Especificaciones de requerimientos del sistema

CAPÍTULO 1: FUNDAMENTACIÓN TEÓRICA

2.5 Especificaciones de requerimientos del sistema

3.1 Nature of Ship Structural Response. The re-sponses of structural components of the ship hull to ex-ternal loads are usually measured by either stresses or deﬂections. Structural performance criteria and the asso-ciated analyses involving stresses are referred to under the general term of strength, whereas deﬂection-based considerations are referred to under the term stiffness.

The ability of a structure to fulﬁll its purpose can be

measured by either or both strength and stiffness con-siderations. The strength of a structural component is inadequate and structural failure would be deemed to have occurred if the component’s material experienced a loss of load-carrying ability through fracture, yield, buck-ling, or some other failure mechanism in response to the applied loading. On the other hand, excessive de-ﬂection may also limit the structural effectiveness of

The detailed procedure for computing the internal tank pressure load for structural evaluation can be found in classiﬁcation rules.

2.10 Transverse Distribution of Wave Loads. To com-pute the secondary or tertiary response of structural components such as panels of stiffened or unstiffened plating, it is necessary to know the distribution of ﬂuid pressures and acceleration loads acting on the surface of the panels. For the purpose of analyzing transverse strength, the distribution of loads transversely around the ship section is required.

To predict the dynamic loads for design and analy-sis, linear strip theory has been widely used as a prac-tical analysis tool. Linear theory has proven to be robust, computationally fast, and provides reasonably accept-able results. However, it does not predict certain nonlin-ear loads, such as the nonlinnonlin-ear hull girder bending and torsional moments and the pressure loads acting on lo-cal structural members, particularly above the still water line, which are crucial in the structural design of vessels for the extreme design condition.

With the advances in free-surface hydrodynamic com-putational methods and improvements in computing speed in the past decade, nonlinear seakeeping computer codes dealing with the nonlinear extreme motions and loads have been developed and are available in the indus-try, as described in Section 2.5. These nonlinear codes show satisfactory predictions for the vertical plane of motion but require further improvements for the lateral plane of motion. As such, the prediction of pressure loads for design and evaluation of local structures con-tinues to rely on the linear strip theory.

The wave and motion-induced distribution of pressure calculated from a linear strip theory is shown in Fig. 36 (Kim 1982). The two plots in this ﬁgure give the ampli-tude (but not the phase) of the dynamic pressure varia-tion around the midship secvaria-tion, and this includes the ef-fects of both ship and wave motions. It can be seen that the greatest dynamic pressure variation is found near the water line in all cases, and in beam or bow seas the am-plitude is greatest on the side facing the incoming waves.

The lowest amplitude of pressure variation is found in

h_dl h

h or h_dl whichever is less

h_d : Hydrodynamic Pressure Head ( ( indicates negative) h_s : Hydrostatic Pressure Head in Still Water

h_t : Total External Pressure Head

h_dl: Hydrodynamic Pressure Head at Waterline h : Freeboard

Fig. 37 Transverse distribution of total external pressure head.

the vicinity of the keel, which will experience the great-est static pressure. It is noted that the pressures in the wave above the still water line are not obtained because the linear hydrodynamic theory computes the ﬂuid force on only the mean immersed portion of the ship. The pres-sure in this area must therefore be estimated separately.

In practical applications, the pressure distribution above the mean water line is generally approximated by a static head of the same value as the dynamic load at mean water line as shown in Fig. 37, where the distribu-tion of total pressure (hydrodynamic and still water) of a vessel in a beam sea condition is presented. In this exam-ple, the hydrostatic pressure offsets the negative hydro-dynamic pressure on the leeward side, whereas on the side exposed to the wave static pressure is added to the dynamic part. This represents a quasi-static pressure dis-tribution of the vessel rolling into the wave where the racking stresses due to rolling reach a maximum in a beam sea each time the vessel completes an oscillation in one direction and is about to return.

Section 3 Analysis of Hull Girder Stress and Deﬂection

The ability of a structure to fulﬁll its purpose can be

a member even though material failure does not oc-cur. If that deﬂection results in a misalignment or other geometric displacement of vital components of the ship’s machinery, navigational equipment, or weapons systems, the system is rendered ineffective.

The present section is concerned with the determi-nation of the response, in the form of stress or deﬂec-tion, of structural members to the applied loads. Once these responses are known, it is necessary to determine whether the structure is adequate to withstand the de-mands placed upon it, and this requires consideration of the several possible failure modes, as discussed in detail in Section 4.

In analyzing the response of the ship structure, it is convenient to subdivide the structural response into cat-egories logically related to the geometry of the structure, the nature of the loading, and the expected response.

Appropriate methods are then chosen to analyze each category of structural component or response, and the results are then combined in an appropriate manner to obtain the total response of the structure.

As noted previously, one of the most important char-acteristics of the ship structure is its composition of an assemblage of plate-stiffener panels. The loading applied to any such panel may contain components in the plane of the plating and components normal to the plane of the plating. The normal components of load originate in the secondary loading resulting from ﬂuid pressures of the water surrounding the ship or from internal liq-uids, and in the weights of supported material such as a distributed bulk cargo and the structural members them-selves. The in-plane loading of the longitudinal members originates mainly in the primary external bending and twisting of the hull. The most obvious example of an in-plane load is the tensile or compressive stress induced in the deck or bottom by the bending of the hull girder in re-sponse to the distribution of weight and water pressure over the ship length.

The in-plane loads on transverse members such as bulkheads result from the edge loads transmitted to these members by the shell plate-stiffener panels and the weights transmitted to them by deck panels. In-plane loads also result from the local bending of stiffened panel components of structure. For example, a panel of stiff-ened bottom plating contained between two transverse bulkheads experiences a combined transverse and lon-gitudinal bending in response to the fluid pressure act-ing upon the panel. In turn, this panel bendact-ing causes stresses in the plane of the plating and in the flanges of the stiffening members. Finally, the individual panels of plating contained between pairs of stiffeners undergo bending out of their initial undeformed plane in response to the normal fluid pressure loading. This results in bend-ing stresses, and the magnitudes of these stresses vary through the plate thickness.

To perform an analysis of the behavior of a part of the ship structure, it is necessary to have available three

types of information concerning the structural compo-nent:

r

The dimensions, arrangement, and material proper-ties of the members making up the component

r

The boundary conditions on the component (i.e., the degree of ﬁxity of the connections of the component to adjacent parts of the structure)

r

The applied loads.

In principle, it is possible using a computer-based method of analysis, such as the ﬁnite element method, to analyze the entire hull at one time without the necessity of such subdivision into simpler components. However, there are at least two reasons for retaining the subdivi-sion into simpler components:

r

By considering the structural behavior of individual components of structure and their interactions with each other, a greater understanding is developed on the part of the naval architect of their functions, and this leads to an improved design.

r

Many of the problems facing the practicing naval ar-chitect involve the design or modiﬁcation of only a lim-ited part of a ship, and a full-scale analysis would be nei-ther necessary nor justiﬁed.

A brief introduction to the ﬁnite element procedure is given in Section 3.16. It is a powerful tool that is widely and routinely used in most aspects of modern structural analysis, and standard computer programs are available from computer service bureaus and a number of other sources.

As noted in Section 2.2, it is convenient to subdi-vide the structural response into primary, secondary, and tertiary components, and we shall here exam-ine these components in detail. Note that the primary and secondary stresses in plate members are mem-brane stresses, uniform (or nearly uniform) through the plate thickness. The tertiary stresses, which result from the bending of the plate member itself, vary through the thickness but may contain a membrane component if the out-of-plane deﬂections are large compared to the plate thickness.

From this, it is seen that the resultant stress at a given point in the ship structure is composed of several parts, each of which may arise from a different cause. In many instances, there is little or no interaction among the three (primary, secondary, tertiary) component stresses or deﬂections, and each component may be computed by methods and considerations entirely independent of the other two. In such cases, the resultant stress is ob-tained by a simple superposition of the three component stresses. An exception occurs if the plate (tertiary) de-ﬂections are large compared the thickness of the plate.

In this case, the primary and secondary stresses will in-teract with this tertiary deﬂection and its corresponding

stress, so that simple superposition may no longer be em-ployed to obtain the resultant stress.

Fortunately for the ship structural analyst, such cases rarely occur with the load magnitudes and member scantlings used in ships, and simple superposition of the three components can usually be performed to obtain the total stress. In performing this superposition, the rel-ative phasing in time of the components must be kept in mind if the components represent responses to time-varying loads such as those caused by waves. Under such circumstances, for a particular location in the structure such as a point in the bottom plating, the maximum value of the primary stress may not necessarily occur at the same instant of time as the maximum of the secondary or tertiary stress at that same location (see sections 2.6.6 to 2.6.8 for more information on combining loads and stresses).

3.2 Primary Longitudinal Bending Stress. For the most part, the structural members involved in the com-putation of primary stresses are the longitudinally con-tinuous members such as deck, side, bottom shell, lon-gitudinal bulkheads, and continuous or fully effective longitudinal primary or secondary stiffening members.

However, the deﬁnition of primary stress also refers to the in-plane stress in transverse bulkheads due to the weights and shear loads transmitted into the bulkhead by the adjacent decks, bottom, and side shells.

Elementary Bernoulli-Euler beam theory is usually used in computing the component of primary stress or deﬂection due to vertical or lateral hull bending loads.

In assessing the applicability of this beam theory to ship structures, it is useful to restate the underlying assump-tions:

r

The beam is prismatic (i.e., all cross sections are the same).

r

Plane cross sections remain plane and merely rotate as the beam deﬂects.

r

Transverse (Poisson) effects on strain are neglected.

r

The material behaves elastically, with the moduli of elasticity in tension and compression being equal.

r

Shear effects (stresses, strains) can be separated from, and do not inﬂuence, bending stresses or strains.

Many experiments have been conducted to investigate the bending behavior of ships or ship-like structures as noted—for example, in Vasta (1958). In many cases, the

Shear Stress Long’l Sress

-Shear Stress l in. = 5,000 psi Long’l Stress l in. = 10,000 psi

Note-- SS Ventura Hills (Basic) - SS Fort Mifflin (Adjusted) - SS Ventura Hills (Basic) - SS Fort Mifflin (Adjusted) Theoretical

Theoretical

(+) (+)

(+)

(−) (−)

(−) Vertical

Shear Stress Distribution

Longitudinal Bending Stress

Distribution C Ship L

Fig. 38 Shear and bending moment study on tankerVentura Hills (Vasta 1958).

q(x)= LOAD DISTRIBUTION

w(x)= DEFLECTION

POSITIVE BENDING MOMENT POSITIVE SHEAR FORCE O X

COMPR.

TENS. σx = STRESS

DISTRIB UTION

Fig. 39 Nomenclature for shear, deﬂection, and loading of elementary beam.

results agree quite well with the predictions of simple beam theory, as shown in Fig. 38, except in the vicinity of abrupt changes in cross section.

In way of deck openings, side ports, or other changes in the hull cross sectional structural arrangements, stress concentrations may occur that can be of determining im-portance in the design of the structural members. Proper design calls for, ﬁrst, the avoidance where possible of abrupt changes in geometry and, second, the introduc-tion of compensating structural reinforcements such as doubler plates where stress concentrations cannot be avoided. In most cases, serious stress raisers are asso-ciated with local features of the structure, and the de-sign of such features is treated in detail in Chapter 17 of Lamb (2003). Because stress concentrations cannot be avoided entirely in a highly complex structure such as a ship, their effects must be included in any comprehen-sive stress analysis. Methods of dealing with stress con-centrations are presented in Section 3.13.

The derivation of the equations for stress and deﬂec-tion under the assumpdeﬂec-tions of elementary beam theory may be found in any textbook on strength of materials—

for instance, Timoshenko (1956). The elastic curve equa-tion for a beam is obtained by equating the resisting mo-ment to the bending momo-ment, M, at section x, all in con-sistent units:

EId²w

dx² = M(x) (131)

where

w = deﬂection (Fig. 39)

E= modulus of elasticity of the material I= moment of inertia of beam cross section

about a horizontal axis through its centroid.

This may be written in terms of the load per unit length, q(x), as:

EId⁴w

dx⁴ = q(x) (132)

The deﬂection of the ship’s hull as a beam is obtained by the multiple integration of either of equations (131) or (132). It can be seen that the deﬂection—hence, the stiffness against bending—depends upon both geometry (moment of inertia, I) and elasticity (E). Thus, a reduc-tion in hull depth or a change to a material such as alu-minum (E approximately one third that of steel) will re-duce the hull stiffness.

Because flexibility is seldom a problem for hulls of normal proportions constructed of mild steel, primary structures are usually designed on the basis of strength considerations rather than deflection. However, classifi-cation society rules deal indirectly with the problem by specifying a limit on the L/D ratio of 15 for ocean-going vessels and 21 for Great Lakes bulk carriers (which ex-perience less severe wave-bending moments). Designs in which L/D exceeds these values must be “specially considered.” There is also a lower limit on hull girder moments of inertia, which likewise have the effect of

limiting deflection, especially if high-strength steels are used. A limit on the moment of inertia will also influence the vibrational response of the ship. An all-aluminum al-loy hull would show considerably less stiffness than a steel hull having the same strength. Therefore, classifica-tion societies agree on the need for some limitaclassifica-tion on deflection, although opinions differ as to how much.

Regarding strength considerations, the plane section assumption together with elastic material behavior re-sults in a longitudinal stress,σx, in the beam that varies linearly over the depth of the cross section. The condi-tion of static equilibrium of longitudinal forces on the beam cross section is satisﬁed ifσxis zero at the height of the centroid of the area of the cross section. A trans-verse axis through the centroid is termed the neutral axis of the beam and is a location of zero stress and strain. Accordingly, the moment of inertia, I, in equa-tions (131) and (132) is taken about the neutral axis.

The longitudinal stress in section x is related to the bending moment by the following relationship, as illus-trated in Fig. 39:

σx=−M(x)

I z (133)

It is clear that the extreme stresses are found at the top or bottom of the beam where z takes on the numerically largest values. The quantity SM= I/zo, where zois either of these extreme values, is the section modulus of the beam. The extreme stress, deck or bottom, is given by

σxo= −M(x)

SM (134)

The sign of the stress, either in tension or compression, is determined by the sign of zo. For a positive bending moment, the top of the beam is in compression and the bottom is in tension (sagging condition). The computa-tion of the seccomputa-tion modulus for a ship hull cross seccomputa-tion, taking into consideration all of the longitudinally contin-uous, load-carrying members, is described later in this section.

Two variations on the previous beam equations may be of importance in ship structures. The ﬁrst concerns beams composed of two or more materials of different moduli of elasticity, for example, steel and aluminum. In this case, the ﬂexural rigidity, EI, is replaced by

E(z)z²d A= 0 (135)

where

A= cross sectional area

E(z)= modulus of elasticity of an element of area dAlocated at distance z from the neutral axis.

A second related modiﬁcation may be described by considering a longitudinal strength member composed of a thin plate with transverse framing. For example, this might represent a portion of the deck structure of a

trans-versely framed ship. Consider one module of a repeated system of deck plate plus transverse frame, as shown in Fig. 40, that is subject to a longitudinal stress,σx, from the primary bending of the hull girder. As a result of the

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