# 3103F.6 Berthing Loads

Berthing loads are quantified in terms of transfer of kinetic energy of the vessel into potential energy dissipated by the fender(s). The terms and equations below are based on those in UFC 4-152-01 [3.19] and PIANC [3.20].

Kinetic energy shall be calculated from the following equation:

(3-15)

**where:**

E_{vessel} | = | Berthing energy of vessel [ft-lbs] |

W | = | Total weight of vessel and cargo in pounds [long tons H 2240] |

g | = | Acceleration due to gravity [32.2 ft/sec^{2}] |

V_{n} | = | Berthing velocity normal to the berth [ft/sec] |

The following correction factors shall be used to modify the actual energy to be absorbed by the fender system for berthing operations:

(3-16)

**where:**

E_{fender} | = | Energy to be absorbed by the fender system |

F_{A} | = | Accidental factor accounting for abnormal conditions such as human error, malfunction, adverse environmental conditions or a combination of these factors. For existing berthing systems, F_{A} may be taken as 1.0. For new berthing systems, F_{A} shall be determined in accordance with Section 5-1.5.3 of UFC 4-152-01 [3.19] or PIANC Section 4.2.8 [3.20]. |

C_{b} | = | Berthing Coefficient |

C_{m} | = | Effective mass or virtual mass coefficient (see Section 3103F.6.6) |

The berthing coefficient, C_{b}, is given by:

(3-17)

**where:**

C_{e} | = | Eccentricity Coefficient |

C_{c} | = | Configuration Coefficient |

C_{g} | = | Geometric Coefficient |

C_{d} | = | Deformation Coefficient |

These coefficients are defined in Sections 3103F.6.2 through 3103F.6.5.

The approximate displacement of the vessel (when only partially loaded) at impact, DT, can be determined from an extension of an equation from Gaythwaite [3.21]:

(3-18)

**where:**

DWT | = | Dead Weight Tonnage (in long tons) |

d_{actual} | = | Actual arrival draft of the vessel |

d_{max} | = | Maximum loaded vessel draft |

The berthing load shall be based on the fender reaction due to the kinetic berthing energy. The structural capacity shall be established based on allowable concrete, steel or timber properties in the structural components, as defined in Section 3107F.

For fender system selection, Section 3105F.4.5 shall be followed.

During the berthing maneuver, when the vessel is not parallel to the berthing line (usually the wharf face), not all the kinetic energy of the vessel will be transmitted to the fenders. Due to the reaction from the fender(s), the vessel will start to rotate around the contact point, thus dissipating part of its energy. Treating the vessel as a rigid rod of negligible width in the analysis of the energy impact on the fenders leads to the equation:

(3-19)

**where:**

k | = | Longitudinal radius of gyration of the vessel [ft] |

a | = | Distance between the vessel's center of gravity and the point of contact on the vessel's side, projected onto the vessel's longitudinal axis [ft] |

The geometric coefficient, Cg, depends upon the geometric configuration of the ship at the point of impact. It varies from 0.85 for an increasing convex curvature to 1.25 for concave curvature. Generally, 0.95 is recommended for the impact point at or beyond the quarter points of the ship, and 1.0 for broadside berthing in which contact is made along the straight side [3.19].

This accounts for the energy reduction effects due to local deformation of the ships hull and deflection of the whole ship along its longitudinal axis. The energy absorbed by the ship depends on the relative stiffness of the ship and the obstruction. The deformation coefficient varies from 0.9 for a nonresilient fender to nearly 1.0 for a flexible fender. For larger ships on energy-absorbing fender systems, little or no deformation of the ship takes place; therefore, a coefficient of 1.0 is recommended.

This factor accounts for the difference between an open pier or wharf and a solid pier or wharf. In the first case, the movements of the water surrounding the berthing vessel is not (or is hardly) affected by the berth. In the second case, the water between the berthing vessel and the structure introduces a cushion effect that represents an extra force on the vessel away from the berth and reduces the energy to be absorbed by the fender system.

For open berth and corners of solid piers, C_{c} = 1.0

For solid piers with parallel approach, C_{c} = 0.8

For berths with different conditions, C_{c} may be interpolated between these values [3.19].

In determining the kinetic energy of a berthing vessel, the effective or the virtual mass is the sum of vessel mass and hydrodynamic mass. The hydrodynamic mass does not necessarily vary with the mass of the vessel, but is closely related to the projected area of the vessel at right angles to the direction of motion.

Other factors, such as the form of vessel, water depth, berthing velocity, and acceleration or deceleration of the vessel, will have some effect on the hydrodynamic mass. Taking into account both model and prototype experiments, the effective or virtual mass coefficient can be estimated as:

(3-20)

**where:**

d_{actual} | = | Actual arrival draft of the vessel |

B | = | Beam of vessel |

The value of C_{m} for use in design should be a minimum of 1.5 and need not exceed 2.0 [3.19].

The berthing velocity, V_{n}, is influenced by a large number of factors such as environmental conditions of the site (wind, current and wave), method of berthing (with or without tugboat assistance), condition of the vessel during berthing (ballast or fully laden) and human factors (experience of the tugboat captain).

The berthing velocity, normal to berth, shall be in accordance with Table 31F-3-7. Site condition is determined from Table 31F-3-8.

Subject to Division approval, if an existing MOT can demonstrate lower velocities by utilizing velocity monitoring equipment, then such a velocity may be used temporarily until the berthing system is compliant with this Code.

VESSEL SIZE (DWT) | TUG BOAT ASSISTANCE | SITE CONDITIONS | ||

Unfavorable | Moderate | Favorable | ||

≤10,000 | No | 1.31 ft/sec | 0.98 ft/sec | 0.53 ft/sec |

≤10,000 | Yes | 0.78 ft/sec | 0.66 ft/sec | 0.33 ft/sec |

50,000 | Yes | 0.53 ft/sec | 0.39 ft/sec | 0.26 ft/sec |

≥100,000 | Yes | 0.39 ft/sec | 0.33 ft/sec | 0.26 ft/sec |

- For vessel sizes not shown, interpolation between velocities may be used.

SITE CONDITIONS | DESCRIPTION | WIND SPEED^{1} | SIGNIFICANT WAVE HEIGHT | CURRENT SPEED^{2} |

Unfavorable | Strong Wind Strong Currents High Waves | > 38 knots | > 6.5 ft | > 2 knots |

Moderate | Strong Wind Moderate Current Moderate Waves | ≥38 knots | ≤6.5 ft | ≤2 knots |

Favorable | Moderate Wind Moderate Current Moderate Waves | < 38 knots | < 6.5 ft | < 2 knots |

- A 30-second duration measured at a height of 33 ft.
- Taken at 0.5 x water depth

In order to obtain the normal berthing velocity, V_{n}, an approach angle, defined as the angle formed by the fender line and the longitudinal axis of the vessel must be determined. The berthing angles, used to compute the normal berthing velocity, for various vessel sizes are shown in Table 31F-3-9.

VESSEL SIZE (DWT) | ANGLE (degrees) |

Barge | 15 |

< 10,000 | 10 |

10,000-50,000 | 8 |

> 50,000 | 6 |

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