DESIGN AND STABILITY OF LARGE STORAGE TANKS AND TALL BINS
PREPARED BY : MUKESH M. CHAUHAN BE-IV CHEMICAL ROLL NO. 803 EXAM NO. 341
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THE MAHARAJA SAYAJIRAO UNIVERSITY OF BARODA
DEPARTMENT OF CHEMICAL ENGINEERING FACULTY OF TECHNOLOGY & ENGINEERING, BARODA.
Certificate This is to certify that Mr. CHAUHAN MUKESH MOHANLAL., a student of B.E-IV Chemical has work on the Project entitled “Design and Stability of Large Storage Tanks and Tall Bins” under my guidance and herewith submits his report in partial fulfillment of the degree of B.E. (Chemical) for the year 2011-12.
Dr. R. A. Sengupta Head and Professor, Chemical Engg. Deptt. Faculty of Technology & Engineering M.S.university of Baroda.
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Acknowledgement I am extremely thankful to Dr. R. A. Sengupta, Head of Department of Chemical Engineering and my guide for his excellent guidance, encouragement and support throughout my dissertation work. His profound knowledge that he readily shared with me has helped me overcome many difficulties. I cannot forget the innumerable time and effort to teaching me both in this seminar and in writing it, that my work will never be able to match. His constant support, encouragement, never ending enthusiasm and confidence in me has been a source of motivation for me. I would also like to express my heartfelt gratitude to Ms. N. H. Tahilramani, who have personally paid attention in the progress of this work Special thanks to library staff of T. K. Gajjar and A.C.E.S library for their kind cooperation. Finally, I express my deepest gratitude to all my family members for their constant love and support and “God”.
Mukesh M Chauhan
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Contents Chapter 1 Introduction to Storage tanks and Bins 1.1 Function of Storage Tanks and Bins …………………………………………………..01 1.2 Types of Storage Tanks and Bins……………………………………………………... 01 1.3 Design codes and Standards ………………………………………………………….04 Chapter 2 Design of Liquid Storage Tanks 2.1 Shell Design …………………………………………………………………………..05 2.2 Roofs …………………………………………………………………………………..09 2.3 Bottom plate …………………………………………………………………………...12 Chapter 3 Design and Stability of Storage Bins 3.1 Introduction ……………………………………………………………………………14 3.2 Functional Design of Bins ……………………………………………………………..14 3.3 Design of Bins-Loadings……………………………………………………………….17 3.4 Structural Design of bins……………………………………………………………….21 Chapter 4 Stability of Storage Tanks 4.1 Provisios for seismic loading…………………………………………………………..29 4.2 Overturning Stability against Wind Loads……………………………………………..41
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List of Figures Figure 1.1 - Types of storage tanks Figure 2.1 – Column supported framed roof Figure 2.2 – Floating roof Figure 2.3 – Joints in floor plates Figure 2.4 – Bottom plate layout Figure 3.1 – Flow patterns of materials in bins Figure 3.2 – Graphical method for calculation of flow pattern Figure 3.3 – Distribution of horinzontal and vertical pressure against depth of stored material Figure 3.4 – Bin dimensions for use in Reinbert‟s and Janssens‟s equation Figure 3.5 – Critical values of axial stresses for cylinders subjected to axial compression Figure 3.6 – Cylinder to cone transition Figure 3.7 – Forces on suspended bottoms Figure 4.1 – Impulsive hydrodynamic pressure on wall Figure 4.2 - convective hydrodynamic pressure on wall Figure 4.3 – Typical stiffener ring section for ring shell Figure 4.4 – Overturning check on tank due to wind load
List of Tables Table 2.1 – Minimum thickness based on Diameter of the tank Table 4.1 – Expressions for parameters of spring mass model Table 4.2 – Importance factor-I
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Chapter 1
Introduction To Storage Tanks & Bins
1.1 Fuction of Storage tanks and Bins 1.1.1 Storage tanks Storage tanks had been widely used in many industrial established particularly in the processing plant such as oil refinery and petrochemical industry. They are used to store a multitude of different products. They come in a range of sizes from small to truly gigantic, product stored range from raw material to finished products, from gases to liquids, solid and mixture thereof. There are a wide variety of storage tanks; they can be constructed above ground, in ground and below ground. In shape, they can be in vertical cylindrical, horizontal cylindrical, spherical or rectangular form, but vertical cylindrical are the most usual used. In a vertical cylindrical storage tank, it is further broken down into various types, including the open top tank, fixed roof tank, external floating roof and internal floating roof tank. The type of storage tank used for specified product is principally determined by safety and environmental requirement. Operation cost and cost effectiveness are the main factors in selecting the type of storage tank. 1.1.2 Storage Bins The storage of granular solids in bulk represents an important stage in the production of many substances derived in raw material form and requiring subsequent processing for final use. These include materials obtained by mining, such as metal ores and coal; agricultural products, such as wheat, maize and other grains; and materials derived from quarrying or excavation processes, for example sand and stone. All need to be held in storage after their initial derivation, and most need further processing to yield semi- or fully-processed products such as coke, cement, flour, concrete aggregates, lime, phosphates and sugar. During this processing stage further periods of storage are necessary.
1.2 Types of Storage tanks and bins 1.2.1 Storage tanks
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1.2.1.1 Open Top Tanks This type of tank has no roof. They shall not be used for petroleum product but may be used for fire water/ cooling water. The product is open to the atmosphere; hence it is atmospheric tank. 1.2.1.2 Fixed Roof Tanks Fixed Roof Tanks can be divided into cone roof and dome roof types. They can be self supported or rafter/ trusses supported depending on the size. Fixed Roof are designed as Atmospheric tank (free vent) Low pressure tanks (approx. 20 mbar of internal pressure) High pressure tanks (approx. 56 mbar of internal pressure) Figure 1.1 illustrates various types of storage tank that are commonly used in the industry today.
Figure 1.1 Types of storage tank 7|Page
1.2.1.3 Floating Roof Tanks Floating roof tanks is which the roof floats directly on top of the product. There are 2 types of floating roof: Internal floating roof is where the roof floats on the product in a fixed roof tank. External Floating roof is where the roof floats on the product in an open tank and the roof is open to atmosphere. Types of external floating roof consist of: Single Deck Pontoon type ( Figure 1.4) Double deck ( Figure 1.5) Special buoy and radially reinforced roofs 1.2.2 Storage bins Regarding descriptive terminology applicable to containment vessels, it should be noted that the word "bin" as used in this text is intended to apply in general to all such Containers, whatever their shape, ie whether circular, square or rectangular in plan, Whether at or above ground level, whatever their height to width ratio, or whether or not They have a hopper bottom. More specific terms, related to particular shapes or Proportions, are given below, but even here it must be noted that the definitions are not Necessarily precise. a) A bin may be squat or tall, depending upon the height to width ratio, Hm/D, where Hm is the height of the stored material from the hopper transition level up to the surcharged material at its level of intersection with the bin wall, with the bin full, and where D is the plan width or diameter of a square or circular bin or the lesser plan width of a rectangular bin. Where Hm/D is equal to or less than 1,0 the bin is defined as squat, and when greater as tall. b) A silo is a tall bin, having either a flat or a hopper bottom. c) The hopper transition level of a bin is the level of the transition between the vertical side and the sloping hopper bottom. d) A bunker is a container square or rectangular in plan and having a flat or hopper bottom.
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e) A hopper, where provided, is the lower part of a bin, designed to facilitate flow during emptying. It may have an inverted cone or pyramid shape or a wedge shape; the wedge hopper extends for the full length of the bin and may have a continuous outlet or several discrete outlets. f) A multi-cell bin or bunker is one that is divided, in plan view, into two or more separate cells or compartments, each able to store part of the material independently of the others. The outlets may be individual pyramidal hoppers (ie one per cell) or may be a continuous wedge hopper with a separate outlet for each cell. g) A ground-mounted bin is one having a flat bottom, supported at ground level. h) An elevated bin or bunker is one supported above ground level on columns, beams or skirt plates and usually having a hopper bottom.
1.3 Design Codes and Standards The design and construction of the storage tanks are bounded and regulated by various codes and standards. List a few here, they are:
American Standards API 650 (Welded Steel Tanks for Oil Storage)
British Standards BS 2654 (Manufacture of Vertical Storage Tanks with Butt welded Shells for the Petroleum Industry
The European Standards - German Code Din 4119 – Part 1 and 2 (Above Ground Cylindrical Flat Bottomed Storage Tanks of Metallic Materials) - The French Code, Codres – (Code Francais de construction des reservoirs cylindriques verticauz en acier U.C.S.I.P. et S.N.C.T.)
The EEMUA Standards (The Engineering Equipments and Materials Users Association)
Company standards such as shell (DEP) and Petronas (PTS)
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Chapter 2
Design of liquid Storage tanks
The design of vertical, cylindrical tanks for the storage of liquids can be divided into three basic areas:
The shell
The bottom
The roof
The design of each of these is discussed in detail in this Chapter.
2.1 Shell Design The cylindrical region of the tank is made up of a number of cylindrical shell courses or tiers, each usually of same height. The courses are usually butt-welded although lap joints are occasionally used. Each course is made up of number of equal length plates. For calculating the thickness of courses two methods are available which are discussed below. 2.1.1 Calculation of Thickness by the 1-Foot Method The 1-foot method calculates the thicknesses required at design points 0.3 m (1 ft) above the bottom of each shell course. This method shall not be used for tanks larger than 60 m (200 ft) in diameter. The required minimum thickness of shell plates shall be the greater of the value computed as followed [API 650, 2007]: Design shell thickness:
Hydrostatic test shell thickness:
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td = design shell thickness, mm tt = hydrostatic test shell thickness, mm D = nominal tank diameter, m H = design liquid level, m G = design specific gravity of the liquid stored C.A = corrosion allowance, mm Sd = allowable stress for the design condition, MPa St = allowable stress for the hydrostatic test condition, MPa 2.1.2 Calculation of Thickness by the Variable-Design-Point Method Note: This procedure normally provides a reduction in shell-course thicknesses and total material weight, but more important is its potential to permit construction of larger diameter tanks within the maximum plate thickness limitation. Design by the variable-design-point method gives shell thicknesses at design points that result in the calculated stresses being relatively close to the actual circumferential shell stresses. This method may only be used when it is not specified that the 1-foot method be used and when the following is true:
L = (500 D t)0.5, in mm, D = tank diameter, in m, t = bottom-course shell thickness, excluding any corrosion allowance, in mm, H = maximum design liquid level, in m. Complete, independent calculations shall be made for all of the courses for the design condition, exclusive of any corrosion allowance, and for the hydrostatic test condition. The required shell thickness for each course shall be the greater of the design shell thickness plus any corrosion allowance or the hydrostatic test shell thickness, but the total shell thickness shall not be less than the shell thickness required by following condition.
The required shell thickness shall be the greater of the design shell thickness, including any corrosion allowance, or the hydrostatic test shell thickness, but the shell thickness shall not be less than the following:
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Nominal Tank Diameter
Nominal Plate Thickness
(m)
(mm)
D<15
5
15
6
36
8
D>60
10
Table 2.1 Minimum Thickness Based on Diameter
The calculated stress for each shell course shall not be greater than the stress permitted for the particular material used for the course. No shell course shall be thinner than the course above it.
2.1.2.1 The bottom-course thicknesses Design shall thickness:
Hydrostatic test shell thickness:
2.1.2.2 Second-course thickness To calculate the second-course thicknesses for both the design condition and the hydrostatic test condition, the value of the following ratio shall be calculated for the bottom course:
Where, h1 = height of the bottom shell course, in mm (in.), r = nominal tank radius, in mm (in.), t1 = calculated thickness of the bottom shell course, less any thickness added for corrosion allowance, in mm (in.), used to calculate t2 (design). The calculated hydrostatic thickness of the bottom shell course shall be used to calculate t2 (hydrostatic test). If the value of the ratio is less than or equal to 1.375: 12 | P a g e
If the value of the ratio is greater than or equal to 2.625:
If the value of the ratio is greater than 1.375 but less than 2.625,:
Where, t2 = minimum design thickness of the second shell course excluding any corrosion allowance, in mm (in.), t2a = thickness of the second shell course, in mm (in.), as calculated for an upper shell course as described in below section exclusive of any corrosion allowance. dn calculating second shell course thickness (t2) for design case and hydrostatic test case, applicable values of t2a and t1 shall be used. 2.1.2.3 Upper-course thicknesses To calculate the upper-course thicknesses for both the design condition and the hydrostatic test condition, a preliminary value tu for the upper-course thickness shall be calculated using the formulas in 2.1.1 excluding any corrosion allowance, and then the distance x of the variable design point from the bottom of the course shall be calculated using the lowest value obtained from the following:
tu = thickness of the upper course at the girth joint, exclusive of any corrosion allowance, in mm, C = [K0.5 (K - 1)] / (1 + K1.5), K = tL / t u , tL = thickness of the lower course at the girth joint, except any corrosion allowance, in mm, H = design liquid level (see 2.1.1), in m. 13 | P a g e
So, the minimum thickness tx for the upper shell courses shall be calculated for both the design condition (tdx) and the hydrostatic test condition (ttx) using the minimum value of x obtained from above conditions.
The steps described in 2.1.2.3 shall be repeated using the calculated value of tx as tu until there is little difference between the calculated values of tx in succession (repeating the steps twice is normally sufficient). Repeating the steps provides a more exact location of the design point for the course under consideration and, consequently, a more accurate shell thickness.
2.2 Roofs There are two main types of roof structures are used, 1). Fixed roof structures : They are most widely used roof structures, 1). Self supporting Framed Roof : This type of roof consist of a series of radial arms overplated with roof sheeting resting on purlins placed over the radial arms. 2). Column supported Framed Roof : This type of roof consist of a shallow cone shape with a slope of 1 in 16 supported at regular intervals on a series of vertical columns. 3). Self-supporting Frameless Roof : Fixed roofs of small diameter tanks (less than 12 m) are prepared by joining plates without any supporting structure. 2). Floating Roof : Floating roofs are installed in oil storage tanks primarily to reduce evaporation, handling losses, to decrease corrosion and to reduce fire hazards. From the above types of roof column supported framed roof and floating roof are widely used for large size storage tanks. Figure 2.1 illustrates these types of storage tank roofs that are commonly used in the industry for large storage tanks.
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2.1 Column supported framed roof
2.2 Floating roof For large storage tanks design of column supported conical roof is as follows, Column supported conical Framed Roof When conical roof is used with structural support, slope of conical roof recommended is 1/16. For steel construction minimum thickness of 5 mm is recommended for the roof plates In this design roof plates are placed between the two rafters, but roof plates are attached to rafters by intermittent lap joint welding. Hence roof plates are supported by rafters & rafters are supported by Girders, central column & periphery ring. 15 | P a g e
Girders are supported by columns. Periphery ring is a top angle attached to shell wall. Design steps 1). Select minimum thickness of roof plate =5 mm + C.A. for structural steel. 2). Keep the slope of conical roof 1/16 3).Determine the pressure created by dead load & live load P = t r ρm + 125
Where, tr = thickness of roof plate in meter ρm = Density of roof plates
4). Select the size of top angle or periphery ring 75mm × 75mm × 10mm 5). Determine the maximum rafter spacing on periphery ring.
l = tr
Where,
2f P
tr = thickness of roof plate f = max allowable stress of roof plate material
6). Determine minimum nos. of rafters that must be provided in between outer most polygon & periphery ring. Min. nos. of rafters required 𝑛𝑚𝑖𝑛 =
𝜋𝐷 𝑙
Where, D = Diameter of storage tank 7). Determine the length of girder of the outer most polygon (girder = side of polygon) length of Girder L = 2R sin Where,
360 2N
N = Nos. Girders in polygon or nos. of the sides of polygon R = radius of circle circum scribing polygon 16 | P a g e
8). Determine the rafter spacing on girder rafter spacing =
Length of Girder L = Nos. of rafters per Girder n/N
rafter spacing should be less than 2 m If rafter spacing > 2. Then increase nos. of rafters. 9). Minimum nos. of rafters required between the two polygon is calculated by equation 𝑛𝑚𝑖𝑛 =
2𝑁𝑅 360 𝑁𝐿 × 𝑠𝑖𝑛 = 𝑙 2𝑁 𝑙
Where, L = Length of girder of the outer most polygon R = Radius of circle circumscribing outer most polygon N = nos. of Girders in Outer most polygon l = Maximum allowable rafter spacing Actual Nos. of rafters in between two polygon should be a multiple of nos. sides in both polygon. 10). Minimum Nos. of rafters required in – between inner most polygon & central column is also calculated by similar equation. In this case, actual nos. of rafters should be a multiple of the Numbers of the sides in inner most polygon.
2.3 Bottom Plate Bottoms of storage tank is constructed from rectangular standard plates. Rectangular plates are joined to gather by single welded lap joint. But, in large capacity storage tanks a ring of peripheral plates known as floor annular plates are provided which have a circular outside circumference and usually a regular polygonal shape inside the tank, and butt-welded together using backing strips. Design criteria are shown below, Bottom plate minimum thickness : 6 mm, excluding any corrosion allowance. Minimum lap in Bottom plates : 5 x the plate thickness.
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Bottom plate extension beyond shell : 50 mm beyond shell.
Fig 2.3 Joints in floor plates
Annular Bottom Plate : Width of the annular is determined by : 𝐿= Where,
215 𝑡𝑏 (𝐻𝐺)0.5
tb = thickness of the annular plate in mm, H = maximum design liquid level in m, G = design specific gravity of the liquid to be stored.
Figure shows the bottom plate arrangement of large capacity storage tanks.
Fig 2.4 Bottom plate Layout
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Chapter 3
Design and stability of Storage bins
3.1 Intoduction Bins are used by a wide range of industries to store bulk solids in quantities ranging from a few tonnes to over one hundred thousand tonnes. Bins are also called bunkers and silos. They can be constructed of steel or reinforced concrete and may discharge by gravity flow or by mechanical means. Steel bins range from heavily stiffened flat plate structures to efficient unstiffened shell structures. They can be supported on columns, load bearing skirts, or they may be hung from floors. Flat bottom bins are usually supported directly on foundations.
Bin design procedures consists of two parts as follows: a). functional design of bins –which includes Determine the strength and flow properties of the bulk solid, then Determine the bin geometry to give the desired capacity, to provide a flowpattern with acceptable flow characteristics and to ensure that discharge is reliable and predictable. b). Design of bins loading c). Structural design of bin
Before the structural design can be carried out, the loads on the bin must be evaluated. Loads from the stored material are dependent, amongst other things, on the flow pattern, the properties of the stored material and the bin geometry while the methods of structural analysis and design depend upon the bin geometry and the flow pattern. The importance of Stages a). and b). of the design should not be underestimated.
3.2 Functional Design of bins 3.2.1 Shapes and types of bins Bins are provided a storage function in the overall process systems and have to be designed accordingly. The process requirements may range from a multiple silo proportioning system to a single load- out silo. In any case the storage capacity of silos, and the required discharge rate must be determined. 3.2.2 Shapes of outlets and hoppers
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The proper solution for selecting adequate and hopper is based on the analysis of the material flow properties and conditions during material discharge outlet. The relevant properties are : -density -angle of internal friction -angle of wall friction(with corresponding values of static and kinetic co-efficient of friction) -moisture content, etc. 3.2.3 Type of Flow Two types of flow are shown in Figure 3.1. They are mass flow and funnel flow. Discharge pressure is influenced by the flow pattern and so the flow assessment must be made before the calculation of loads from the stored material. In mass flow bins, all the contents of the bin flow as a single mass and flow is on a first-in first-out basis. The stored material in funnel flow bins flows down a central core of stationary stored material and flow is on a last-in, first-out basis.
Figure 3.1 Flow Patterns The flow type depends on the inclination of the hopper walls and the coefficient of wall friction. Mass flow occurs in deep bins with steep hopper walls whereas funnel flow occurs in squat bins with shallow hopper walls. Eurocode 1 gives a graphical method (shown in Figure 3.2) for determining the flow pattern in conical and wedge shaped hoppers for the purpose of 20 | P a g e
structural design only. Bins with hoppers between the boundaries of both the mass and the funnel flows should be designed for both situations.
Figure 3.2 Graphical method for calculation of flow pattern 3.2.4 Structural Material of bins Most bins are constructed from steel or reinforced concrete. The main disadvantages of steel bins are the necessity of maintenance to prevent corrosion, the steel walls may require lining to prevent excessive wear, and the steel walls are prone to condensation which may damage stored products such as grain and sugar, etc. which are moisture sensitive. The selection of structural material for the wall may depend upon the bin geometry. A bin wall is subject to both vertical and horizontal forces. The vertical forces are due to friction between the wall and stored materials, while the horizontal forces are due to lateral thrust from the stored materials. Reinforced concrete bins carry vertical compressive forces with ease and so tend to fail in tension due to the high lateral thrusts. Steel bins, circular in plan, usually carry the lateral forces by hoop tension. They are more prone to failure by buckling under excessive vertical forces. The increase of horizontal and vertical pressure with depth is shown in Figure 3.3. Increases in horizontal pressure are negligible beyond a certain depth and therefore concrete bins are more efficient if they are tall, whereas steel bins tend to be shallower structures.
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Figure 3.3 Distribution of horizontal and vertical pressure against depth of stored material
3.3 Design of bins –Loadings Material stored in a bin applies lateral forces to the side walls, vertical force (through friction) to the side walls, vertical forces to the horizontal bottoms and both normal and frictional forces to the inclined surfaces. The static values of these forces, resulting from materials at rest, are all modified during the withdrawl of the material. In general, all forces will increase, so that the loads during withdrawl tend to control the design. The procedure for bins loading involves determining the static pressures and then multiplying these forces by an “overpressure” factor to obtain the design pressures. 3.3.1 Static Loads Two methods are generally used for determining of static pressure 1). Janssen‟s method 2).Reimberts‟s method Before analyzing this method the pressure exerted by a stored pulverulent mass shall be defined first. When this material is poured onto a plane, it heaps up into a volume conical in shape, the generatrices of which form a specific angle 𝜑 with the horizontal . It exerts pressure on the walls and on the bottom of it, the resultant of which is the thrust. This thrust has two component, one N normal to the wall considered, and other tangential T parallel to the wall. If 𝜑 ′ is the angle of friction of the material on the wall, the corresponding coefficient of the friction is tan𝜑′. So, T is therefor the load balanced by the friction corresponding to the thrust N is : 22 | P a g e
𝑇 = 𝑁 tan 𝜑 At given depth inside the bin, the load on the bottom or total vertical pressure, is the difference between the total weight of the stored material and the total load balanced by the friction of the material on the wall. 3.3.1.1 Janssens’s Method The Vertical static unit pressure at depth z below the surface is : 𝑞=
𝛾𝑟 ′ 1 − 𝑒 −𝜇 𝑘 𝑧/𝑟 𝜇𝑘
Where, 𝛾 = weight per unit volume for stored material r = Hydraulic radius of horizontal cross- section of the inside of the bin 𝜇 ′ = coefficient of friction between stored material and wall = tan 𝜑′ k = ratio of p to q
Figure 3.4 Bin dimensions for use in Reimbert’s and Janssen’s equation
The lateral static unit pressure at depth z is 𝑝= Where
𝛾𝑟 ′ 𝑧 1 − 𝑒 −𝜇 𝑘 𝑟 = 𝑞𝑘 ′ 𝜇
𝑝
k =𝑞
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The ratio p/q is assumed by Jassen to be constant at all depths and has the value 𝑘=
𝑝 1 − sin 𝜑 𝜋 𝜑 = 𝑡𝑎𝑛2 − 𝑞 1 − 𝑠𝑖𝑛𝜑 4 2
At the limit pmax = q max × k =
γr μ′
γr
= tan φ′
For circular bins, 𝑆
𝑟=𝐿=
𝜋𝐷 2 4
×
1 𝜋𝐷
=
𝐷 4
Whare S = area of the bin L = perimeter of the bin D = diameter of the bin 3.3.1.2 Reimbert’s Method The vertical static unit pressure at depth z below the surface is 𝑍
q = 𝛾[𝑧(𝐶 + 1)−1 +
𝑠 3
]
The lateral static unit pressure at depth z is 𝑍
p = 𝑝𝑚𝑎𝑥 [1 – (𝐶 + 1)−2 ] = ∈ 𝑝𝑚𝑎𝑥 𝑝𝑚𝑎𝑥 is the maximum lateral unit pressure C is the “characteristic abscissa” 𝑝𝑚𝑎𝑥 =
𝛾𝐷 4 tan 𝜑′
And 𝑐=
𝐷 4 tan 𝜑 ′ tan2
𝑠 𝜋 𝜑 − 3 4− 2
For polygonal bins or bins having more than four sides 24 | P a g e
𝑝𝑚𝑎𝑥 =
𝛾𝑟 tan 𝜑 ′
And
𝑐=
𝐿 1 𝜋 4 tan 𝜑′ tan2 𝜋 − 𝜑 4 2
−
𝑠 3
For rectangular bins- on shorter wall “a” (𝑝𝑚𝑎𝑥 )𝑎 =
𝛾𝑎 4 tan 𝜑′
And 𝑐𝑎 =
𝑎 𝜋 tan 𝜑 ′ tan2
𝑠 𝜋 𝜑 − 3 4− 2
For rectangular bins- on longer wall “b” (𝑃𝑚𝑎𝑥 )𝑏 =
𝛾𝑎′ 4 tan 𝜑 ′
And 𝑐𝑏 =
𝑎′
𝑠 − 𝜋 𝜑 3 𝜇 tan 𝜑 ′ tan2 ( 4 − 2 )
Where 𝑎′ =
2 𝑎𝑏 − 𝑎2 𝑏
For design purposes, the granular material is usually assumed level at the top of the bin, therefore
𝑠 = 0
It should be observed that theory developed by Reimbert takes into consideration the variation of the ratio p/q with depth and also with the shape of the bins. 3.3.2 Static Forces –Vertical Friction
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For circular, square and regular polygonal bins, the total static frictional forces per foot – wide vertical strip of wall above depth z is approximetly: By Reimbert‟s method : 𝑉=
(𝛾𝑧 − 𝑞)𝐴 𝐿
By Janssen‟s method: 𝑉=
𝛾𝑧 − 0.8𝑞 𝐴 𝐿
Where A = area of the horizontal cross- section of the bin L = perimeter of the horizontal cross- section of the bin 3.3.3 Static pressure on silo Hoppers The static horizontal pressures, p, and vertical q, on inclined hopper wall are calculated by the Janssen or Reimbert formulas. The Hydraulic radius r, may be reduced with in the hopper depth, but usually is assumed constant and equal to that of the bin. The static unit pressure normal to the inclined surface, at depth z from the top of the fill is 𝑞𝛼 = 𝑝 𝑠𝑖𝑛2 𝛼 + 𝑞𝑐𝑜𝑠 2 𝛼 Before, the stresses in the hopper bins were most easily calculated by graphic method or by a combination of algebraic and graphical methods.
3.4 Structural Design of Bins Once the different pressures acting on the walls of the bin have been defined, designer is ready to determine the thickness of the bin‟s walls. To provid stabitity to the bins against various loads acting due to wind loads and materials to be stored. Stiffeners are provided on the walls of the bins which is also discussed in this section. 3.4.1 Cylindrical Shells The calculation of the size of the vertical walls of cylindrical bins does not present special difficulties. Beyond the self weight of the walls, they are acted upon by two main forces: the 26 | P a g e
lateral pressure and the vertical friction force due to the frication of the material on the walls, which generates vertical compression stresses on the walls. If 𝑝𝑧 is the lateral pressure and r the internal radius of the bin, the thickness of the wall must designed to withstand a circumferential tensile or hoop stress of; 𝑓𝑡 =
𝑝𝑧 𝑟 𝑡
For small bins, stiffeners may not be required. For large and deep bins, because the cylindrical wall may buckle under vertical compressive loads, and may bend under bending moments induced from uneven distribution of the wall pressure due to dynamic effects and due to eccentrically located outlets, etc,. ring stiffeners or rings and vertical stiffeners are recommended. After calculation of the hoop stress as mentioned before the vertical pressure will be calculated. The longitudinal compressive stress is, following Reimbert‟s theory: 𝑓𝑐 =
𝑉 𝑡
=
(𝛾𝑧 −𝑞)𝜋𝑟 2 2𝜋𝑟𝑡
=
𝛾𝑧 –𝑞 𝑟 2𝑡
It should be noted that the above Equation applies only when 𝛾𝑧 > 𝑞 To find the maximum stress in the plate at the level considered, ft and fc may be combined in the form: ft‟ = ft + v fc fc‟ = fc + v ft Where v = 0.3, poisons ratio for steel ft ‟ = maximum tensile stress in the plate fc‟ = max. Compressive stress in the plate ft = circumferential tensile stress or hoop stress fc = longitudinal compressive stress
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For max. compressive stresses in the bin walls, considerations must be given to the portions of bin walls at the stiffener and to those portions of bin walls which lie between stiffeners. The load distribution and their corresponding stresses may be calculated as follows : 𝑞𝑠 =
𝐴𝑠 + 2𝑏𝑒 𝑡 𝐹𝐶𝑆 𝐴𝑠 + 2𝑏𝑒 𝑡 𝐹𝐶𝑆 + 𝑏 − 2𝑏𝑒 𝑡𝐹𝑐𝑢 𝑞𝑢 = 𝑞 − 𝑞𝑠 𝑓𝑐𝑠 =
𝑞𝑠 𝑛(𝐴𝑠 + 2𝑏𝑒 𝑡)
𝑓𝑐𝑢 =
𝑞𝑢 𝑛(𝑏 − 2𝑏𝑒 )𝑡
Where Fcs , Fcu = allowable compressive stress of stiffened and unstiffened shell respectively fcs , fcu = vertical compressive stress of stiffened and unstiffened shell respectively b = horizontal spacing of vertical stiffeners be = effective width of the plate n = no. of vertical stiffeners 3.4.1.1 Stiffened shells The portions of bin shells near the stiffeners have greater load – carrying capacity. If “n” is the total no. of equally spaced vertical stiffeners, and be is the effective width of the shell on each side of the stiffeners, as cshown in figure 4.1, the effective width be will be : 𝑏𝑒 = 0.95𝑡 1 − 0.475
𝑡 𝐸𝑠 𝐸𝑠 𝑏 𝐹𝑐𝑠 𝐹𝑐𝑠
𝐹𝑐𝑠 is the allowable stress of the stiffener and plate column determined by the appropriate column formula with the vertical spacing 𝑙 of the horizontal stiffeners as the column length. Since, the allowable stress 𝐹𝑐𝑠 and the effective width 𝑏𝑒 are interdependent it is necessary to use a trial- and -error method by assuming 𝑏𝑒 ,to calculate 𝐹𝑐𝑠 , or vice versa . After𝐹𝑐𝑠 and 𝑏𝑒 have been determined, the capacity of the stiffened shells of the bin can be calculated as : 𝑞𝑠 = 𝑛 𝐹𝑐𝑠 (𝐴𝑠 + 2𝑏𝑒 𝑡)
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For quick and approximate evaluation, 𝑏𝑒 may be assumed to be 30 to 40 t, where t is the thickness of the plate. It should be noted that the above effective width is taken as approx. equal to that of a flate plate. In the case of a cylindrical panel the load carrying capacity will be increased Due to its curvature. Let λ1 be the slenderness ratio of the stiffener and shell column, and λ2 =20
𝑟 𝑡
,
Where “r” is the shell radius in feet, and “t” the wall thickness in inches, then the combined slenderness ratio can be calculated by : λ=
λ1 λ2 λ1 2 + λ2 2
3.4.2 Stiffeners Due to the effect of wind pressure, arching of material, and uneven distribution of lateral pressure in the horizontal section during filling and emptying are possible, stiffeners are always recommended vertical spacing of the horizontal stiffeners of 10 to 15 ft, and horizontal spacing of the vertical stiffeners of 4 to 10 ft may be recommended as the normal practice. The vertical stiffeners can be designed as a portion of a stiffener and shell column, as discussed in stiffened shells. The horizontal stiffeners should be designed to support the vertical stiffeners against buckling. The minimum width of such a horizontal stiffener to be recommended here is one- hundredth of the diameter of the bin, with a central filling or central discharging device. For bins with non- central fillings or non- central discharging devices, The horizontal stiffeners should be designed for one sided pressure effect. The recommendation by many designers for the design of each horizontal stiffener is: 𝑀 = 0.04 𝛾𝑟 2 𝑑𝑒 𝑙 tan 𝜑 , for 𝑙 < 2 r tan 𝜑 𝑀 = 0.08 𝛾𝑟 3 𝑑𝑒 𝑙 tan2 𝜑 , for 𝑙 > 2 r tan 𝜑 Where 𝑑𝑒 = the eccentric distance of the outlet from the centre of the bin, and M = the moment in the stiffeners 29 | P a g e
In no case , shall the width of the horizontal stiffener be less than one-hundredth of the diameter of the bin, as recommended for bins with central filling or central discharging devices. 3.4.3 Hoppers The shells of the silos are terminated at their lower part, by hoppers, their shape being usually that of a truncated cone in the case of cylindrical shell, in order to permit complete discharge of the stored material through the discharge trap placed at the lowest point. In calculating the thickness of the walls of hoppers, it is assumed that the stored pulverulent materials transmit to the walls of the hoppers the vertical pressure which they exert at the level of the connection to the vertical walls, i.e., at the level of the junction of the walls of the shells to the walls at these hoppers. The following loads are considered : a). The vertical pressure exerted by the stored material at the lower level of the vertical walls. b). The weight of the stored material filling the hopper. c). The weight of the devices fixed onto the hopper (if any). The plates forming the cone will be subjected to both the hoop tension and the meridional tension. Janssen‟s or Reimbert‟s expressions for both lateral and horizontal pressure may be used, but some modifications of a minor nature will be necessary. For application, we will use Janssen‟s expressions. The mean hydraulic radius “r” should be replaced by half the appropriate cone radius
𝑟1 2
and
the co-efficient of friction on the wall 𝜇‟ by the corresponding internal friction coefficient, 𝜇. Those modifications take into account the fact that in this area the material is sliding against the material located outside the radius 𝑟1 , instead of sliding against the bin wall, The lateral pressure would therefore be : 𝑃=
𝛾𝑟1 1 − 𝑒 −2𝜇𝑘𝑧 /𝑟1 2𝜇
Giving a hoop tension of : 30 | P a g e
TH = P𝑟1 Resulting in a hoop stress of : 𝑓𝐻 =
𝑃𝑟1 𝑡
Similarly, the longitudinal tension would take the form : 𝑇𝐿 =
𝑊1 𝑐𝑜𝑠𝑒𝑐 𝜑 2𝜋𝑟1
In above equation 𝑊1 = 𝑞𝜋𝑟1 2 + 𝛾𝑟1 2 𝜋
𝑍′ + 𝑠𝑒𝑙𝑓 𝑤𝑒𝑖𝑔𝑡 3
𝑞𝜋𝑟1 2 = vertical pressure of stored material at lower level Where 𝑞=
𝛾𝑟1 1 − 𝑒 −2𝜇𝑘𝑧 /𝑟 2𝜇𝐾
𝛾𝑟1 2 = weight of the stored material Self weight = weight of the hopper Resulting in a meridional stress of : 𝑓𝐿 =
𝑊1 𝑐𝑜𝑠𝑒𝑐 𝜑 2𝜋𝑟1 𝑡
Both 𝑓 and 𝑓𝐿 will be a maximum at the waist, and a minimum at the outlet. 3.4.4 Roofs The roof should be a self supporting structure. It may be flat, or in the form of a cone or dome. However, in view of the fact that a partial vacuum may develop, above the stored material due to the arching action, larger vents should be provided to prevent any inward buckling of the silo walls or of the roof, itself, from this cause. 3.4.5 Buckling
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In the horizontal planes, both circular and rectangular steel bins are under axial tension and there is no danger of buckling. In vertical planes, the uniformly distributed compressive loading due to the own weight of bin walls, the frictional force of the stored material and roof and equipment loads, buckling of the bin walls may occure at a certain value of the comp. load. 3.4.5.1 Cylindrical Bins The buckling stress for cylindrical bins is given by the classical solution for axially compressed cylinders. 𝜎𝑐𝑟 =
𝐸/𝑎 1
[3 1 − 𝑣 2 ]2
Where h is the wall thickness and 𝑎 is the avg. surface radius, (with h<< 𝑎) The critical values of axial stresses for cylinders subjected to axial compression are conveniently expressed as a function of the so- called Batdorf parameter Z 𝑍=
1 𝐿2 (1 − 𝑣)2 𝑎
With the corresponding values of factor Ka, as shown in Figure 𝐾𝑎 =
𝐿2 𝜎 𝜋 2 𝐷 𝑐𝑟
Figure 3.5 Critical values of axial stresses for cylinders subjected to axial compression
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𝐷=
𝐸 12 1 − 𝑣 2
For thew values of Z > 2.85, long cylinders, the values of 𝑣𝑐𝑟 given by above fig. and equation for 𝜎𝑐𝑟 are the same.(Z < 2.85 represents the short cylinders). 3.4.5.2 Compression ring between cylinder and hopper When the transition from a cylinder to a cone is made abruptly, a compression ring must be provided to resist the horizontal inward pull from the cone, as shown in fig.
Figure 3.6 Cylinder to cone transition
Figure 3.7 Forces on suspended bottoms
This steel ring should be designed for an allowable stress of 10000 psi. This relatively low value is used to minimize deflection and hence the secondary bending stress. But, the compression ring must be checked particularly for buckling. Using a factor of safety of 3, in Levy‟s formula for buckling of a ring under uniform pressure: 𝑇𝐻𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 =
3𝐸𝐼 𝑅𝑟3
Where 𝑇𝐻 = horizontal component of T2 Where T2 = meridional force Fig. Rr = centroidal radius of a ring E = Young‟s modulus I = minimum moment of inertia Using this steps structural design of bins can be done. 33 | P a g e
Chapter 4
Stability of storage tanks The stability of Storage tanks and tall bins are mostly affected By the
seismic loadings and Due to wind loading acting on their structure. So, this storage structures must be designed for with stand this loadings to remain stable. Wind load and seismic load on the tall bins causes vibration in the vessel due to the wind and sudden acceleration in earth‟s crust. Under these conditions the vessel under this loading acts as a cantilever beam and starts vibrating same as the cantilever beam. Slender columns are more able to absorb seismic forces. On the other hand, the reverse is true under the influence of wind forces. If the column is rigid, it will with stand higher wind forces. So, stability consideration is taken for wind load only in the Tall Bins.
4.1 Provisions for Seismic Loading Storage tanks The seismic design of the storage tank is accordance to API 650 (2007) There are three major analyses to be performed in the seismic design, and they are: i) Overturning Stability check - The overturning moment will be calculated and check for the anchorage requirement. The number of anchor bolt required and the anchor bolt size will also be determined based on the overturning moment. ii) Maximum base shear iii) Freeboard required for the sloshing wave height – It is essential for a floating roof tank to have sufficient freeboard to ensure the roof seal remain within the height the tank shell. 4.1.1 - General Hydrodynamic forces exerted by liquid on tank wall shall be considered in the analysis in addition to hydrostatic forces. These hydrodynamic forces are evaluated with the help of spring mass model of tanks.
4.1.2 - Spring Mass Model for Seismic Analysis
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When a tank containing liquid vibrates, the liquid exerts impulsive and convective hydrodynamic pressure on the tank wall and the tank base in addition to the hydrostatic pressure. In order to include the effect of hydrodynamic pressure in the analysis, tank can be idealized by an equivalent spring mass model, which includes the effect of tank wall – liquid interaction. The parameters of this model depend on geometry of the tank and its flexibility. Ground supported tanks can be idealized as spring-mass model shown in Figure 1. The impulsive mass of liquid, mi is rigidly attached to tank wall at height hi (or hi* ). Similarly, convective mass, mc is attached to the tank wall at height hc (or hc* ) by a spring of stiffness Kc . Equations are given below,
Table 4.1 Expression for parameters of spring mass model 35 | P a g e
4.1.3 – Time Period 4.1.3.1 – Impulsive Mode For a ground supported circular tank, wherein wall is rigidly connected with the base slab, time period of impulsive mode of vibration Ti , in seconds, is given by
Ci = Coefficient of time period for impulsive mode. Value of Ci can be obtained from
h = Maximum depth of liquid, D = Inner diameter of circular tank, t = Thickness of tank wall, E = Modulus of elasticity of tank wall, and ρ = Mass density of liquid. 4.1.3.2 – Convective Mode Time period of convective mode, in seconds, is given by
Where,
Cc = Coefficient of time period for convective mode. Value of Cc can be obtained by
D = Inner diameter of tank For tanks resting on soft soil, effect of flexibility of soil may be considered while evaluating the time period. Generally, soil flexibility does not affect the convective mode time period. However, soil flexibility may affect impulsive mode time period.
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4.1.4 – Damping Damping in the convective mode for all types of liquids and for all types of tanks shall be taken as 0.5% of the critical. Damping in the impulsive mode shall be taken as 2% of the critical for steel tanks and 5% of the critical for concrete or masonry tanks. 4.1.5 – Design Horizontal Seismic Coefficient Design horizontal seismic coefficient, Ah shall be obtained by the following expression,
Where Z = Zone factor I = Importance factor given in table, R = Response reduction factor (2.5 - 3.0) Sa/g = Average response acceleration coefficient
Type of liquid storage tank
I
Tanks used for storing drinking water, non-volatile
Table 4. 2 – Importance factor,I
material, low inflammable petrochemicals etc. and intended for emergency services such as fire
1.5
fighting services. Tanks of post earthquake importance. All other tanks with no risk to life and with negligible consequences to environment, society
1.0
and economy.
4.1.6 - Base Shear Base shear in impulsive mode, at the bottom of tank wall is given by
and base shear in convective mode is given by
where, (Ah)i = Design horizontal seismic coefficient for impulsive mode, (Ah)c = Design horizontal seismic coefficient for convective mode, mi = Impulsive mass of water 37 | P a g e
mw = Mass of tank wall mt = Mass of roof slab, and
;
g = Acceleration due to gravity.
Total base shear V, can be obtained by combining the base shear in impulsive and convective mode through Square root of Sum of Squares (SRSS) rule and is given as follows
4.1.7 – Overturning Moment at the Base
For obtaining bending moment at the bottom of tank wall, effect of hydrodynamic pressure on wall is considered. Overturning moment in impulsive mode to be used for checking the tank stability at the bottom of base slab/plate is given by
and overturning moment in convective mode is given by
where hw = Height of center of gravity of wall mass, and ht = Height of center of gravity of roof mass. mc =Convective mass of liquid mi= Impulsive mass of liquid mt = Mass of roof slab mw = Mass of tank wall hc *= Height of convective mass above bottom of tank wall (considering base pressure) hi* = Height of impulsive mass above bottom of tank wall (considering base pressure) Mc*= Overturning moment in convective mode at the base Mi* = Overturning moment in impulsive mode at the base t b = Thickness of base slab
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4.1.8 – Hydrodynamic Pressure
During lateral base excitation, tank wall is subjected to lateral hydrodynamic pressure and tank base is subjected to hydrodynamic pressure in vertical direction 4.1.8.1 – Impulsive Hydrodynamic Pressure The impulsive hydrodynamic pressure exerted by the liquid on the tank wall and base for the circular tanks Lateral hydrodynamic impulsive pressure on the wall, piw , is given by
Where ρ = Mass density of liquid, φ = Circumferential angle, and y = Vertical distance of a point on tank wall from the bottom of tank wall. Coefficient of impulsive hydrodynamic pressure on wall, Qiw (y) can be obtained from Figure.
Fig. 4.1 Impulsive Hydrodynamic Pressure on wall
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Impulsive hydrodynamic pressure in vertical direction, on base slab (y = 0) on a strip of length l', is given by
Where
x = Horizontal distance of a point on base of tank in the direction of seismic force, from the center of tank.
4.1.8.2 – Convective Hydrodynamic Pressure The convective pressure exerted by the oscillating liquid on the tank wall and base shall be calculated as follows: Lateral convective pressure on the wall pcw , is given by
The value of Qcw (y) can be read from the graph
Fig 4.2 Convective Hydrodynamic Pressure on wall
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Convective pressure in vertical direction, on the base slab (y = 0) is given by
4.1.9 – Effect of Vertical Ground Acceleration
Vertical ground acceleration induces hydrodynamic pressure on wall in addition to that due to horizontal ground acceleration. In circular tanks, this pressure is uniformly distributed in the circumferential direction. Which will cause One of the most important type of damage is the „elephant foot ‘ buckling of the lowest course of the tank wall. Hydrodynamic pressure on tank wall due to vertical ground acceleration may be taken as
where y = vertical distance of point under consideration from bottom of tank wall, and Sa / g = Average response acceleration The maximum value of hydrodynamic pressure should be obtained by combining pressure due to horizontal and vertical excitation through square root of sum of squares (SRSS) rule, which can be given as
4.1.10 – Sloshing Wave Height
To provide sufficient free board to eliminate damage during earthquake sloshing wave height is calculated. Maximum sloshing wave height is given by
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where ( Ah )c = Design horizontal seismic coefficient corresponding to convective time period. Free board to be provided in a tank may be based on maximum value of sloshing wave height. This is particularly important for tanks containing toxic liquids, where loss of liquid needs to be prevented. If sufficient free board is not provided roof structure should be designed to resist the uplift pressure due to sloshing of liquid. 4.1.11 – Anchorage Requirement As mentioned above during seismic loading tanks are subjected to many pressure loads and overturning moments. So for stability of storage tanks anchorage is provided using anchor bolts. Circular ground supported tanks shall beanchored to their foundation (Figure)when
If we Consider a tank which is about to rock (Figure ). Let Mtot denotes the total mass of the tank-liquid system, D denote the tank diameter, and (Ah )i g denote the peak response acceleration. Taking moments about the edge,
Thus, when h / D exceeds the value indicated above, the tank should be anchored to its foundation.
4.2 Provisions for Wind Loading
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Wind loading and presence of vacuum in the tank are external pressures and tend to destabilise the tank geometry resulting in collapse by buckling. In fixed roof structures fixed roof provides some stabilising effect. But, In open top and external floating roof tanks do not have the benefit of this shell rigidity and therefore a circumferential stiffeners are provided at the top of the shell & also at regular intervals.
4.2.1 Top Stiffener and Intermediate Wind Girder Design 4.2.1.1 Top Stiffener/ Top Wind Girder Stiffener rings of top wind girder are to be provided in an open-top tank to maintain the roundness when the tank is subjected to wind load. The stiffener rings shall be located at or near the top course and outside of the tank shell. The girder can also be used as an access and maintenance platform. There are five numbers of typical stiffener rings sections for the tank shell given in API 650 (2007) and they are shown in Figure 2.5 [API 650, 2007].
Fig 4.3 Typical stiffener ring section for ring shell
The requirement in API 650 (2007) stated that when the stiffener rings or top wind girder are located more than 0.6 m below the top of the shell, the tank shall be provided with a minimum size of 64 x 64 x 4.8 mm top curb angle for shells thickness 5 mm, and with a 76 x 43 | P a g e
76 x 6.4 mm angle for shell more than 5 mm thick. A top wind girder in my tank is designed to locate at 1 m from the top of tank and therefore for a top curb angle of size 75 x 75 x 10 mm is used in conjunction with the stiffener detail a) in Figure 2.5. The top wind girder is designed based on the equation for the minimum required section modules of the stiffener ring [API 650, 2007].
Where Z = Minimum required section modulus, cm³ D = Nominal tank diameter, m H2 = Height of the tank shell, in m, including any freeboard provided above the maximum filling height V = design wind speed (3-sec gust), km/h The term ( 𝑉 190
𝐷2𝐻 17
) on the equation is based on a wind speed of 190 km/h and therefore the
2
term is included in the equation for the desire design wind speed.
Accordance to API 60 (2007) clause 5.9.5, support shall be provided for all stiffener rings when the dimension of the horizontal leg or web exceeds 16 times the leg or web thickness [API 650, 2007]. The supports shall be spaced at the interval required for the dead load and vertical live load. 4.2.1.2 Intermediate Wind Girder The shell of the storage tank is susceptible to buckling under influence of wind and internal vacuum, especially when in a near empty or empty condition. It is essential to analysis the shell to ensure that it is stable under these conditions. Intermediate stiffener or wind girder will be provided if necessary. To determine whether the intermediate wind girder is required, the maximum height of the un-stiffened shell shall be determined. The maximum height of the un-stiffener shell will be calculated as follows [API 650, 2007]:
44 | P a g e
Where H1 = Vertical distance, in m, between the intermediate wind girder and top wind girder t = Thickness of the top shell course, mm D = Nonimal tank diameter, m V = design wind speed (3-sec gust), km/h As stated in earlier, the shell is made of up diminishing thickness and it makes the analysis difficult. The equivalent shell method is employed to convert the multi-thickness shell into an equivalent shell having the equal thickness as to the top shell course. The actual width of each shell course in changed into a transposed width of each shell course having the top shell course thickness by the following formula [API 650, 2007]:
Where Wtr = Transposed width of each shell course, mm W = Actual width of each shell course, mm tuniform = Thickness of the top shell course, mm tactual = Thickness of the shell course for which the transpose width is being calculated, mm The sum of the transposed width of the courses will be the height of the transformed shell (H2). If the height of transformed shell is greater than the maximum height of un-stiffened shell, intermediate wind girder is required. The total number intermediate wind girder required can be determined by simply divide the height of transformed shell with the maximum unstiffened shell height. Similarly, minimum required section modulus of the intermediate wind girder has to be determined. The same equation in the top wind girder can be used, but instead of the total shell height H2, the vertical distance between the intermediate wind girder and top wind girder is used.
45 | P a g e
4.2.2 Overturning Stability against Wind Load The overturning stability of the tank shall be analyzed against the wind pressure, and to determine the stability of the tank with and without anchorage. The wind pressure used in the analysis is given as per API 650 (2007). The wind load (Fs) on the shell is calculated by multiplying the wind pressure ws to the projected area of the shell, and the wind load (Fr) on the roof will be zero as the roof will be floating on the liquid into the tank, where there will be no projected area for the roof.
Figure 4.4 Overturning check on tank due to wind load As per API 650 (2007), the tank will be structurally stable without anchorage when the below uplift criteria are meet [API 650, 2007].
Where Mpi = moment about the shell-to-bottom from design internal pressure (Pi) and it can be calculated by the formula Mw = Overturning moment about the shell-to-bottom joint from horizontal plus vertical wind pressure and is equal to Fr.Lr + Fs.Ls. Fr and Fs is the wind load acting on the roof and shell respectively and Lr and Ls is the height from tank bottom to the roof center and shell center respectively. 46 | P a g e
MDL = Moment about the shell-to-bottom joint from the weight of the shell and roof supported by the shell and is calculated as 0.5 D. WDL. The weight of the roof is zero since the roof is floating on the liquid. MF = Moment about the shell-to-bottom joint from liquid weight and is equal to
47 | P a g e
References 1. API Standard 650, “Welded Steel Tanks For Oil Storage” American Petroleum Institute, Eleventh Edition, (June 2007). 2. Bob Long and Bob Garner, “Guide to Storage Tank and Equipment “, volume 1,page no.1173 Professional Engineering Publishing, UK (1977).
3. K. Rajagopalan, “Storage Structure”. McGraw-Hill, New York (1989). 4. Antonio Di Carluccio." Dynamic Behavior of Atmospheric storage tank,” Chapter 4, in "Structural Characterisation and Seismic Evaluation of Steel Equipments in Industrial Plants", (2007). 5. Indian Institute of Technology Kanpur, Gujarat State Disaster Management Authority. “Guidelines for seismic design of Liquid storage tanks”, (October 2007).
6. Gerard L. Xavier, “Structural Design of steel bins” Chapter 1-4, (1979) 7. Kuan, Siew Yeng, “Design, Construction and Operation of the Floating Roof Tank Page 46-79, (October 2009). 8. Brownell L.E. and Young, E.H., “Process Equipment Design”, John Wiley, New York, 1959. 9. B.C. Bhattacharyya, “Chemical engineering equipment design”, CBS Publishers (2001) 10. No author identified, no date. “structural design of bin” Retrieved from http// www.fgg.uni-lj.si/kmk/esdep/master/wg15c/l0400.html [Accessed 14/1/12.] 11. J. W. Carson and R. T. Jenkyn, “Load development and structural Considerations in silo design”, Jenike & Johansan incorporated, page 1-16. 12. Bureau of Indian Standards, “Criteria for design of steel bins for storage of bulk materials IS : 9178 (Part 1), Edition 1.2 (1992-08)
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