Marine_Structural_Design Episode 9 doc

Chapter 14 qffshore Structures Under Impact Loads 299 possible procedure to account for the indentation effect is to reduce the plastic yield capacity of the element nodes at the impact

298 Part 11 Ultimate Strength

The plastic yield condition used in this example is the same as in EXAMPLE 14.2

The ABAQUS FEM analysis employs the true stresdtrue strain curve, shown in Figure 14.5

(b) This analysis assumes the material has linear kinematic strain hardening and each side of the beam is modeled as one element Figures 14.5 (c-e) show that the structural response is sensitive to the yield stress However, the agreement between the results predicted by both programs is good

The examples presented in this section demonstrated that the nodal displacements and forces predicted by the actual beam-column element agree with those obtained by experiments and

by general finite element program analyses Reasonable results can be obtained by the beam- column element even when the structural member is discretized by the absolute minimum number of elements (normally one element per member)

14.4.3 Application to Practical Collision Problems

The procedure implemented in the SANDY program can be used to simulate many different ship collision problems, such as side central collisions, bow collisions, and stem collisions

against structures like offshore platforms and ridges The simulation results include: motion

(displacements), velocities/accelerations of the striking and the struck structures, indentation

in the striking ship and the hit member, impact forces, member forces, base shear and overturning moments for the affected structures, kinetic energy, and elastidplastic deformation energy of the striking and the affected structures

In this section three typical ship collision problems are selected These are ship-unmanned, platform, and ship-jacket platform collisions

EXAMPLE 14.5: Unmanned Platform Struck by a Supply Ship

The small unmanned platform, shown in Figure 14.6 (a), which is struck by a 5000 ton supply vessel, is considered first The dominant design criterion for this platform type is often ship collisions, while it is normally wave loading for traditional platforms The supply ship is supported to drift sideways with a speed 2.0 ms-1 under calm sea conditions The added mass for the sideways ship sway motion is taken to be 0.5 times the ship mass The force-

indentation relationship for the ship is taken as is shown in Figure 14.6 (b) The added mass is

included following Morison's equation and the added mass and drag coefficients are taken to

be 1.0 The tubes under the water surface are assumed to be filled with water Therefore, the mass due to the entrapped water is also included The force-indentation relationship is

established by following Eqs (14.2) and (14.7) by following further approximations such as

multi-linear lines, as illustrated in Figure 14.6 (c) The soil-structure interaction is taken into account using linear springs

First, a linear analysis was carried out by using a load vector given by the gravity loading on the structures Then, a dynamic analysis considering large displacements, plasticity, and hardening effects followed The plastic yield condition was taken to be:

(14.24)

It is noted that the indentation in the hit tube will reduce the load carrying capacity of the tube greatly This effect has not been taken into account in the present analysis However, a

Chapter 14 qffshore Structures Under Impact Loads 299

possible procedure to account for the indentation effect is to reduce the plastic yield capacity

of the element nodes at the impact point using the procedure suggested by Yao et a1 (1986)

The numerical results are shown in Figures 14.6 (d-e) The effect of strain hardening in these figures is indicated; when the strain hardening is included, the structure becomes stiffer and more energy will be absorbed by the ship Therefore, the deck displacement is smaller, and the collision force and overturning moment increase

c Local force-indentation relati nship for the hit tube

d Deck displacement time history of the platform

e Impact force time history

f Overturning moment time history of the platform

EXAMPLE 14.6: Jacket Platform Struck by a Supply Ship

The four-legged steel jacket platform shown in Figure 14.7 (a) is struck by a 4590-ton supply ship Both the platform and the ship are existent structures The ship is supposed to surge into

the platform with the velocities 0.5, 2, and 6 ms-1 corresponding to operation impact, accidental impact, and passing vessel collision, respectively The force-indentation relationship for the ship bow is obtained using axial crushing elements in which a mean crushing force applied by a rigid-plastic theory has been adopted The local indentation curve for the hit tubular member in the jacket platform is established following Eqs (14.2) and

Chapter I4 qffshore Structures Under Impact Loads

(14.7) Both indentation curves are hrther approximated as multi-linear curves First, a linear

static analysis is carried out for the gravity loading and after, a nonlinear dynamic analysis is performed which includes fluid-structure interaction, soil-structure interaction, large displacements, and plasticity and kinematic strain-hardening effects for the affected platform The time history of the impact deflections is shown in Figure 14.7 (b) Figures 14.7 (c-e) show how the energy is shifted between the ship and the platform and between kinetic energy, elastic deformation energy, and plastic deformation energy

Using the present procedure, impact forces, dent in ship, and local dent depth of the hit member, can be obtained, provided the impact velocity and indentation curve of the ship are known The main results of the example are listed in Table 14.2

Finally, the distribution of the plastic nodes for an impact velocity of 5ms-1 at time 1.45s is shown in Figure 14.7(a)

Table 14.2 Main Results of Ship-Jacket Platform Collisions

302 Part II Ultimate Strength

Figure 14.7 Response caused by Collision between Supply Ship and

Jacket Platform

a Jacket platform struck by supply ship showing distribution of plastic nodes (Ship velocity, vo =Sins-' time

1.45s)

b Impact displacement time histories of the platform

c Time history of energies during ship impact on jacket platform (Impact velocity, V, = 0.5ms-')

d Time history of energies during ship impact on jacket platform Ompact velocity, V, = 2ms-' )

e Time history of energies during ship impact on jacket platform (Impact velocity, V, = 5ms-' )

Chapter I 4 Offshore Structures Under Impact Loads 303

14.5 Conclusions

A consistent procedure has been presented for collision analysis A nonlinear force- displacement relationship has been derived for the determination of the local indentation of the hit member and a three-dimensional beam-column element has been developed for the modeling of the damaged structure The elastic large displacement analysis theory and the plastic node method have been combined in order to describe the effects of large deformation, plasticity, and strain hardening of the beam-column members

The accuracy and efficiency of the beam-column elements have been examined through simple numerical examples by comparing the present results with those obtained by experiments and finite element program analyses using the MARC and ABAQUS programs It

is shown that the present beam-column elements enable accurate modeling of the dynamic plastic behavior of frame structures by using the absolute minimum number of elements per structural member

In addition, examples, where the dynamic elastic-plastic behavior of offshore platforms and bridges in typical collision situations is calculated, have been presented

All examples show that strain-hardening plays an important role in the impact response of the struck or affected structure The strain-hardening results in smaller deformations and more energy will be absorbed by the striking structure Therefore, the impact force is bigger Thus, a rational collision analysis should take the strain hardening effect into account

Bai, Y and Pedersen, P Temdrup, (1991), “Earthquake Response of Offshore Structure”, Proc 10th int Conf on Offshore Mechanics arctic Engineering, OMAEP1, June

Bai Y and Pedersen, P Temdrup, (1993), “Elastic-Plastic Behavior of Offshore Steel Structures Under Impact Loads”, Intemat J Impact Engng, 13 (1) pp.99-117

Ellinas, C.P and Walker, A.C (1983), “Damage of Offshore Tubular Bracing Members”, Proc IABSE Colloquium on Ship Collision with Bridges and Offshore Structures, Copenhagen, pp 253-261

Fujikubo, M., Bai, Y., and Ueda, Y., (1991), “Dynamic Elastic-Plastic Analysis of Offshore Framed Structures by Plastic Node Method Considering Strain-Hardening Effects”, Int J Offshore Polar Engng Conf 1 (3), 220-227

Fujikubo, M., Bai, Y., and Ueda, Y., (1991), “Application of the Plastic Node Method

to Elastic-Plastic Analysis of Framed Structures Under Cyclic Loads”, Int Conf on Computing in Engineering science, ICES’91, August

Petersen, M.J., and Pedersen, P Temdrup, (1981), “Collisions Between Ships and Offshore Platforms”, Proc 13th Annual offshore Technology Conference, OTC 41 34 Pedersen P Temdrup and Jensen, J Juncher, (1991), “Ship Impact Analysis for Bottom Supported Offshore Structures”, Second Int Conf on advances in Marine

304 Part 11 Ultimate Strength

structures, Dunfermline, Scotland, May 1991 (edited by Smith and Dow), pp 276-297

11 Ueda, Y Murakawa, H., and Xiang, D (1989), “Classification of Dynamic Response

of a Tubular Beam Under Collision”, Proc 8th Int Conf on Offshore Mechanics and Arctic Engineering, Vol 2, pp 645-652

Ueda, Y and Fujikubo, M., (1986), “Plastic Node Method Considering Strain- Hardening Effects”, J SOC Naval Arch Japan 160,306-317 (in Japanese)

Yao, T., Taby, J and Moan, T (1988), “Ultimate Strength and Post-Ultimate Strength Behaviour of Damaged Tubular Members in Offshore Structures”, J Offshore Mech Arctic Engng, ASMA 110,254-262

Yu, J and Jones, N (1989), ‘1vumerical Simulation of a Clamped Beam Under Impact Loading”, Comp Struct 32(2), 281-293

12

13

14

Part I1 Ultimate Strength

Chapter 15 Offshore Structures Under Earthquake Loads

15.1 General

Bottom supported offshore structures in seismic areas may be subjected to intensive ground shaking causing the structures to undergo large deformations well into the plastic range Previous research in this area has mainly resulted in procedures where the solutions have been sought in the frequency plane (Penzien, 1976) The present chapter is devoted to time domain solutions such that the development of plastic deformations can be examined in detail

The basic dynamics of earthquake action on structures has been discussed in Clough and Penzien (1975) and Chopra (1995) There have been extensive investigations on earthquake response of building structures in the time domain (Powell, 1973) Unfortunately, most of works have been limited to plane frames Furthermore, for offshore structures hydrodynamic loads have to be taken into account and the geometrical nonliearities become more important than in building structures Therefore, there is a need for a procedure to predict earthquake response of offshore structures including both geometrical and material nonlinearities

Methods for analysis of frame structures including geometrical nonlinearities have been based

on either the finite element approach (Nedergaard and Pedersen, 1986) or on the beam-column approach (Yao et al, 1986) Nedergaard and Pedersen, (1986) derived a deformation stiffness matrix for beam-column elements this matrix is a function of element deformations and incorporates coupling between axial and lateral deformations It is used together with the linear and geometrical stiffhess matrices

Material nonlinearity can be taken into account in an efficient and accurate way by use of the plastic node method (Ueda and Yao, 1982) Using ordinary finite elements, the plastic deformation of the elements is concentrated to the nodes in a mechanism similar to plastic hinges Applying the plastic flow theory, the elastic-plastic stiffness matrices are derived without numerical integration

In this Chapter, a procedure based on the finite element and the plastic node method is proposed for earthquake response analysis of three-dimensional frames with geometrical and material nonlinearities Using the proposed procedure, earthquake response of a jacket platform is investigated Part of this Chapter appeared in Bai and Pedersen (1991) The new extension is to outline earthquake design of fixed platforms based on API RF'2A

15.2 Earthquake Design as per API FW2A

API RP2A (1991) applies in general to all fixed platform types Most of the recommendations are, however, typical for pile steel jacket platforms The principles and procedures given in

306 Part II Ultimate Strength

API (1991) are summarized below The design philosophy for earthquake leads in API (1991)

is illustrated in Table 15.1

Table 15.1 Earthquake Design Philosophy, API RP2A

I Strength Level Earthquake (SLE)

No significant structural damage, essentially elastic response

Ductility Level Earthquake @LE) I

Prevent loss of life and maintain well control

Rare intense ground shaking that unlikely to occur during the platform life

No collapse, although structural damage is allowed; inelastic response

The AFT’S seismic design recommendation are based upon a two level design approach, these are

Strength Requirements

The platform is designed for a severe earthquake which has reasonable likelihood of not being exceeded during the platform life (typical return period hundreds of years, Strength Level Earthquake SLE)

Ductility Requirements

The platform is then checked for a rare earthquake with a very low probability of occurrence (typical return period thousands of years, Ductility Level Earthquake DLE) The objective of the strength requirements is to prevent significant interruption of normal

platform operations after exposure to a relatively severe earthquake Response spectrum method of time history approach is normally applied

The objective of the ductility requirements is to ensure that the platform has adequate capacity

to prevent total collapse under a rare intense earthquake Member damage such as in-elastic member yielding and member buckling are allowed to occur, but the structure foundation system should be ductile under severe earthquakes, such that it absorbs the imposed energy The energy absorbed by the foundation is expected to be mostly dissipated through non-linear behaviour of the soil

For some typical jacket structures, both strength and ductility requirements are by API

considered satisfied if the below listed previsions are implemented in the strength design of these platforms:

Strength requirements for strength level earthquake loads (SLE) are in general documented Strength requirements are documented for jacket legs, including enclosed piles, using 2 times the strength level earthquake loads (Le 2*SLE)

Rare, intense earthquake ground motion is less than 2 times the earthquake ground motions applied for documentation of strength level requirements (Le DLE < 2*SLE)

Chapter15 offshore Structures Under Earthquake Loads

Geometrical and ultimate strength requirements for primary members and their connections as given in API are satisfied These requirements concern number of legs, jacket foundation system, diagonal bracing configuration in vertical frames, horizontal members, slenderness and diameter/thickness ratio of diagonal bracing, and tubular joint capacities

15.3 Equations and Motion

an assembly of three-dimensional ground motions

We shall here assume that at the time of the earthquake there is no wind, wave or current loading on the structure According to the Morison equation (Sarpkaya and Isaacson, 1981),

the hydrodynamic load per unit length along a tubular beam member can be evaluated as

where p is the mass density of the surrounding water, D is the beam diameter, CA is an added mass coefficient, CD the drag coefficient, A=xD2/4, and {ti"} denotes the normal components

of the absolute velocity vector The absolute velocity vector is

Using a standard lumping technique, Eq (15.1) can be rewritten as

where [Ma] is an added mass matrix containing the added mass terms of Eq (15.2) The increments of drag force terms from time (t) to (t+dt) are evaluated as

(@D 1 = c [ T + d t I' V D - c [T 1' {fD >o (15.5) where denotes summation along all members in the water, while {fD} are results of integration of the drag force terms of Eq (15.2) along the member [TJ is the transformation matrix the equations of motion Eq (1 5.4) are solved by the Newmark-P method (Newmark, 1959)

308 part II Utimate Strength

15.3.2 Nonlinear Finite Element Model

The finite element model was given in Part I1 Chapter 12

Some of the features of the present analysis procedure are:

A acceleration record, such as EL CENTRO N-S, is scaled by a scale factor to match the probable earthquake in the areas where the structure will be installed

A frame model is established by three-dimensional finite elements Soil structure interaction is taken into account by used of spring elements

Fluid-structure interaction is induced The contribution form the added mass in taken into

accounted by an increase of the mass of the beam-column element s the drag forces are

treated as external loads

A linear static analysis is performed for the structure subjected gravity loading The results

are used as an initial condition for the subsequent dynamic analysis

The structure mass matrix may consist of both masses applied directly at the nodes, and element masses which are evaluated using either a lumped mass method or a consistent mass method

Geometrical and material nonlinearities are taken in account by use of the theory described in the proceeding chapters

Time history, and maximum and minimum values of displacements, and forces are presented

as calculation results From these results, the structural integrity against the earthquake is assessed

The procedure has been implemented in the computer program SANDY (Bai, 1990), and used

in several analyses

15.4 Numerical Examples

EXAMPLE 15.1: Clamped Beam Under Lateral Load

This example (see Figure 15.1) is chosen to show the efficiency of the present procedure In the present analysis, only one beam-column element is used to model half of the beam The

linear and geometrical stiffness matrices as well as the deformation matrix are used The plastic yield condition used for rectangular cross-section is taken as

(15.6)

where the subscript “p“ indicates fully-plastic values for each stress components

Figure 15.1 shows that the present results agree with the experimental results and the limit load theory results (Haythomthwaite, 1957) The limit load is P, when the geometrical nonlinearity is not taken into account

ChapterI5 Oflshore Structures Under Earthquake Loads 309

b.wldIh of h a m

unit mm

E = I379 Y IO' Nlmm'

P =qbIy/L 4.253.05 Nlmm'

Central deflrclion w l l

Figure 15.1 Elastic-Plastic Large Displacement Analysis of a Clamped

Beam Under Central load

310 Part II Ultimate Strength

27.318 N/mm 29.244 N/mm

(4 Roof

c

49.550 Nlmm (b) All floors

64496 N

Figure 15.3 Lumped Masses and Static Loads Applied on the 2-D Frame

EXAMPLE 15.2: Two-Dimensional Frame Subjected to Earthquake Loading

The ten story, three bay frame shown in Figure 15.2 has been taken from the user's guide of

DRAIN-2D, which is a well known nonlinear earthquake response analysis program for plane

structures (Kannan and Powell, 1973) Using the static load shown in Figure 15.3, a linear

static analysis is performed The results are used as the initial conditions for the dynamic

analysis The frame has been analyzed for the first 7seconds of the EL CENTRO, 1940, N-S

record, scaled by a factor of 1.57, to give a peak ground acceleration of 0.5 g the mass lumped

at the nodes are based on the dead load of the structure The damping matrix is determined as

[C] = 0.3 [MI The frame is modeled by using one element per physical member Horizontal

nodal displacements at each floor are constrained to be identical In the analysis, the

geometrical nonlinearity is not taken into account The plastic yield condition for the i steel

beam is assumed as:

Typical results are shown in Figure 15.4, together with those predicted by DRAIN-2D The

agreement between the two programs is good

EXAMPLE 15.3: Offshore Jacket Platform Subjected to Earthquake Loading

The four-legged steel jacket platform shown in Figure 15.5 is an existing structure It is

subjected to a horizontal earthquake loading The applied ground acceleration time history is

again the first 7 seconds of EL CENTRO N-S, with amplification factors A linear static

analysis is carried out using dead load applied on the deck Fluid-structure interaction, soil-

structure interaction, and geometrical and material nonlinearities are taken into account Each

structural member is modelled as only one beam-column element The plastic yield condition

used for thin-walled circular tubs is expressed as

( K I M , Y + (My / M Y P Y + (Mz / M z p Y +

(15.8)

The effects of earthquake acceleration amplification factors have been shown in Figure 15.8

Plastic nodes have been observed when the amplification is bigger than 2.25 the distribution

of plastic nodes at time 3.00 second for a scale factor 4.5 has been shown in Figure 15.5 The

ChapterI5 qffshore Structures Under Earthquake Loads 311

structure undergoes large deformations as well as plasticity when it is subjected to intensive ground shaking

-

-400 600 t

Figure 15.4 Time History of Roof Displacement for the 2-D Frame

Plaslic

Figure 15.5 Offshore Jacket Platform Subjected to Earthquake Loading

Showing Distribution of Plastic Nodes (Earthquake Scale Factor 4.5, Time 3.0 Second)

312 Part II UIiimate Strength

- Including drag forcer

Not including drag forces

-1200 -800 t

Figure 15.7 Hydrodynamic Damping Effect Associated With Drag Forces

(Earthquake Acceleration Scale Factor 3.0)

Figure 15.7 shows time histories of the lateral displacements at the deck of the platform in X- direction for a scale factor 3.0 It is observed that in this example the hydrodynamic damping effect associated with drag forces can be ignored

Figure15.8 Presents foundation stifiess effects on the time histories of the lateral displacements The vibration period and maximum displacement increase greatly as the soil stiffness decrease No plastic node has been observed when soil stiffness has been scaled by a factor 0.1 This figure also shows the importance of modelling soil-structure interaction reasonably accurate The maximum value of the lateral displacement will be very large and it will cause problems for the piping system and equipment on the deck

ChapterI5 Offshore Structures Under Earthquake Loads

The numerical examples show that the procedure is efficient and accurate In addition time to prepare input data is low It can also be applied to nonlinear dynamic response analysis of offshore structures under collision loads

From Example 15.3, the following results have been observed

In an analysis of a structure subjected to strong earthquake loading, It is important to take both geometrical and material nonlinearities into account

The hydrodynamic damping effects associated with drag forces are small

The foundation stiffness effects are very significant and it is important to accurately model

soil-structure interaction

Archer, J.S., (1965), “Consistent Matrix Formulations for Structural Analysis using Finite Element Techniques”, AIAAjoumal, Vol 3, pp 1910-1918

Bai, Y., (1990), “SANDY-A Structural Analysis Program for Static and Dynamic Response of Nonlinear Systems”, Theoretical Manual User’s Manual and Demonstration Problem Manual, Century Research Center Corporation, Japan

Bai, Y and Terndrup Pedersen, P (1991), “Earthquake Response of Offshore Structures”, Proc 10” int Conf on Offshore Mechanics Arctic Engineering, OMAE ‘91, June

Chopra, A.K (1995), “Dynamics of Structures, Theory and Applications to Earthquake Engineering”, Prentice-Hall, Inc

Clough, R.W and Penzien, J (1979, “Dynamics of Structures”, MsGrwa-Hill

Haythomthwaite, R.M., (1957), “Beams with Full End Fixity”, Engineering, Vol 183 pp

1 10-1 12

Kannan, A.E and Powell, G.H., (1973), “DRAIN-2D - A General Purpose Computer

Program for Dynamic Response of Inelastic Plane Structures”, User’s Guide, Report No

EERC 73-6 University of California, Berkeley

Nedergaard, H and Pedersen, P.T., (1986), “Analysis Procedure for Space Frames with Material and Geometrical Nonlinearities”, Europe-US Symposium - Finte Element Methods for Nonlinear Problems, Edited by Bergan, Bathe and Wunderlich, Springer, pp

Newmark, N.M., (1 959), “A Method of Computation for Structural Dynamics”, Journal

of Engineering Mechanics Division, ASCE, Vol 85, pp 67-94

Penzien, J., (1976), “Seismic Analysis of Gravity Platforms Including Soil-sttructure Interaction Effects”, Offshore Technology Conference (OTC), Paper No 2674

Przemieniecki, J.S., (1968), “Theory of Matrix Structural Analysis”, McGraw-Hill, Inc Sarpkaya, T and Isaacson, M., (1981), “Mechanics of Wave Forces on mshore Structures”, Van Nostrand Reinhold Company

Ueda, Y and Yao, T., (1982), “The Plastic Node Method: A New Method of Plastic Analysis”, Computer Methods in Applied Mechanics and Engineering, Vol 34, pp

Yao, T., Fujikubo, M., Bai, Y.; Nawata T and Tamehiro, M., (1986), “Local Buckling

of Bracing Members in Semi-submersible Drilling Unit (1” Report)”, Journal of the Society of Naval Architects of Japan, Vol 160, pp 359-371 (in Japanese)

211-230

1089-1104

Part 111: Fatigue and Fracture

Part I11 Fatigue and Fracture Chapter 16 Mechanism of Fatigue and Fracture

16.1 Introduction

Fatigue is the cumulative material damage caused by cyclic loading Many structural members must withstand numerous stress reversals during their service life Examples of this type of loading in marine structures include alternating stresses associated with the wave induced loading, vortex-induced-vibration (VIV) and load fluctuations due to the wind and other environmental effects In the following Sections, the basic fatigue mechanism will be reviewed A detailed theoretical background for fatigue analysis is given by Almar-Naess (1985), Gurney (1979), Maddox (1991), Suresh (1991), Dover and Madhav Rao (1996) An

extensive list of recently published papers may be found from the proceedings of ISSC (1988,

1991, 1994, 1997, 2000) AWS (1985) can be considered as a representative code for fatigue strength design Recent developments in ship fatigue research may be found in Xu (1997) and

Basic mechanism of fatigue and fracture

Fatigue criteria such as S-N curves, stress concentration factors

Fatigue loads and stresses determined based on deterministic methods, stochastical methods and Weibull distribution

Simplified fatigue assessment based on a Weibull distribution of long-term stress range

Spectral fatigue analysis and time-domain fatigue analysis and their applications to structural design

Fracture mechanics and its applications to the assessment of crack propagation, final fracture and calibration of fatigue design S-N curves

Material selection and damage tolerance criteria

16.2 Fatigue Overview

Generally, the load amplitude of each cycle is not large enough to cause the structural failure

by itself But failure could occur when the accumulated damage experienced by the structure reaches a critical level The fatigue life of a structural detail is directly linked to the fatigue process, which can be grouped into the following three stages:

Crack initiation