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Calculating the radius of gyration

To calculate the radius of gyration for the cross-section of the beam in the

diagram, start with the values of I that were calculated earlier.

Ixx = 33.3 x 106 mm4

Iyy = 2.08 x 106 mm4

Refer to the diagram for the values of b and d that are used in the calculation

of A.

A = Area of cross-section = 50 mm x 200 mm = 10,000 mm2

Substitute I and A into the formula for r to give:

This is the value of the radius of gyration about the x-x axis.

In structural engineering, the two-dimensional radius of gyration is used to describe the

distribution of  cross sectional area in a column around its centroidal axis. The radius of 

gyration is given by the following formula

or 

where I is the second moment of area and A is the total cross-sectional area. The gyration

radius is useful in estimating the stiffness of a column. However, if the principalmoments of the two-dimensional gyration tensor are not equal, the column will tend to

 buckle around the axis with the smaller principal moment. For example, a column with anelliptical cross-section will tend to buckle in the direction of the smaller semiaxis.

It also can be referred to as the radial distance from a given axis at which the mass of a body could be concentrated without altering the rotational inertia of the body about that

axis.

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In engineering, where people deal with continuous bodies of matter, the radius of 

gyration is usually calculated as an integral.

[edit] Applications in mechanics

The radius of gyration (r ) about a given axis can be computed in terms of the massmoment of inertia  I around that axis, and the total mass m;

or 

 I is a scalar , and is not the moment of inertia tensor . [1]

http://www.efunda.com/formulae/solid_mechanics/columns/calc_column_structural_steel

.cfmhttp://www.efunda.com/formulae/solid_mechanics/columns/calc_column_structural_ 

steel.cfm

his calculator is designed specifically for structural steel columns. Columns made byother materials (e.g. aluminum alloys) should use other formulas.

Given the material properties (Young's modulus E , yield stress σ  y, proportional limit

σ  pl ) and the column geometry (effective length  Leff and radius of gyration r ), thiscalculator will compute the allowable stress with respect to a given safety factor.

Note: 1.

The proportional stress is equal to the yield stress minus the maximum

compression residual stress σ res left over from any hot or cold forming

operation,

σ  pl = σ  y - σ res

Typically, the proportional stress is 50% to 100% of the yield stress,

σ  pl = (0.5 ~ 1)·σ  y.2

.Radius of gyration , where I is the area moment of inertia of the cross

section and A is the cross section area.

3.

If a safety factor less than the AISC-recommended value (which ranges from1.67 to 1.92) is entered, the calculator will use the larger ASIC value. ASIC

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stands for the American Institute of Steel Construction

 

Inputs

Young's Modulus ( E ):  

Yield Stress (σ  y):  

Proportional Limit (σ  pl ):  

Effective Length of the column ( L eff ):  

Radius of Gyration (r ):  

Safety Factor (SF ):  

Answers

Allowable Stress (σ allow): 237 MPaSafety Factor (SF ): 1.69

Slenderness Ratio ( Leff  / r ): 5.00

Critical Slenderness Ratio (SRc): 99.3

Equations behind the Calculator

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The formulas used in this calculator are based on the Guide to Stability Design Criteria

 for Metal Structures by the Structural Stability Research Council. Anyone designing

metal columns should consult this guide or other well estabilshed publications.

The column is classified as either long or short/intermediate, and two different formulas

are used in these two regions.

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The critical slenderness ratio SRc separates long columns from short/intermediate

columns. Basically, SRc corresponds to the case when the stress due to the axial load

reaches the proportional limit and the critical load at the same time.

If  Leff  / r < SRc, the column is considered short/intermediate. Inelastic buckling is likely

to be the cause of failure, where the stress exceeds the proportional limit before reaching

the critical load. The ASIC safety factor and resulting allowable stress are given by,

If  Leff  / r > SRc, the column is considered long. Elastic buckling in accordance with Euler's 

formula is expected. The ASIC safety factor and resulting allowable stress are given by,

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If the safety factor specified by the user is larger than the ASIC safety factor in the above

formulas, the user's value will be used in calculating the allowable stress

http://www.calculatorsoup.com/calculators/construction/tank.php

Tank Volume & Fill Calculator 

Tank Type:

(insidedimensions)

Feet Inches

Length (l) =

Diameter (d) =

Filled Depth (f)

=

Total Volume = 0.00Filled Volume* = 0.00

Tank Schematic:

Horizontal Cylinder

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About this Calculator

Estimate the total and filled volumes of tanks such as oil tanks and water tanks. Assumesinside dimensions of the tank .

*Actual fill volumes will differ. Tank volume calculations are based on tank geometriesshown below. These tank shapes are calculated assuming exact geometric solid shapes

such as cylinders, circles and spheres. Actual water and oil tanks may not be perfectgeometric shapes or might have other features not accounted for here so, thesecalculations should only be considered estimates.

Methods to calculate the volume of tanks and the

volume of a liquid inside a tank.

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These calculations will give you cubic measures such as ft3 or m3 depending on your units

of measure.

Horizontal Cylinder Tank

Total volume of a cylinder shaped tank is the area, A, of the circular end times the length,l. A = πr 2 where r is the radius which is equal to 1/2 the diameter or d/2. Therefore:V(tank) = πr2l

The filled volume of a horizontal cylinder tank is calculated by first finding the area, A,of a circular segment and multiplying it by the length, l.

Area of the circular segment, the grey shaded area, is A = (1/2)r 2(θ - sinθ ) where θ =2*arccos(m/r). Therefore, V(segment) = (1/2)r 2(θ - sinθ )l. If the fill height f is less than

1/2 of d then we use the segment created from the filled height and V(fill) =V(segment). However, if the fill height f is greater than 1/2 of d then we use the segmentthat is created by the empty portion of the tank and subtract it from the total volume to

get the filled volume; V(fill) = V(tank) - V(segment).

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Vertical Cylinder Tank

Total volume of a cylinder shaped tank is the area, A, of the circular end times the height,h. A = πr 2 where r is the radius which is equal to d/2. Therefore:V(tank) = πr2h

The filled volume of a vertical cylinder tank is just a shorter cylinder with the same

radius, r, and diameter, d, but height is now the fill height or f. Therefore:V(fill) = πr2f 

Rectangle Tank

Total volume of a rectangular prism shaped tank is length times width times height.

Therefore,V(tank) = lwh

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The filled volume of a rectangular tank is just a shorter height with the same length and

width. The new height is the fill height or f. Therefore:V(fill) = lwf 

Horizontal Oval Tank

Volume of an oval tank is calculated by finding the area, A, of the end, which is the

shape of a stadium, and multiplying it by the length, l. A = πr 2 + 2ra and it can be proven

that r = h/2 and a = w - h where w>h must always be true. Therefore:V(tank) = (πr2 + 2ra)l 

Volume of fill of a horizontal oval tank is best calculated if we assume it is 2 halves of a

cylinder separated by a rectangular tank. We then calculate fill volume of 1) aHorizontal Cylinder Tank where l = l, f = f, and diameter d = h, and 2) a Rectangle

Tank where l = l, f = f, and rectangle width w is a = w - h of the oval tank.V(fill) = V(fill-horizontal-cylinder) + V(fill-rectangle)

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Vertical Oval Tank

Volume of an oval tank is calculated by finding the area, A, of the end, which is the

shape of a stadium, and multiplying it by the length, l. A = πr 2 + 2ra and it can be proventhat r = w/2 and a = h - w where h>w must always be true. Therefore:

V(tank) = (πr2

+ 2ra)h

Volume of fill of a vertical oval tank is best calculated if we assume it is 2 halves of a

cylinder separated by a rectangular tank. With r = w/2 = hieght of the semicircle ends, wecan define 3 general fill position areas.

• Fill, f < r 

We calculate fill volume using the circular segment method, as in a Horizontal

Cylinder Tank, for the filled portion.• Fill, f > r and f < (r+a)

The filled volume is exactly 1/2 of the cylinder portion plus the volume of fill

inside the rectangular portion.• Fill, f > (r+a) and f < h

We calculate fill volume using the circular segment method, as in a Horizontal

Cylinder Tank, for the empty portion. Volume will be V(tank) - V(segment).

Horizontal Capsule Tank

We treat a capsule as a sphere of diameter d split in half and separated by a cylinder of 

diameter d and height a. Where r = d/2.

V(sphere) = (4/3)πr 3, andV(cylinder) = πr 2a, therefore

V(capsule) = πr 2((4/3)r + a)

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Volume of fill for a horizontal capsule is done by using the circular segment method for 

the Horizontal Cylinder and, with a similar approach, using calculations of a spherical

cap for the sphere section of the tank where,

V(spherical cap) = (1/3)πh2(3R - h)

Vertical Capsule Tank

We treat a capsule as a sphere of diameter d split in half and separated by a cylinder of 

diameter d and height a. Where r = d/2.

V(capsule) = πr 2((4/3)r + a)

Volume of fill for a vertical capsule is calculated in a fashion similar to the method used

for the Vertical Oval Tank where r = d/2 = height of each hemisphere end.

• Fill, f < r 

We calculate fill volume using the spherical cap method, for the filled portion.

• Fill, f > r and f < (r+a)

The filled volume is exactly 1/2 of the sphere portion plus the volume of fill

inside the vertical cylinder portion.

• Fill, f > (r+a) and f < h

We calculate fill volume using the spherical cap method for the empty portion.

Volume will be V(tank) - V(spherical cap).

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Free Pop up Tank Volume and Fill Calculator. Directions.

Tank Volume Calculator 

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http://www.efunda.com/DesignStandards/design_home.cfm

http://en.wikipedia.org/wiki/Metacentric_height

http://www.portfenders.com/fenderdesign.htm

Metacentric heightFrom Wikipedia, the free encyclopedia

Ship Stability diagram showing centre of gravity (G), centre of buoyancy (B), andmetacentre (M) with ship upright and heeled over to one side. Note that for small angles,

G and M are fixed, while B moves as the ship heels, and for big angles - B and M aremoving.

The metacentric height is a measurement of the static stability of a floating body. It iscalculated as the distance between the centre of gravity of a ship and its metacentre 

(GM). A larger metacentric height implies greater stability against overturning.Metacentric height also has implication on the natural period of rolling of a hull, with

very large metacentric heights being associated with shorter periods of roll which are

uncomfortable for passengers. Hence, a sufficiently high but not excessively highmetacentric height is considered ideal for passenger ships.

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Contents

[hide]

• 1 Metacentre

• 2 Different centreso 2.1 Righting arm

• 3 Stability

o 3.1 GM and rolling period

o 3.2 Damaged Stability

• 4 Free surface effect

• 5 Transverse and longitudinal metacentric heights

• 6 Measurement

• 7 See also

• 8 References

[edit] Metacentre

How quickly or slowly a boat rolls is like a pendulum or metronome, having a natural

frequency. That frequency is determined (like with a metronome) by the amount of mass on some length of swing arm being pulled by gravity. Greater mass and/or arm length

means a slower swing; and less mass and/or shorter arm length means a faster swing.

In a boat, the swing arm is a distance called "GM or metacentric height", being the

distance between two points: "G" the center of gravity of the boat and "M" which is animaginary point called the metacentre.

Metacenter is determined by a ratio of the inertia resistance of the boat divided by the

volume of the boat. (The inertia resistance is a quantified description of how the

waterline width of the boat resists overturning.) Wide and shallow or narrow and deephulls have high transverse metacenters (relative to the keel), and the opposite have low

metacenters; the extreme opposite is shaped like a log or round bottomed boat.

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Ignoring the ballast, wide and shallow or narrow and deep means the ship is very quick to

roll and very hard to overturn and is stiff. And log shaped round bottomed means slow

rolls and easy to overturn and tender.

The bottom point of the swinging pendulum arm, "G", is the center of gravity. "GM", the

swinging pendulum length of a boat, can be lengthened by lowering the center of gravityor changing the hull form (and thus changing the volume displaced and second moment

of area of the waterplane.

An ideal boat strikes a balance. Very tender boats with very slow roll periods are at risk 

of overturning and have uncomfortable feel for passengers. However, vessels with a

higher metacentric height are "excessively stable" with a short roll period resulting in

high accelerations at the deck level.

When a ship is heeled, the centre of buoyancy of the ship moves laterally. The point at

which a vertical line through the heeled centre of buoyancy crosses the line through the

original, vertical centre of buoyancy is the metacentre. The metacentre remains directlyabove the centre of buoyancy regardless of the tilt of a floating body, such as a ship. In

the diagram to the right the two Bs show the centres of buoyancy of a ship in the upright

and heeled condition, and M is the metacentre. The metacentre is considered to be fixed

for small angles of heel; however, at larger angles of heel the metacentre can no longer beconsidered fixed, and other means must be found to calculate the ship's stability.

The metacentre can be calculated using the formulae:

 KM = KB + BM 

Where KB is the centre of buoyancy (height above the keel), I is the Second moment of area of the waterplane in metres4 and V is the volume of displacement in metres3. KM is

the distance from the keel to the metacentre. [1]

[edit] Different centres

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Initially the second moment of area increases as the surface area increases, increasing

BM, so Mφ moves to the opposite side, thus increasing the stability arm. When the deck is flooded, the stability arm rapidly decreases.

The centre of buoyancy, is the centre of the volume of  water  which the hull displaces.

This point is referred to as B in naval architecture. The centre of gravity of the ship is

commonly denoted as point G or VCG. When a ship is stable, the centre of buoyancy isvertically in line with the centre of gravity of the ship.[2]

The metacentre is the point where the lines intersect (at angle φ) of the upward force of 

 buoyancy of φ ± dφ. When the ship is vertical the metacentre lies above the centre of gravity and so moves in the opposite direction of heel as the ship rolls. The metacentre is

commonly designated as point MT in naval architecture.

The distance between the centre of gravity and the metacentre is called the metacentric

height. This distance is also abbreviated as GM. As the ship heels over, the centre of gravity generally remains fixed with respect to the ship because it just depends upon

 position of the ship's weight and cargo, but the surface area increases, increasing BMφ.

The metacentre, Mφ, moves up and sideways in the opposite direction in which the ship

has rolled and is no longer directly over the centre of gravity.[3]

The righting force on the ship is then caused by gravity pulling down on the hull(effectively acting on its centre of gravity) and the buoyancy pushing the hull upwards

(effectively acting along the vertical line passing through the centre of buoyancy and themetacentre above it). This creates a righting moment (a kind of torque) which rotates the

hull upright again and is proportional to the horizontal distance between the centre of 

gravity and the metacentre. The metacentric height is important because the righting

force is proportional to the metacentric height times the sine of the angle of heel.

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When setting a common reference for the centres, the molded (within the plate or 

 planking) line of the keel (K ) is generally chosen; thus, the reference heights are:

KB - Centre of BuoyancyKG - Centre of Gravity

KMT - Transverse Metacentre

[edit] Righting arm

Distance GZ is the righting arm: a notional lever through which the force of buoyancy

acts.

Sailing vessels are designed to operate with a higher degree of heel than motorized

vessels and the righting moment at extreme angles is of high importance. This is

expressed as the righting arm (known also as GZ — see diagram): the horizontal

distance between the centre of buoyancy and the centre of gravity.[3]

GZ = GM sin φ [2]

Monohulled sailing vessels should be designed to have a positive righting arm (the limit 

of positive stability) to at least 120º of heel,[4] although some racing sailboats have

stability limits down to 90º (masts flat to the surface). As the displacement of the hull atany particular degree of list is not proportional, calculations can be difficult, and the

concept was not introduced formally into naval architecture until about 1970.[5]

[edit] Stability

[edit] GM and rolling period

Metacentre has a direct relationship with a ship's rolling period. A ship with a small GM

will be "tender" - have a long roll period. An excessively low or negative GM increases

the risk of a ship capsizing in rough weather, for example HMS Captain  or the Vasa. Italso puts the vessel at risk of potential for large angles of heel if the cargo or ballast

shifts, such as with the Cougar Ace. A ship with low GM is less safe if damaged and

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 partially flooded because the lower metacentric height leaves less safety margin. For this

reason, maritime regulatory agencies such as the International Maritime Organization 

specify minimum safety margins for sea-going vessels. A larger metacentric height on theother hand can cause a vessel to be too "stiff"; excessive stability is uncomfortable for 

 passengers and crew. This is because the stiff vessel quickly responds to the sea as it

attempts to assume the slope of the wave. An overly stiff vessel rolls with a short periodand high amplitude which results in high angular acceleration. This increases the risk of 

damage to the ship and to cargo. In contrast a "tender" ship lags behind the motion of the

waves and tends to roll at lesser amplitudes. A passenger ship will typically have a longrolling period for comfort, perhaps 12 seconds while a tanker or freighter might have a

rolling period of 6 to 8 seconds.

The period of roll can be estimated from the following equation [2]

Where g is the gravitational constant, k is the radius of gyration about the longitudinal

axis through the centre of gravity and is the stability index.

[edit] Damaged Stability

If a ship floods, the loss of stability is caused by the increase in B, the centre of  buoyancy, and the loss of waterplane area - thus a loss of the waterplane moment of 

inertia - which decreases the metacentric height.[2] This additional mass will also reduce

freeboard (distance from water to the deck) and the ship's angle of down flooding

(minimum angle of heel at which water will be able to flow into the hull). The range of  positive stability will be reduced to the angle of down flooding resulting in a reduced

righting lever. When the vessel is inclined, the fluid in the flooded volume will move to

the lower side, shifting its centre of gravity toward the list, further extending the heelingforce. This is known as the free surface effect.

[edit] Free surface effect

Further information: Free surface effect

In tanks or spaces that are partially filled with a fluid or semi-fluid (fish, ice or grain for 

example) as the tank is inclined the surface of the liquid, or semi-fluid, stays level. Thisresults in a displacement of the centre of gravity of the tank or space relative to the

overall centre of gravity. The effect is similar to that of carrying a large flat tray of water.When an edge is tipped, the water rushes to that side, which exacerbates the tip even

further.

The significance of this effect is proportional to the square of the width of the tank or 

compartment, so two baffles separating the area into thirds will reduce the displacement

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of the centre of gravity of the fluid by a factor of 9. This is of significance in ship fuel

tanks or ballast tanks, tanker cargo tanks, and in flooded or partially flooded

compartments of damaged ships. Another worrying feature of free surface effect is that a positive feedback loop can be established, in which the period of the roll is equal or 

almost equal to the period of the motion of the centre of gravity in the fluid, resulting in

each roll increasing in magnitude until the loop is broken or the ship capsizes.

This has been significant in historic capsizes, most notably the MS Herald of FreeEnterprise.

[edit] Transverse and longitudinal metacentric heights

There is also a similar consideration in the movement of the metacentre forward and aft

as a ship pitches. Metacentres are usually separately calculated for transverse (side toside) rolling motion and for lengthwise longitudinal pitching motion. These are variously

known as and , GM(t) and GM(l), or sometimes GMt and GMl .

Technically, there are different metacentric heights for any combination of pitch and rollmotion, depending on the moment of inertia of the waterplane area of the ship around the

axis of rotation under consideration, but they are normally only calculated and stated as

specific values for the limiting pure pitch and roll motion.

[edit] Measurement

The metacentric height is normally estimated during the design of a ship but can be

determined by an inclining test once it has been built. This can also be done when a ship

or offshore floating platform is in service. It can be calculated by theoretical formulas based on the shape of the structure.

The angle(s) obtained during the inclining experiment are directly related to GM. Prior to

the inclining experiment, an accounting of the 'as-built' centre of gravity is done;

knowing KM and KG, the metacentric height (GM) can be calculated.

Fender Design Criteria:

Introduction:The principal function of the fender system is to prevent the vessel or the dock from

being damaged during the mooring process or during the berthing periods. Forcesduring the vessel berthing or anchoring may be in the form of impact, abrasive

action from vessels, or direct pressure. These forces may extensive damage to theship and structure if suitable means are not employed to counteract them. The

amount of energy absorbed and the maximum impact force imparted are the primarycriteria applied in accepted fender design practices.

Selection of fender system type:A variety of factors affect the proper selection of a fender system. These include, but

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not limited to, local marine environment, exposure of harbor basins, class andconfiguration of ships, speed and direction of approach of ships when berthing,

available docking assistance, type of berthing structure, and even the skills of pilotsor ship captains. It is considered impractical to standardize fender designs since port

conditions are rarely identical. Previous local experience in the application of satisfactory fender systems should be considered, particularly as it applies to cost-

effectiveness characteristics. Here is a good guide for selecting a fender system fitfor your needs. We follow the PIANC 2002 and other Standards set forth by other manufacturers with a long history in the marine fender industry.

General Design Procedure:

The design of a fender system is based on the law of conservation of energy . Theamount of energy being introduced into the system must be determined, and then a

means devised to absorb the energy within the force and stress limitations of theship's hull, the fender, and the pier. General design procedures are as follows:

1. Determine the energy that will be delivered to the pier upon initial impact. It isrecommended to consider the heaviest/largest vessel capable or allowed to use your

dock.

2. Determine the energy that can be absorbed by the pier or wharf (distribution of 

loading must be considered ). For structures that are linearly elastic, the energy is

one-half the maximum static load level times the amount of deflection. Allowanceshould also be made in cases where other vessels may be moored at the pier. If the

structure is exceptionally rigid, it can be assumed to absorb no energy.

3. Subtract the energy that the pier will absorb from the effective impact energy of the ship to determine the amount of energy that must be absorbed by the fender.

4. Select a fender design capable of absorbing the amount of energy determinedabove without exceeding the maximum allowable force in the pier. Please contact us

for our product catalogue. You can get specific performance information of ourproducts.

 I. Terminology:

Gross Tonnage(GT): Total Volume of vessel and cargo. This is derived by

dividing the total interior capacity of a vessel by 100 cubic feet.

Net Tonnage(NT): Total Volume of cargo that is carried by the vessel.

Displacement Tonnage(DPT): Total weight of the vessel and cargo

when the ship is loaded to draft line.

Dead Weight Tonnage(DWT): Weight of cargo, fuel, passenger, crew

and food on the vessel.

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Light Weight(LOW): Weight of Vessel.

Ballast Weight(BW): Weight of ship and the water added to the ballast

compartment to improve its stability after it has discharged its cargo.

 

 II. Calculation of the Normal Berthing Energy or Effective Berthing Energy:

Side Berthing:

 

Side Berthing is the most typical case for docks. The Berthing Energy is calculated by

the following kinetic equation:

Where E B : Berthing energy (KJ, N*m, or LbF *ft)

W D : Water displacement of the berthing ship (Tons, Kg, Lbs). - This is

the Total Displacement Tonnage(DPT) of the vessel. If you do not have thisinformation you may use our tables to view standard vessel's information by type

and sizes. Please click here to view our tables.

V B : Berthing velocity of the Ship at the movement of impact against 

the fender (m/sec, ft/sec) - Berthing velocity is an important parameter in

fender system design. It depends on the size of the vessel, loading condition, port

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structure, and the ease of difficulty of the approach. Therefore the berthing velocityis preferred to be obtained from actual measurements or relevant existing statistical

information. When the actual measured velocity is not available, the most widelyused guide to estimate the berthing velovity is the Brolsma table, adopted by BSI,

PIANC and other standards. To facilitate the calculations, designers can use tables,graphs or equations shown below.

V a: Easy Berthing, sheltered. V b: Difficult Berthing, sheltered. V c : Easy

Berthing, exposed. V d : Difficult Berthing, exposed.

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C  M  : Virtual mass factor - As a vessel makes contact with the berth and its

movement is suddenly stopped by the fenders, the mass of water moving with thevessel adds to the energy possessed by the vessel. This is called "Mass Factor" or

"Added Mass Coefficient" and the weight of the water is generally called " Additional Weight ". The added mass coefficient makes up for the body of water carried along

with the ship as it moves sideways through the water. As the vessel is berthing abody of water is carried along with the ship as it moves sideways through the water.

As the ship is stopped by the fenders, the momentum of the entrained watercontinues to push against the ship and this effectively increases its overall mass. CM

is normally calculated with the following formula:

where,

D: Full Load Draft(m, ft)B: Molded Breadth(m, ft)

 

Another calculation method for the virtual mass factor is:

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where,  D: Full Load Draft

  L: Ship Length  ρ: Sea Water Density(1.025 t/m3)

 

C E  : Eccentricity factor - In the case when a vessel contacts a berth at a point

near its bow or stern, the reaction force with give a rotational movement, which will

dissipate a part of the vessel's energy.

To determine the Eccentricity Coefficient, you must firstly calculate the radius of 

gyration(K), the distance from the vessels center of mass to point of impact(R), the

velocity vector angle( ) and berthing angle( ) using the following formulas:

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Where K : Radius of rotation of the vessel (usually 1/4 of the vessel's length)  R: Distance of the line paralleled to wharf measured from the vessel's center

of gravity to the point of contact. Usually 1/4- 1/5 of vessel's length.

  C B: Block Coefficient, which is related to the hull shape and is is calculated asfollows:

 

Where, WD: Water displacement of the berthing ship(Tons, Kg, Lbs)

: Sea Water density(1.025 Tons/m3)

  LBP : Length between perpendiculars. Please see sketch below for better

explanation:

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   x : Distance from bow to point of impact  B: Beam(m, ft)

If the Length, beam and draft are not known, this table can be used to estimate the

block coefficient:

Typical Block Coefficients(CB)Type of Vessel

CB

BS 6349

CB

PIANC 2002 

Tankers 0.72~0.85 0.85

Bullk Carriers 0.72~0.85 0.72~0.85

Container Ships 0.65~0.75 0.60~0.80

General Cargo 0.60~0.75 0.72~0.85

RoRo Vessels 0.65~0.70 0.70~0.80

Ferries 0.50~0.65 0.55~0.65

 

You may also use the following formula to calculate the eccentricity

coefficient:

Some designers prefer to calculate the eccentricity coefficient using the simplified

formula above. Care should be used as this method can lead to an underestimation

of Berthing Energy when the berthing angle( ) is greater than 10 degrees and/orthe point of impact is aft of quarter-point(x > LBP /4). To verify your calculations, theeccentricity coefficient values generally fall within the following limits:

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C C  : Berth configuration factor - This is the portion of berthing energy which is

absorbed by the cushion effect of water between the approaching vessel and the

quay wall. The smaller the draft(D) of the vessel is, or the larger the under keel

clearance(K C ), the more trapped water can escape under the vessel, and would givea higher C C  value. Also, if the berthing angle of the vessel is greater than 5°, we can

consider C C = 1.

Case 1: Closed Dock

A Closed Dock would be a wharf, where you have a concrete wall going directly tothe sea ground. In this case the quay wall will push back all the water that is being

moved by the vessel. This creates a resistance factor that can be calculated as

follows:

If K C  ≤ D / 2, CC ≈ 0.8 

If K C  > D / 2, CC ≈ 0.9

Case 2: Open or Semi-Closed Dock

A Semi-Closed Dock is a Dock that water can flow underneath the dock, but thedepth changes below the dock. Open Dock is usually a dock with piles underneath

and the water can flow freely underneath the dock. In such case we can assume thefollowing value of 1.

CC ≈ 1

 

C S : Softness factor - This is the portion of berthing energy which is absorbed by

the deformation of the vessel's hull and fender. When a soft fender is used, C Scan be

ignored. Otherwise, we can assume a value for C S ≈ 0.9

 

 II. Fender Selection:

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After the effective berthing Energy(E B) of the ship is calculated as explained above,the selection of the fender system should be conducted in accordance with the

fenders performance(Reaction Force, Energy absorption, and deflection curve). Thefender system selection has the following requirements:

1. Energy absorption of the selected fender system exceeds effective impacting

energy of ships(E B).2. Reaction force of the selected fender system is less than the ship's allowablereaction force.

3. Surface pressure of the selected fender system is less than the allowable hullsurface pressure. You can meet the requirements by changing the dimensions of the

frontal panel.4. When the ship is berthing in a slanting direction, the fenders will bear a angular

compression which will decrease the energy absorption at point of impact. Thereforethe fender performance should be adjusted in accordance with the berthing angles

when selecting the fender system.5. The selected fender system should satisfy special requirements of extreme

environments(high/cold temperature, strong winds, waves, high/low tides, etc.)6. The selected fender system should be chosen wisely for the

investment(performance/price). The price of maintenance and installation should beconsidered in your investment. Fenders that have an easy installation and

maintenance are a better option for your investment.

Fender Spacing:

This calculations are critical, due to the possibility of a vessel hitting the dockstructure while berthing at an angle. As per British Standards, for continuous quay,

the installation pitch is recommended to be less than 15% of the vessel. Minimum

installation pitch of fender can be calculated with the following equation:

Where 

S : Maximum spacing between fenders

RB: Bow radius of board side of vessel(m, ft)P U : Uncompressed Height of fender including panel(m, ft)

C : Fender height in rated compression.

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: Fender deflection(m, ft)

If the bent radius(RB) is not known, we can estimate by the vessel's overall

length(LOA) and width(B) as follows:

 

For vertical orientation arrangement, the types and sizes of all ships berthing shallbe considered. All possible tides vary scope. To assure safe berthing we must

consider the height and draft of the smallest and largest vessels to determine thepoint of contact on the structure. Do not design your arrangements considering only

the largest vessels berthing in your dock, since your design might not work forsmaller vessels berthing in your dock.

Fender Panel Design:

Hull Pressures:Permissible hull pressures vary greatly with the class and size ship. The best guide to

hull pressure is the designer's experience in similar cases. If this information isunavailable, then the following table may be used as an approximate guide for

design: 

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Allowed Hull Pressures

Type of Vessel HullPressure

KN/m2

Tankers 150~250

ULCC & VLCC(Coastal Tankers) 250~350Product & Chemical Tankers 300~400

Bullk Carriers 150~250

Post-Panamax Container Ships 200~300

Panamax Container Ships 300~400

Sub-Panamax Container Ships 400~500

General Cargo 300~600

Gas Carriers 100~200

Hull pressures are calculatedusing the frontal panel

area(excluding lead-in

chamfers) as follows:

 

Where 

P : Hull Pressure(N/m2, psi) ΣR: Combined Reaction Forces of all rubber fenders

 A1: Valid Panel Width excluding lead-in chamfers(m)B1: Valid Panel Height excluding lead-in chamfers(m)

P P : Permissible hull pressure(N/m2, psi)

 

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Approximate Hull Pressure for other fender types:

The above formula and table apply to berths fitted with frontal panel systems.

However, many berths use Cylindrical and Arch fenders safely and without damagingthe ship's hull, despite the fact that these fenders exert higher hull pressures. The

Arch Fenders have hull pressures of 760~1300kN/m2. Cylindrical Fenders have460~780kN/m2. Also bear in mind that when cylindrical fenders are used with large

chains or bar fixings through the central bore, the hull pressure will be higher toapproximately double the above figures. Again there is no evidence to show that this

causes hull damage.

 

Selection and Calculation of 

Chain:

There are threetypes of chains in

fender systems:1. Tension

Chain: The mainfunction of the

tension chain is toprotect the fender

from damage

while it is undercompression.

2. Weight Chain:The weight

chained is used tosupport the weight

of the frontal andface panel.

3. Shear Chain:This chain protects

the fender from

damage while inshear deflection.

The followingshould be noted in

the chain design:

-Chain dimensionsshould be as exact

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as possible. Not too loose, not too tight.-The chain can not be twisted as this reduces the load capacity.

-Open Link is preferred.-The initial(static) angle of the chain is important. Normally weight chains are set at

a static angle of 15 - 25° to the vertical and shear chains are set to 20 - 30° to thehorizontal.

-All chains must be designed or selected with a safety factor of 2 to 3 times of thework load.-The dimensions of the shackle is usually the same as the chain, but if the shackle is

required to bear the same load with the chain, then a thicker shackle is preferred.

Where,Ф1: Static Angle of Chain(°)

h1: Static offset between brackets(m, ft)Ф2: Dynamic Angle of Chain(°)

h2: Dynamic offset between brackets at F(m, ft)D: Fender compression(m, ft)

R: Reaction Force of rubber units behind the frontal panel(N, Lbs)W : Weight of the panel face(N, Lbs)

F L: Safe working Load of chain(N, Lbs)L: Bearing length of chain(m, ft)

n: number of chains acting together μ: Friction coefficient of face pad. Usually equals 0.15 for UHMW-PE facings.

F M : Minimum Breaking Load(N, Lbs)F S : Safety Factor(2~3 times)

 III. Other Berthing Scenarios:

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Dolphin Berthing:

 

Passing Lock Entrance:

 

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Ship to Ship Berthing:

 

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End Berthing:

 

Please note that this information is only for reference. Please allow us to confirm

your fender selection. Provide us with all the information needed to assure yourselection. Please contact us. We will provide you with support for your fender

system. We are committed to our clients from the design to the installation and evenfor future maintenance inspections and consulting. Please fill up our design condition

form and send it to us. To download or access our design inquiry form, please clickhere.

http://www.evergreen-maritime.com.cn/Fenders/Berthing-Energy.html

Berthing Energy

The designed energy to be absorbed by the fender can be calculated as:

Ed = 0.5 x M x VB2 x CM x CE x CC x CS

Where:Ed = Design energy (under normal conditions) to be absorbed by fender system (in KN)M = Mass of design vessel (displacement in tones), at chosen confidence level, Usually 95% confidence levelVB = Approach velocity of the vessel perpendicular to the berthing line (m/s).CM = Added mass coeffi cientCE = Eccentricity factor CC = Berth configuration configuration factor or cushion factor CS = Softness factor 

M: Water displacement of the berthing ship (Tons, Kg, Lbs). - This is the Total Displacement Tonnage(DPT) of thevessel. If you do not have this information you may use our tables to view standard vessel's information by type and sizes.

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VB: Berthing velocity of the Ship at themovement of impact against the fender (m/sec, ft/sec) - Berthing velocity is animportant parameter in fender systemdesign. It depends on the size of the vessel,loading condition, port structure, and theease of difficulty of the approach. Thereforethe berthing velocity is preferred to be

obtained from actual measurements or relevant existing statistical information.When the actual measured velocity is notavailable, the most widely used guide toestimate the berthing velovity is the Brolsmatable, adopted by BSI, PIANC and other standards. To facilitate the calculations,designers can use tables, graphs or equations shown below.

CM: Virtual mass factor - As a vessel makes contact with the berth and its movement is suddenly stopped by the fenders,

the mass of water moving with the vessel adds to the energy possessed by the vessel. This is called "Mass Factor" or 

"Added Mass Coefficient" and the weight of the water is generally called "Additional Weight". The added mass coefficient

makes up for the body of water carried along with the ship as it moves sideways through the water. As the vessel is

berthing a body of water is carried along with the ship as it moves sideways through the water. As the ship is stopped by

the fenders, the momentum of the entrained water continues to push against the ship and this effectively increases its

overall mass. CM is normally calculated with the following formula:

CM = 1 + 2 x D/B

where,

D: Full Load Draft(m, ft)

B: Molded Breadth(m, ft)

 

Another calculation method for the virtual mass factor is: CM = π x D2 x L x ρ / (4 xWD)

where,

D: Full Load Draft

L: Ship Lengthρ: Sea Water Density(1.025 t/m3)

CE: Eccentricity factor - In the case when a vessel contacts a berth at a point near its bow or stern, the reaction force withgive a rotational movement, which will dissipate a part of the vessel's energy.

To determine the Eccentricity Coefficient, you must firstly calculate the radius of gyration(K), the distance from the vesselscenter of mass to point of impact(R), the velocityvector angle and berthingangle using the followingformulas:

 CE = [K2 + (R2 x Cos2r)] / (K2 x R2)

 r = 900 - α - α x Sin[B/(2●R)]

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K = (0.19xCB) + 0.11) x LBP

Where:K: Radius of rotation of the vessel (usually 1/4 of the vessel's length)R: Distance of the line paralleled to wharf measured from the vessel's center of gravity to the point of contact. Usually 1/4-1/5 of vessel's length.CB: Block Coefficient, which is related to the hull shape and is is calculated as follows:CB = M / (LBP●B●D●ρSW 

Where:M: Water displacement of the berthing ship(Tons, Kg, Lbs)ρSW: Sea Water density(1.025 Tons/m3)LBP: Length between perpendiculars. Please see sketch below for better explanation:

 x: Distance from bow to point of impactB: Beam(m, ft)If the Length, beam and draft are not known, this table can be used to estimate the block coefficient:

Typical Block Coefficients(CB)

Type of Vessel

CB CB

BS 6349 PIANC 2002  

Tankers 0.72~0.85 0.85

Bullk Carriers 0.72~0.85 0.72~0.85

Container Ships

0.65~0.75 0.60~0.80

GeneralCargo

0.60~0.75 0.72~0.85

RoRoVessels

0.65~0.70 0.70~0.80

Ferries 0.50~0.65 0.55~0.65

You may also use the following formula to calculate the eccentricity coefficient:

CE = K2 / (K2+R2)

Some designers prefer to calculate the eccentricity coefficient using the simplified formula above. Care should be used as

this method can lead to an underestimation of Berthing Energy when the berthing angle(α) is greater than 10 degrees

and/or the point of impact is aft of quarter-point(x > LBP/4). To verify your calculations, the eccentricity coefficient values

generally fall within the following limits:

Quarter-point berthing: x = L/4 Ce = 0.5Third-point berthing: x = L/3 Ce= 0.6~0.8

Mid-ships berthing: x = L/2 Ce = 1

CC : Berth configuration factor - This is the portion of berthing energy which is absorbed by the cushion effect of water between the approaching vessel and the quay wall. The smaller the draft(D) of the vessel is, or the larger the under keelclearance(KC), the more trapped water can escape under the vessel, and would give a higher CC value. Also, if theberthing angle of the vessel is greater than 5°, we can consider CC = 1.

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Case 1: Closed DockA Closed Dock would be a wharf, where you have a concrete wall going directly to the sea ground. In this case the quaywall will push back all the water that is being moved by the vessel. This creates a resistance factor that can be calculatedas follows:If KC ≤ D / 2, CC ≈ 0.8If KC > D / 2, CC ≈ 0.9

Case 2: Open or Semi-Closed Dock

A Semi-Closed Dock is a Dock that water can flow underneath the dock, but the depth changes below the dock. OpenDock is usually a dock with piles underneath and the water can flow freely underneath the dock. In such case we canassume the following value of 1.CC ≈ 1CS : Softness factor - This is the portion of berthing energy which is absorbed by the deformation of the vessel's hull andfender. When a soft fender is used, CS can be ignored. Otherwise, we can assume a value for CS ≈ 0.9

Please contact us to get more information about the calculation of other berthing modes, Dolphin berthing, EndBerthing, Lock Entrance, Ship-to-ship berthing.