Calculations Tank S6

8/10/2019 Calculations Tank S6

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Project

Reference

Revision 00

TANK

REFURBISHMENT

TANZANIA

TANK LOADING CALCULATIONS & BUCKLING ANALYSIS

DOCID

Revision Date Description Written Checked Approved

V1 17/11/2014 First Draft Issue GDL ARM RBN


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C A L C U L A T I O N S R E P O R T Page 2of 19

1. INTRODUCTION 3

1.1 Calculation Introduction 4

1.2 Basic Calculation Data 5

1.3 Calculation of Maximum Allowable Product Design Stress SdAnd Maximum Allowable Hydrostatic Test

Stress StAccording To API 650 Eleventh Edition 6

1.4 Wind Calculation 7

1.4.1 Reynolds Number Error! Bookmark not defined.

1.4.2 Force Coefficient Error! Bookmark not defined.

1.4.3 Peak Velocity Pressure Error! Bookmark not defined.

1.5 Buckling Stress Calculations of Unstiffened Tank Shell 11

1.5.1 General 13

1.5.2 Transformation of stepped shell into equivalent shell 13

1.5.3 Circumferential (Hoop) Compression 16

1.5.3.1 Critical Circumferential Buckling Stresses 16

1.5.4 Meridional (Axial) Compression 18

1.5.4.1 Critical Meridional Buckling Stresses 18


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1. INTRODUCTION

In the 50 years of operation the tank shell has been exposed to corrosion and designed shell thickness

has been reduced.

In the operation period the tanks shell has been also distorted, especially distortion is present on tank

shell S6.

The Client has requested from Contractor the solution for reinforcement of tank shell.

The distortion of the tanks has been elaborated by Contractor in documents as follows:

1. DIMENSIONAL TOLERANCES STUDY TANK S6.... R02-ENI-QUA-REP-0003-00-E

From 27.02.2014

Ref. Standard API 650, API 653

2. DIMENSIONAL TOLERANCES STUDY TANK S5.... R02-ENI-QUA-DSH-0002-00-E

From 13.03.2014

Ref. Standard API 650, API 653

According to the above presented documents the distortion is outside acceptable tolerances.

The distortion is also outside acceptable tolerances according to standards as follows:

EN 14015: 2004 Specification for the design and manufacture of site built, vertical, cylindrical,

flat bottomed, above ground, welded, steel tank for thestorage of liquids at ambient

temperature and above.

EUROCODE 3design of steel structuresPat1-6: Strength and stability of Shell Structures.

Therefore we propose to Client Stiffening Tank S6 shell with 84 longitudinal stiffeners.


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1.1

Calculation Introduction

The following data we received from the Client:

1.

Content of the tank: Diesel

2.

Density of the content 8.85/ Density of water for hydro test 1

3.

Peak ground acceleration PGA


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1.2

Basic Calculation Data

Inner tank diameter Di= 54.870m

Shell total height H = 16.550m

Volume V = 39.134 m3

Height of stored liquid Hm = 15m

Stored liquid Diesel

Spec. Gravity 0.85

Corrosion allowance Shell Corroded plate thickness as per Rosen report

Design temperature 500C

Design pressure atmospheric

Maximum wind velocity 100 km/h (27.7 m/s)

Shell material St 35

Tensile Strength M= 340-480 N/mm2

Yield Strength 20 0C 0.2 = 235 N/mm2

Allowable Stress Hydrostatic Test St = 145 N/mm2

Allowable Stress 500C Sd = 136 N/mm

2


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1.3

Calculation of Maximum Allowable Product Design Stress SdAnd

Maximum Allowable Hydrostatic Test Stress StAccording To API 650

Eleventh Edition

Mechanical properties of St35

0.2 = 235 N/mm2

M= 340 N/mm2

According to API 650 section 5.6.2.1 and 5.6.2.2

Calculation of maximum allowable design stress Sd

2/3 Y = 0.666 x 235 = 156.67N/mm2

2/5T = 0.4 x 340 = 136 N/mm2

We shall use 136 N/mm2 in our calculations for the first 2 courses.

Calculation of maximum allowable hydrostatic test St

3/4 Y = 0.75 x 235 = 176.25N/mm2

3/7 T = 0.429 x 340 = 145.71 N/mm2

We shall use 145.71 N/mm2 in our calculations for the remaining upper courses.


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1.4

Wind Calculation

The wind loading calculation was carried out with accordance to EN1991-1-4 (2004). The maximum

design wind speed was taken as 100 km/h, that is, 27.7 m/s (Reference: X).

1.4.1 Peak Velocity Pressure

The peak velocity pressure, qp(z), was then determined as described in section 4.5 of the EN1991-1-4.

[ ] Equation IWhere;

The density of air

ce(z) The exposure factor given by:

qb The basic velocity pressure given by the following:

Where,

Cdir The directional factor and is equal to 1.0 as described in section 4.2EN1991-1-4;

Cseason The seasonal factor which is also equivalent to 1.0as described in section 4.2EN1991-1-4;

Vb,o The fundamental value of the basic wind velocity taken as 27.7 m/s

The value obtained for vbis 27.7 m/s.


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Then, the mean wind velocity was determined from:

Where;

The roughness factor; calculated below; The orography factor, equal to 1.0 as per section 4.3EN1991-1-4.The value for Krwas determined according to section 4.3.2 by:

Where;

Zo The roughness length;

Zo,II 0.05 m (terrain category II)

The roughness factor, Cr,was obtained using:

( ) NOTE: Values for Zoand Zo,II were obtained from table 4.1-Terrain categories and terrain parameters,

located in section 4.3.2 EN199-1-4.

The turbulence intensity, Iv, was determined from section 4.4:

According from above mentioned section, the value of was taken as 1 in the calculation.


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The above calculated values was replaced in equation I accordingly:

[ ]

[ ] 1.4.2 Reynolds Number

From section 7.9.1 of the EN1991-1-4, the external pressure coefficients are given depend upon the

Reynolds Number defined by:

Equation II

b The diameter of the tank

v The kinematic viscosity of air (v = 15 x 10-6m2/s)

v (ze) The peak wind velocity defined below:

From Equation I, the resulting Re = 1.7 x 108.

1.4.3 Force Coefficient

The force coefficient is given in section 7.9.2 EN 1991-1-4:

Equation IIIWhere;

Cfo The force coefficient of cylinders without free end flow and is equivalent to 1.063 and was

obtained from Figure 7.28 of above mentioned section;


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The end effect factor which is equal to 0.66 and was calculated from Figure 7.36 if abovementioned section

Upon substituting respective values in equation II, the value obtained for Cfeis equal to 0.702.

1.4.4 Wind Pressure on Shell

The wind pressure on the surface on the tank is determined according to the equation in section 5.3 of

EN1991-1-14:2004 as follow:

Equation IV

Where;

CsCd is the structural factor and taken as 1 as defined in section 6 of EN1991-1-14:2004.

Cf is the force coefficient for the structure as defined in section 7.

qp is the peak velocity pressure at reference zeas calculated as per section 4.5.

Aref is the reference projected area of the structure.

The wind force acting on the tank was determined as follow:

Therefore the wind pressure was calculated to be equivalent to 1.079 KPa.


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1.4.5

Vertical Suction Force (Wind Uplift)

The values for the external pressure coefficient acting on domes roof with circular base are given in

Figure 7.12 in section 7.2.8 EN 191-1-4:2004

Values of Cpefor the different zones of the dome:

Zone A = -1.1

Zone B = -0.7

Zone C = -0.25

Fig 1.1: Vertical Suction Force for domes with

circular base (zones)


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The wind pressures acting on the surface of the dome was calculated from equation as per section 5.2 of

En 1991-1-4:2004 :

Equation VWhere ;

qp(ze) is the peak velocity pressure

Cpe is the pressure coefficient for the external pressure

From Equation V, the vertical suction force at different zones were calculated:

At zone A ; At zone B;

At zone C;


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1.5

Buckling Stress Calculations of Unstiffened Tank Shell

1.5.1

General

The unstiffened shell buckling evaluation was checked according to EN1993-1-6 (2007). The stress

design approach, in which the buckling resistance is expressed in terms of stresses that are compared

with the shell analysis stresses, was deemed the most appropriate. For a tank with variable shell

thickness, the unstiffened cylindrical shell of stepwise variable wall thicknessapproach was used.

1.5.2

Transformation of stepped shell into equivalent shell

As per section D.2.3 of EN1993-1-6, the shell consisting of more than three sections with different wall

thicknesses was replaced by an equivalent shell comprising three sections, namely, A, B and C.

The length laof the upper section A of the shell was calculated by adding the heights of the first three

top courses, that is, courses 9, 8 and 7.

The length of the two other sections were calculated based on equation below.

If Where,

L The overall shell length,

The section B of the equivalent shell

The section C of the equivalent shell


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The fictitious wall thicknesses ta, tb and tc of the three sections were determined as the weighted

average of the wall thickness over each of the three fictitious sections as shown below.

Where;

tj the constant wall thickness of section j of the shell;

lj the length of section j of the shell

The following values were obtained:

[ ]

[ ]

[ ]


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The three-section-shell was then replaced by an equivalent single shell of effective length leff and of

uniform wall thickness t = ta. The effective length of the shell was calculated as follows:

Where

k a dimensionless factor obtained from graph D.6 and equivalent to 1.0


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1.5.3

Circumferential (Hoop) Compression

1.5.3.1 Critical Circumferential Buckling Stresses

The shell sections not satisfying equation D.64 of EN1993-1-6, were assumed to be moderate to short

length sections. The elastic critical circumferential buckling stress of each shell sectionjof the original

shell of stepwise wall thickness was determined from:

( ) Equation VIWhere;

The effective elastic critical circumferential buckling stress derived below;C The external pressure buckling factor and equivalent to 1.0

The effective elastic critical circumferential buckling stress was determined from:

Equation VIIWhere;

E The Youngs Modulus and equivalent to 210 000 MPa;

R The radius of shell middle surface;

A dimensionless length parameter determined from:

Equation VIIICS The external buckling pressure factor for short shells and calculated using;

Equation IX


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The shell section was assumed to be short length since the following condition was satisfied.

The effective elastic critical circumferential buckling stress was then calculated to be equal to 8.48 MPa

by substituting the respective values into Equation V.

Then, the elastic critical circumferential buckling stress for each section was obtained by substituting

respective values into Equation IV as shown below.

For section A,

() For section B,

() For section C,

( )


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1.5.4

Meridional (Axial) Compression

1.5.4.1 Critical Meridional Buckling Stresses

The elastic critical circumferential buckling stress of each shell sectionjof the original shell of stepwise

wall thickness was determined from:

Equation XWhere;

Cx A parameter depending on the boundary conditions and depending on the values of ;

E The Youngs modulus and equivalent to 210 000 MPa;

tj The constant wall thickness of section j of the shell;

r The radius of the cylinder middle surface

The dimensionless length parameter for each section was calculated as per section D.2.2, using the

following equation:

Equation XIThe values obtained are as follows:


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The shell sections satisfying equation D.3 of EN1993-1-6, were assumed to be medium length sections

and therefore, Cxis taken as 1.0. The condition is as follows:

The critical meridional buckling stress was calculated for each section and the results are as follows:

For section A,

( ) For section B,

( ) For section C,

( )

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Calculations Tank S6