Hull Girder Response - Quasi-Static Analysis

1 / 24

# Hull Girder Response - Quasi-Static Analysis - PowerPoint PPT Presentation

Hull Girder Response - Quasi-Static Analysis. Basic Relationships. Model the hull as a Free-Free box beam. Beam on an elastic foundation Must maintain overall Static Equilibrium. Force of Buoyancy = Weight of the Ship LCB must be in line with the LCG. Basic Relationships.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Hull Girder Response - Quasi-Static Analysis' - raya-walls

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Basic Relationships
• Model the hull as a Free-Free box beam.
• Beam on an elastic foundation
• Must maintain overall Static Equilibrium.
• Force of Buoyancy = Weight of the Ship
• LCB must be in line with the LCG
Basic Relationships
• From Beam Theory – governing equation for bending moment:
• Beam is experiencing bending due to the differences between the Weight and Buoyancy distributions

Where f(x) is a distributed vertical load.

Buoyancyrga(x)

Weightgm(x)

Basic Relationships

buoyancy curve - b(x)

weight curve - w(x)

net load curve - f(x) = b(x) - w(x)

Sign Convention

Positive

Upwards

+ f

Basic Relationships
• The solution for M(x) requires two integrations:
• The first integration yields the transverse shear force distribution, Q(x)
• Impose static equilibrium on a differential element

f

M

Q

Q + dQ

M + dM

dx

But ships are “Free-Free” Beams - No shear at ends!Q(0) = 0 and Q(L) = 0, so C = 0

Finding Shear Distribution

Sign Convention

Positive

Upwards

+ f :

Shear Force - Q

+ Q

Positive

Clockwise

+ Q :

- Q

Basic Relationships
• The second integration yields the longitudinal bending moment distribution, M(x):
• Sum of the moments about the right hand side = 0

0

f

M

Q

Q + dQ

M + dM

dx

Again, ships are “Free-Free” Beams - No moment at ends!M(0) = 0 and M(L) = 0, so D = 0

Finding Bending Moment Distribution

Shear Force - Q

Sign Convention

+ Q

Positive

Clockwise

+ Q :

- Q

Bending Moment - M

Positive

Sagging

+ M :

- M

Shear & Moment Curve Characteristics
• Zero shear and bending moments at the ends.
• Points of zero net load correspond to points of minimum or maximum shear.
• Points of zero shear correspond to points of minimum or maximum bending moment.
• Points of minimum or maximum shear correspond to inflection points on bending moment curve.
• On ships, there is no shear or bending moments at the forward or aft ends.
Still Water Condition
• Static Analysis - No Waves Present
• Most Warships tend to Sag in this Condition

Putting Deck in Compression

Putting Bottom in Tension

Quasi-Static Analysis
• Simplified way to treat dynamic effect of waves on hull girder bending
• Attempts to choose two “worst case”conditions and analyze them.
• Hogging Wave Condition
• Wave with crest at bow, trough at midships, crest at stern.
• Sagging Wave Condition
• Wave with a trough at bow, crest at midships, trough at stern.
• Wave height chosen to represent a “reasonable extreme”
• Typically:
• Ship is “balanced” on the wave and a static analysis is done.
Wave Elevation Profiles
• The wave usually chosen for this analysis is a Trochoidal wave. It has a steeper crest and flatter trough.
• Chosen because it gives a better representation of an actual sea wave than a sinusoidal wave.
• Some use a cnoidal wave for shallow water as it has even steeper crests.
Sagging Wave

Excess Weight Amidships - Excess Buoyancy on the Ends

Compression

Tension

Hogging Wave

Excess Buoyancy Amidships - Excess Weight on the Ends

Tension

Compression

Weight Curve Generation
• The weight curve can be generated by numerous methods:
• Distinct Items (same method as for LCG)
• Parabolic approximation
• Trapezoidal approximation
• Biles Method (similar to trapezoidal)
• They all give similar results for shear and bending moment calculations. Select based on the easiest in your situation.
Distinct Item Method

Each component is located by its l, t and v position and weight

Can be misleading for long components

Weight Item Information
• For each weight item, need W, lcg, fwd and aft

W

fwd

lcg

aft

FP

Trapezoid Method
• Models weight item as a trapezoid
• Best used for semi-concentrated weight items
• Need the following information:
• Item weight – W (or mass, M)
• Location of weight centroid wrt FP - lcg
• Forward boundary wrt FP - fwd
• Aft boundary wrt FP - aft
• lcg must be in middle 1/3 of trapezoid
Trapezoid Method
• Find l and x
• Solve for wfand wa so trapezoid’s area equals W and the centroid is at the lcg

FP

lcg

x

wa

G

wf

fwd

l/2

l

aft

Biles Method
• Used for weight items which are nearly continuous over the length of the ship.
• Assumes that weight decreases near bow & stern.
• Assumes that there is a significant amount of parallel middle body.
• Models the material with two trapezoids and a rectangle.
Biles Method

lcg

x

G

1.2h

wa

wf

aft

FP