consider vertical force and hydrostatic forces on the dam to find the moment about point A.

Answer

Therefore, the moment about point A is .