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4. Hydraulic
E ect
(con’t)
F. Vasco Costa's formula for the "Hydrodynamic Mass" considers a factor of:
The calculated energy should be multiplied by this factor.
Other designers consider the mass of a cylinder of water whose diameter is equal to the draft and whose length equals the length of a ship.
The weight of this cylinder is to be added to the ship's displacement when computing the kinetic energy.
These two theories do not result in the same values. Also, the dimensions used for the draft, beam and length will vary because of the different
ships and cargo being serviced by the pier. Yet it is desirable to consider the hydraulic effect in the energy computations, and for this reason, it is
suggested that an average value be used. By averaging the results obtained by using these two approaches, an approximate factor of 0.35 can be
determined. The amount of energy possessed by the vessel should be increased by 35% to include the hydraulic effect (HA). Therefore to compute
the total energy to be absorbed by the fenders, including the berthing coefficient and the hydraulic effect, the following formula should be used:
5. Dock
design
To select the proper size and type of Dock Fender the design of the
dock must be considered.
If the dock does not have a separate frontal system:
the fenders can be
mounted directly onto the dock face. Common methods of attaching
fenders to this type of dock face include:
A.
Festooning cylindrical fenders by suspending them with chain.
B.
Directly bolting Rectangular, Wingtype, D Shaped or
Trapezoidal fenders to the dock face.
For either attachment method the fenders can be positioned in a
horizontal or diagonal pattern depending on the tidal conditions and
the type of vessels being serviced by the pier. In areas of relatively high
tides, or on piers that will handle barges as well as ships, it is good
practice to mount the fenders in a diagonal pattern in order to protect
a greater portion of the dock face.
For docks that have a protective frontal system made up of piles and
wales:
Rectangular or Trapezoidal fenders are generally mounted
between the dock face and the wales.
The design strength of the dock also has a bearing on the size and the
type of fender to be used. Piers and dolphins which are supported by
piles have design limitations with respect to the loads that can be
imposed. In these cases, a fender system must be selected that will
absorb the energy of the berthing ship and remain within the design
limits of the structure.
Having determined the amount of energy to be absorbed and the type
of dock to be protected, the next step is to select the proper size and
type of fender to specify. Also, the method of attaching the fender can
be determined.
Cylinder Fender Values
Size
De ection
Energy
Load
15" x 7½"
7¾"
4,000 ft-lbs/ft
37,000 lb/ft
18' x 9"
9"
4,000 ft-lbs/ft
15,000 lb/ft
Rectangular Fender Values
Size
De ection
Energy
Load
10' x 10"
3½"
4,000 ft-lbs/ft
40,000 lb/ft
12" x 12"
3¾"
4,000 ft-lbs/ft
28,000 lb/ft
Trapezoidal Fender Values
Size
De ection
Energy
Load
10"
4¾"
4,000 ft-lbs/ft
28,000 lb/ft
13"
4½"
4,000 ft-lbs/ft
17,000 lb/ft
Sample Problem
Determine the size and type of fenders to
be specified for a pile supported by a pier
having a concrete cap. The vertical face of the
concrete cap is 5 feet. The maximum load the dock
is designed to take is 20,000 pounds per foot. Using
the previous example, the energy to be absorbed is
79,000 ft-lbs.
Experience has shown that a vessel in the 40,000 ton class would
contact a minimum of 20 feet of dock face. Therefore, we can
determine that the energy to be absorbed per foot of fender will be:
79,000 ft-lbs/20 ft = 3950 ft-lbs/ft
Referring to the Energy-De ection and Load-De ection curves, the
following information can be found:
1 + 2D/B where D = draft and B = beam.
(3) KE = ½WV
E
2
(C
B
)(H
A
) where W = displacement tonnage
g = acceleration due to gravity (32.2 ft/sec)
g
V
E
= velocity normal to the dock
C
B
= berthing coefficient H
A
= hydraulic effect
This equation can be simpli ed to:
(4) KE = 23,48 WV
E
2
Sample problem
Determine the energy to be absorbed for the following conditions:
Displacement tonnage = 40,000 tons
Forward velocity = 1 knot
Approach angle = 10
o
Using equation (2)
V
E
= (1)(1.09)(sine 10
o
) = 0.29 ft per second
Using equation (4)
KE = KE = (23.48)(40,000)(0.29)
2
= 79,000 ft-lbs
From a study of these figures, it can be seen that either an 18" x 9" Cylindrical Fender or a 13" Trapezoidal Fender would absorb the energy
and remain within the load limitation of the structure.
The most economical and effective means of mounting Cylindrical fenders would be to suspend them by chain along the dock
face. Trapezoidal fenders would be rigidly mounted by bolting.
Because of the adaptability of the Goodyear Engineered Products Dock Fenders, mounting patterns and methods can be
varied to solve your particular fendering problems. Assistance is available by contacting Goodyear Engineered Products.