Tank Sloshing in .NET Compose qr codes in .NET Tank Sloshing

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4.10 Tank Sloshing generate, create qrcode none with .net projects How to Use Visual Studio 2010 P(t). Po Pe Idealized I = Pe = P( t ) dt Figure 4.5. An impact-pressure action pro le and its idealization. Actual time concept that de nes an equivalent quasistatic pressure situation in place of the real impact-pressure situation. We recognize that this approach does not necessarily re ect the impact-pressure characteristics relevantly. The structural damage by this concept may be underestimated in some cases and overestimated in other cases, indicating that the concept is not consistent in terms of strength assessment.

However, by appropriate calibration in comparison to cases of damage versus no damage, it appears that workable design procedures can be attained as well. For practical design purposes, the problem of impact-pressure actions in terms of structural behavior can be idealized within three domains of behavior depending on the ratio of the duration of impact actions to the natural period of the structure, as follows (NORSOK 1999): r Quasistatic domain when 3 t/T r Dynamic/impact domain when 0.3 t/T < 3 r Impulsive domain when t/T < 0.

3 where t = duration of impact actions; and T = natural period of the structure. The impact-pressure action arising from green water, bow slamming, or sloshing is generally characterized by four parameters: (1) rise time until the peak pressure, (2) peak pressure, (3) pressure decay type beyond the peak pressure, and (4) pressure duration time, as illustrated in Figure 4.5.

The peak pressure value often approaches some 2 3 times the collapse pressure loads of structural components under quasistatic actions. But the rise time is very short, a few milliseconds or less. The duration (persistence) time of impact pressure is often in the range of 10 50 milliseconds.

It is important to realize that, unless anticipated and designed for, the structural damage due to impact-pressure actions can be signi cant even though the duration time is very short as long as the associated impulse itself is large enough (Paik et al. 2004). When the rise and duration times of impact pressure are very short, however, it is possible that the impact-pressure response can be approximated to an impulsive type of action that is characterized by only two parameters: equivalent peak pressure Pe and duration time , as long as the corresponding impulse is identical (Paik et al.

2004). In this case, it can then be approximated that the impact-pressure actions. Environmental Phenomena and Application to Design arising from sl oshing, slamming, or green water can be characterized by Pe and , as shown in Figure 4.5. The two parameters may be de ned so that the actual and idealized impulses of the impact-pressure action are equal: I = Pe = P (t) dt, (4.

6). where I = impul QR Code for .NET se of the impact-pressure action; t = time; Pe = effective peak pressure; and = duration time of Pe. Simple formulae to calculate sloshing impactpressure distribution for trading tankers that may be useful for ship-shaped offshore units are given by IACS (2005), applying the quasistatic equivalence concept.

Taking Pe as the same as Po (peak pressure value) can be unduly pessimistic for obvious reasons; thus, Pe is often obtained by multiplying a relevant knock-down factor to Po . Once the impulse I and the effective peak pressure value Pe are de ned, the duration time can then be determined from Eq. (4.

6). In predicting structural damage due to impact-pressure actions, Po and will be dealt with as parameters of in uence. An acceptance criterion to be safe against impact-pressure actions can be based on the serviceability limit state in terms of the permanent set de ection of ship-shaped offshore structure panels, as follows: wpa wp wpa , or 1 = 1, (4.

7a) wp where wp = factored permanent set de ection; wpa = allowable (factored) target value of permanent set de ection, which may be taken as a few times the plate thickness; and 1 = measure of structural adequacy related to the permanent set de ection. The acceptance criterion should also be considered for the ultimate limit state in terms of maximum pressure loads or associated impulse capacity, as follows: Pu Pd Pu , or 2 = 1, (4.7b) Pd Iu Id Iu , or 3 = 1, (4.

7c) Id where Pd , Id = design (factored) peak pressure or impulse at the design duration time, respectively; Pu , Iu = factored maximum impact pressure or impulse capacity at the corresponding duration time until structural failure (e.g., buckling, fracture) takes place, respectively; and 2 , 3 = measures of structural adequacy related to impact pressure or impulse capacity, respectively.

As indicated in Eq. (4.6), the impulse can be calculated by integrating the area below the impact pressure versus time history.

The maximum impact pressure and impulse capacity can be obtained by dynamic nonlinear structural behavior analyses using numerical methods such as those presented in Section 8.4.3 in 8.

It is important to realize that the dynamic nonlinear structural behavior may depend signi cantly on dynamic material properties (e.g., strain-rate sensitivity, viscoelasticity, damping) and, therefore, the effects of dynamic material properties should be taken into account in the dynamic structural capacity analyses.

Another important issue is damage accumulation. In reality, impact-pressure actions may be applied repeatedly; thus, the resulting structural damage can be.
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