Iosif StrucDesign

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1 INTRODUCTION

1.1 Large Pipe Bends for Water Industry

GHD has undertaken a number of Finite ElementAnalyses [7] on a range of large pipe segmented

bends on behalf of a Water Authority Client. Theaim of this study was to develop an alternative

design methodology in the belief that currentstandards such as AS 4041 was producinguneconomical designs.

The results of the study indicate that localisedpeak stresses approximately twice as much as thenormal pipe hoop tension develop on the inside ofthe mitre cut joint (intrados). The major finding ofthis study was that the intrados stress wasindependent of the segment length, which is indisagreement with current Standards in Australia(AS 4041) and the United States (ANSI/AWWAC208). An alternative design methodology was

proposed such that the peak stress on the inside ofthe mitre cut joint be limited to yield based on theVon Mises Criterion for combined stress.

1.2 Dubai Drydocks

GHD was contracted to conduct FE analyses toinvestigate and assess the structural integrity ofDubai Drydocks Caissons and provide a moreeconomical optimized re-design of the caissonswalls. Complex analyses of Ultimate Loadcase

Combinations concluded that a number of redundantwalls can be removed without affecting thestructural integrity of the Caissons and substantiallyreducing Clients repairs and maintenance costs.

1.3 Tank Vibration

High vibration levels were observed and recorded ona spent surge liquor tank typical to AluminaIndustry. Such vibrations are known to lead tocatastrophic fatigue failures and therefore must becontained.

GHD designed structural modifications to thetank based on the analysis of the natural frequenciesof the tank and its internals, stress levels, modeshapes and participation factors.

2 TECHNICAL APPROACH AND FEMODELLING


A literature review of relevant design models eithercurrently or previously relevant to segmented pipe

bends was undertaken as a preliminary phase. Thekey design codes and their approach to the design ofmitre bends is essentially given by: AWWA C208 1996 [2] and 2001 [3]. Thesestandards recommend dimensions only and do notaddress working pressures or admissible stress.Reference is made to AWWA M11 [4] for dealingwith these parameters. An Official Note to C208 [1] was given whichrecommends the following relationship be used forR/D


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P = pressure

A = segment length as in Figure 1

D = diameter

Sa = admissible stress (0.5 x yield stress of material)

= segment angle as shown in Figure 1

Figure 1. FE model and terminology

For R/D = 2.5 and above, the bend can be treatedas a straight pipe with admissible stress given bymaximum admissible hoop stress. In terms ofmaximum admissible hoop stress, AWWA M11 [4]sets this limit to 0.5 x yield stress based on steadystate pressure while ANSI/ASME B31.3 and AS4041 sets this limit to a maximum of 0.67 x yieldstress based on full working pressure. According to AWWA M11 [4] a safety factor ofat least two to ultimate tensile stress isrecommended for maximum working pressure. In

other words a bend designed for Working PressureWP should not reach UTS at pressure 2 x WP.AS 4041 - Appendix I nominates a safety factor onUTS of 2.35.

AS4041-1998 Pressure Piping Clause 3.15.4.3

recommends multiple mitre bends angle of cut to be

less than 22.5 and allowable working pressures to

be the lesser calculated from two equations.

Equation (1) is independent of the segment length

and is the most limiting and generally to less than

half of normal hoop stress. Equation (2) is based on

the same parameter as C208 (1) above and is

dependent on segment length A.

In the light of the abovementioned Standards,calculations have been performed to plot various

design methods. Figure 2a shows the WorkingPressure vs. Segment Length A for a bend of OD1400 and t=11 mm. This figure compares the abovestandards with the FEA analysis and the currentWater Authority standard rating.

Figures 2a, 2b, 2c: Standards recommendations

The curves represented in Figure 2a, 2b and 2c showquite different allowable maximum working

pressures depending on which method of analysis is

used.In Figure 2a the plots show that for AS 4041, the

equation 1 criteria in all cases set the maximumadmissible pressure. This equation does not takeinto account the dimension A in the segmented bend.


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The two upper curves are based on AWWA C208 -M11 and AS 4041 equation 3.15.4.3(2). Theserelationships include in their formulation: segmentlength A and the dependency on bend radius R ie(R=f(A)).

Three distinct diameter bends were analysed forvarious segment length A including:

FEA model 1: OD 1400, t=11mm, A=400 mm FEA model 2: OD 1400, t=11mm, A=1050 mm FEA model 3: OD 1400, t=11mm, A=725 mm FEA model 4: OD 1000, t=8mm, A=300 mm FEA model 5: OD 1000, t=8mm, A=600 mm FEA model 6: OD 1000, t=8mm, A=900 mm FEA model 7: OD 500, t=5mm, A=200 mm FEA model 8: OD 500, t=5mm, A=400 mm FEA model 9: OD 500, t=8mm, A=600 mm

These nine models were analysed for a wide rangeof internal working pressures (WPs). Since someWPs produced stress above the yield point of the

material, the non-linear module of AbaqusTM wasused.

The following material properties were assignedto the models:Youngs modulus 210,000 MPaPoissons ratio 0.29For OD 1000 and OD 500 bends:Yield stress =300 MPa with strain hardening to UTS410 MPaFor OD 1400:Yield stress 250 MPa with strain hardening to UTS

410 MPaThe models consist of shell elements with 6 degreesof freedom and five integration (Gauss) pointsacross thickness. The FE models were built with

pipe legs of approximately 10 times the diameter ofthe bend and were constrained as shown in Figure 1.

2.2 Dubai Drydocks

Effects associated with the rebar/concrete interface,such as bond slip and dowel action, are modeledapproximately by introducing some tensionstiffening into the concrete modeling to simulateload transfer across cracks through the rebar.

The postfailure behavior for direct straining acrosscracks is modeled with the TENSION STIFFENINGoption, which allows the user to define the strain-softening behavior for cracked concrete. This isachieved by specifying a postfailure stress-strainrelation or by applying a fracture energy crackingcriterion.

Postfailure stress-strain relation

Specification of strain softening behavior inreinforced concrete generally means specifying the

postfailure stress as a function of strain across thecrack. The tension stiffening effect depends on suchfactors as the density of reinforcement, the quality of

the bond between the rebar and the concrete, therelative size of the concrete aggregate compared tothe rebar diameter, and the mesh. A reasonablestarting point for relatively heavily reinforcedconcrete modeled with a fairly detailed mesh is toassume that the strain softening after failure reducesthe stress linearly to zero at a total strain of about10 times the strain at failure. The strain at failure in

standard concretes is typically 10

-4

, which suggeststhat tension stiffening that reduces the stress to zeroat a total strain of about 103 is reasonable.

The choice of tension stiffening parameters isimportant in ABAQUS/Standard since,generally, more tension stiffening makes iteasier to obtain numerical solutions. Too little

tension stiffening will cause the local crackingfailure in the concrete to introduce temporarilyunstable behavior in the overall response ofthe model. Few practical designs exhibit suchbehavior, so that the presence of this type ofresponse in the analysis model usuallyindicates that the tension stiffening isunreasonably low.

Figure 3: Tension stiffening model

As the concrete cracks, its shear stiffness isdiminished. This effect is defined with the SHEARRETENTION option by specifying the reduction inthe shear modulus as a function of the opening strainacross the crack.

A number of two caisson types are presented in this

paper as seen in figures 6 and 7. The complexity ofthe rebar reinforcement is illustrated in Figure 5.This is to our knowledge, the first full 3D FiniteElement analysis attempted in the world for themodeling of large dry-dock Caissons which takesinto consideration all aspects of steel-concreteinteraction under combined loading.

The primary loads were as follows:

1. Earth Pressure

2. Internal Water Pressure

3. External Water Force

a. One Side (i.e. dock empty)

b. Both sides


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4. Deck Surcharge

5. Hauling-in (one side)

a. Position 1 (one end of caisson)

Force perpendicular to hauling in

beam toward edge

b. Position 2 (Central) Force

perpendicular to hauling in beam

toward edge

c. Position 3 (opposite end of caisson to

Position 1) Force perpendicular to

hauling in beam toward edge

d. Central Force along hauling in

beam, up page direction

6. Crane load

7. Ship load

8. 150 T Bollard loada. 150 T force applied perpendicular to

cope beam towards edge

b. 150 T force applied along cope beam,

down page direction

9. 250 T Bollard

a. Each bollard, 250 T force applied

perpendicular to hauling in beam,

away from edge

b. Each bollard, 250 T force applied at45 degrees to hauling in beam, away

from edge, up page direction.

c. Each bollard, 83 T force applied

perpendicular the hauling in beam,

towards edge

d. Each bollard, 83 T force applied

along hauling in beam, up page

direction

10. Capstan

a. 25 T applied perpendicular to hauling

in beam, towards edge

b. 25 T applied perpendicular to hauling

in beam, away from edge

c. 25 T applied along hauling in beam

up page direction.

11.Fender Load

Figure 4: Solid model

Figure 5: Detail showing reinforcement (rebars) inwalls and bollard


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Figure 6: Finite Element model of Caissons 1-1 (1).Rebars were modeled as embedded elements.

Figure 7: Finite Element model of Caisson 1-1(4).Interaction rebar-concrete modeled.

2.3 Tank Vibration

This project aimed at developing structuralmodifications to the tank structure (Figure 8) inorder to contain tanks strong shell vibrations below8 Hz.

Figure 8: Finite Element model of the tank and its

internals (deflected shape)

At this point it is worth mentioning the following:

The vibration experienced by the tank shellbelow 8 Hz suggests the existence offorced vibration.

When the level of the liquid inside the tank isat 14 m, the first natural frequency of thetank shell in the absence of attached bafflesis just above 8 Hz.

Baffles normal modes start from as low as 2Hz. The baffles can therefore be excited atf >2 Hz and reach resonance if forcing

frequency is the same with any of the bafflesnatural frequency. As baffles naturalfrequencies between 2 and 8 Hz arenumerous and closely spaced, with large

participating effective mass, the resonance ofthe baffles becomes possible.

We can therefore assume that the forced vibrationthat excites tanks shell below 7-8 Hz can occur:a) Internally: via the baffles which start to vibrate

under a forcing harmonic load F=F0sin(t)produced by the liquid intake-discharge, sloshingor air pressure pulses

b) Externally: via the piping system attached to theexternal shell of the tank vibrating at forcingfrequencies.

c) as a combination of both

The immediate aim was to shift baffles naturalfrequencies to higher values as currently they arefree to vibrate at frequencies as low as 2 Hz withmodes very closely spaced in frequency domain,large modal participation factors and effective mass.

According to the Clients vibration measurements ofthe tank shell, large frequency peaks were recordedat frequencies below 7 Hz.

3 RESULTS


The results of the nine FEA models are summarisedas follows:

The peak stress occurs over a narrow bond ofthe inside joint of the mitre cut, termed theintrados. The peak stress is approximatelydouble the normal hoop stress.

The development of stress at the intrados isindependent of the segment length A, for A

greater than 0.25OD. Therefore an increasein segment length would not result in anyeconomies. As the stress at the intradosindicates localised outward deformationunder pipe pressure it is not surprising that


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extending the segment length has no effect atthe intrados.

Stress at intrados was found to be dependentof A only for values of A


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the deformation pattern of Caisson 1.1-(4) underUltimate Load CombinationsLC_A= 1.4 x (L1 + L2 + L3a) + 1.6 x (L6 + L9a +L10b) + 2.0 x L11where loads L# are the primary loads defined inSection 2.2

Figure 12: Caisson 1-1(1). Displaced pattern underLoads 1+2+4

Figure 13: Caisson 1-1(4). Displaced pattern underUltimate Loadcase Combination

The maximum tensile stress in concrete for LC_Ais localized over a small area as shown in Figure 14.The concrete relies on reinforcement in the areaswhere the tensile stress is larger than 3MPa. Basedon maintenance and operational consideration,certain walls in the caissons were to be removed andthe existing walls remodeled. In the analysis, just

prior to the removal step, the FEA code stores theforces/fluxes that the region to be removed is

exerting on the remaining part of the model at thenodes on the boundary between them. These forcesare ramped down to zero during the removal step;therefore, the effect of the removed region on therest of the model is completely absent only at the

end of the removal step. The forces are rampeddown gradually to ensure that element removal has asmooth effect on the model. No further elementcalculations are performed for elements beingremoved, starting from the beginning of the step inwhich they are removed.The simulation of the Ultimate State loadcasesshowed that the removal of certain walls may affect

the structural integrity of caissons while the removalof others is perfectly safe. The walls wereremodeled in such a manner to allow compliancewith Standards.

Figure 14: LC_A. Maximum principal stress

3.3 Tank Vibration

3.3.1 As-Is Tank

Tank analysis filled to 14 metres and all internalspresent.

The Von Mises stress levels obtained as a result ofhydrostatic pressure and self weight are belowadmissible stress levels. Maximum stress in the tankshell is around 80 MPa; higher values are predictedaround the bottom nozzles.

The dynamic analysis of the tank predicts naturalfrequencies which are very closely spaced. At lowfrequencies between 2 and 8 Hz, the baffles tend tovibrate excessively due to a high number of closelyspaced normal modes. Tanks shell also vibrates inthe areas adjacent to baffles. The baffles vibrateeither independently (5-7 Hz).

At frequencies above 8 Hz tanks shell vibrate allaround its circumference which suggests that thevibration in the shell is not controlled only by the

baffles.These results agree very well with the results

described derived in previous work when the baffleswere removed to independently derive the naturalfrequencies of the tanks shell.


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Tank analysis filled to 5 metres and all internalspresent.

As in the previous case it is predicted that at lowfrequencies (below 5 Hz), the baffles have thelargest vibration amplitudes. Tanks shell vibratesaround and in line with the baffles.

At frequencies above 5 Hz (see Figues 16) theshell vibrates quite independently (of the baffles)

around its circumference as baffles continue todisplay large mode shapes.

Tank analysis filled to 14 metres and no baffles.

The objective of this analysis was to derive thenatural frequencies of the shell in the absence of the

baffles as in previous two analyses it was difficult toascertain how the tanks shell behaves without beingexcited by the baffles.

The first natural frequency of the tank is at 7.8 Hz

and occurs in the roof only. This correlatesaccurately with the natural frequency of the roofmeasured by the Client. There are no naturalfrequencies of tank shell below 7.8 Hz.

Tanks shell natural frequencies occur above 8Hz and are not as closely spaced as in previous twocases.

Modal participation factors are high which showsthat tanks shell can be excited between 8-10 Hzindependent of the baffles vibration. This is a veryimportant result which suggests that both the bafflesand tank shell should be stiffened.

3.3.2 Stiffened Tank

A new stiffening system was proposed andsubsequently implemented in order to reduce

baffles vibration and shown in Figure 17a,b,c.

tank shell stiffeners: The shell of the tankwas stiffened at elevations 9000mm,13000mm, 14500mm, 16250mm and 17750mm. The stiffening system comprised of

100x100x6 L profiles radially welded to thetank shell through the use of 60 plates(250x150x10). In doing this the radial space

between two consecutive plates is 583 mmwhich is less that the minimum recordedwidth of a vibration amplitude.

baffles stiffeners through the use of arectangular plates 550x1250x12 welded onthe passive side of the baffles, spaced at 1100mm from one another mm connecting the

baffles with the tank shell

Liquid level 14 m

The advantage of the proposed design is that thetank and its baffles do not have any naturalfrequency under 5.5 Hz.

The baffles first natural frequency is at 5.5 Hz,followed by 6.5 and 6.8 Hz. All these 3 modes arelocalised in nature (occur at the baffles edge close to

the tank wall and between two consecutive existingstiffeners) and unless excitation force (of a natureunknown to us) is extremely strong, resonance of the

baffles and subsequent vibration of the shell will benon-existent.

From the measurements taken by Client, forcingfrequencies above 7 Hz induce relatively low levelsof vibration (relatively low peaks) so that stiffeningthe baffles using connecting plates was found to be afeasible solution.

However, the baffles and adjacent tank shell havetwo normal modes at 7.2 and 9 Hz which can beexcited. If these two are not excited, the nextdangerous frequency is at 9.6 Hz, usually too high to

produce considerable vibration in the tank shell.Indeed, subsequent measurements taken over a

period of one year did nor record any vibrations onthe stiffened tank.

The absence of tanks shell circular rings (stiffeners)is reflected in some loss of structural stiffness. Ifonly the baffles are stiffened, the baffles and tank

shell can vibrate strongly starting from f = 6 Hzwhereas in the presence of the circular rings theshell can vibrate more predominantly after 9 Hz ifexcited by forcing frequency.

Liquid level 7 m

For a 7 metres liquid level the baffles vibrate andcan easily be excited at values as low as 6 Hz

despite stiffening the shell and baffles.The tank shell vibrates freely with the baffles ifforcing frequency is present and resonance of thetank shell at around 7 Hz can easily be reached.

From the structural dynamic point of view it isnot recommended to run the tank with a liquid levelwell below 14 m. In practice, the level of liquid isnot allowed below 14 m level with running pump.


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Figure 15: Localised natural frequency of baffles

Figure 16: Natural frequency of the tank shell at 5Hz when tank is emptied to 5 m liquid level.

Figure 17 (a,b,c): Structural modifications to thebaffles and tanks shell.

3.4 References

1. American Water Works Association, Official Note

Addendum to ANSI/AWWA C208 83 Standard for

Dimensions for Fabricated Steel Water Pipe Fittings

2. ANSI/AWWA C208-96 AWWA Standard for

Dimensions for Fabricated Steel Water Pipe Fittings

3. ANSI/AWWA C208-01 AWWA Standard forDimensions for Fabricated Steel Water Pipe Fittings

4. AWWA M11 Manual of Water Supply Practices.

Steel Pipe A Guide for Design and Installation


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5. AS 4041. Pressure Piping ASME B31.3 1996

Edition. Process Piping

6. API Recommended Practice 1111 Limit State

Design

7. AbaqusTM version 6.4.1: ABAQUS Inc.

3.5 ConclusionsFinite Element Modeling constitutes a valuable toolin the design and analysis of various structures toStandard requirements. The usefulness of FEAextends to exploring new design alternatives andevaluating multiple design approaches that entailcomplex loading, nonlinear materials and complexgeometries. The FEA programs can concentrate onthat handful of crucial variables adjusting them up tofind an optimum solution.

The futureThe next step beyond design optimization isbehavioral modelling. As the software exploresmultiple combinations it organises the results in atree-like structure of cause-and-effect relationship.Major variables are represented as big brancheswhile sub-branches show the options available usingvarious parameters. Such design approach can bedatabased and overall design can be revised almostinstantly.

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