Rectangular Tank Design

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Rectangular Tank

Design

Basic approach and practical tips

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Main Acceptance Criteria

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Calculated Stress shall be limited to ASME Code Allowable Stress [or] Actual corroded thickness provided shall not be less than required

corroded plate thickness calculated using ASME Code Allowable Stress 2) Maximum deflection limited to one half of the corroded plate thickness

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Nomenclature

TOP EDGE STIFFENER

R1 – Unit Load (Uniform on entire span of top edge stiffener)

HORIZONTAL STIIFENER

R2 – Unit Load (Uniform on entire span of intermediate stiffener)

VERTICAL STIFFENER

“l” - distance between vertical stiffeners (important parameter for shell plate thickness design)

“L” – length of tank (important parameter for top edge stiffener design)

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Nomenclature (continued)

Primary Stiffener

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Nomenclature (continued)

Load on VERTICAL STIFFENERS: UNIFORMLY INCREASING

Load on SHELL (SIDE VERTICAL PLATE) : UNIFORMLY INCREASING

Load on HORIZONTAL STIFFENERS: UNIFORM ON ENTIR SPAN

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List of parts or sections to be designed or checked:

Shell (side plate): Thickness, stiffeners (size and spacing), weld size

Top plate: Thickness, stiffeners (size and spacing), weld size

Bottom plate: Thickness, stiffeners (size and spacing), weld size

Base frame member sizing, weld size, supporting points

Lifting lugs and other attachments

Additional Check for the whole tank and anchoring

Check total tank for wind/seismic/wave/transportation etc. including anchor design.

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Design Input and Conditions

•Tank size: Width x Height x Length, normally inside dimensions

•Internal pressure, if any

•Material / maximum allowable stress values

•Wind loads, seismic loads, wave loads, transportation loads etc. •Calculate maximum pressure against side wall due to weight of contents (p= 0.433  H  s (in psi))

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General Notes and assumptions:

► Design is based on open top basis, which is conservative. The effect of top plate is not considered

► If top edge stiffener of sufficient size is provided, top side of shell plate can be considered as supported on all 4 edges

► Consider either vertical stiffeners or horizontal stiffeners as primary or main stiffeners and let us call, other one “secondary stiffeners”, that are perpendicular to preliminary stiffeners

► Selection of primary stiffeners (vertical or horizontal) is based on tank size and dimensions

► Secondary stiffeners are considered to reduce plate thickness required and to transfer load to main stiffeners

► There is no simple formula or procedure to analysis or design rectangular tank with both horizontal and vertical stiffeners

► All stiffeners shall be continuous and welded at corners

► Shell plate welds shall be full penetration

► Tank design can be optimized on total weight or plate thickness and/or stiffener size

► Tank plate thickness shall be at least 3/16" (5mm) + corrosion allowance

► Suitable corrosion allowance shall be considered

► Use appropriate and consistent units

► Do not combine both vertical stiffeners and horizontal stiffeners at the same time

► If very large tank, consider internal tie-rods. Internal baffles, if any, can be considered as stiffeners. This will reduce tank plate thickness/weight.

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Types of Rectangular Tanks

Let us classify the rectangular tanks into 9 types based on stiffeners arrangement and design procedure.

Types 1 to 4 are simple in construction and design procedures are also simple. Reference [1] or reference [2] can be used directly for design of type 1 to 4 tanks.

The references [1] & [2] do not give direct procedures for type 5 to 8. Hence design approaches for types 5 to 8 are explained below. Type 7 tanks can be designed using reference [6]. Type 9 Tank is designed with Tie-rods and reference [1] gives a procedure.

Design of rectangular tank shell plate (side vertical plate) is critical and procedures are given below. Design procedures for top plate, bottom plate, bottom frame etc. are explained separately. Refer to sketch showing different types of tanks with stiffener arrangement commonly used.

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Types of Rectangular Tanks (Type-1 to 4)

(Classification for design approach)

Type-1

Type-2

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Types of Rectangular Tanks (Type - 5 to 8)

(Classification for design approach)

Type-5 Type-1

Type-1 Type-1 Type-5 Type-6

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Types of Rectangular Tanks (Type - 9)

(Classification for design approach)

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Other Types of Rectangular Tanks

(Not discussed here)

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Type-1: Open top tank without any stiffeners

Shell Plate: Calculate required thickness (tr) and maximum deflection (ymax)

•

Use Roark’s Case 2(d), 3 edges simply supported and 1 edge free, subjected to hydro-static pressure uniformly increasing (zero at top to maximum pressure at bottom)

Required thickness t r = SQRT (pb²/Sa), but not less than 3/16” Y max =   p  b^4 / (E  ta^3), limited to (ta/2)

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Type-2: Tank with Top Edge Stiffener and/or with top plate

If top edge stiffener of sufficient size is provided or top plate is welded to shell plates with or without top edge stiffener, all 4 edges may be considered as supported for shell plate design and Roark’s Case 1 (e) can be used to

calculate required shell plate thickness (tr) and maximum deflection (Ymax). Acceptance criteria shall be stress and deflection.

•

Calculate uniform load on entire span (R1) acting on the top edge stiffener. Consider top edge stiffener as a beam fixed both ends

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Top edge stiffener Imin=R1  b^4 /192  E  ta and select stiffener with I more than I min calculated, however the stiffener angle shall not be less than 2.5” x 2.5” x 0.25”

•

Recalculate shell plate thickness, deflection Roark’s Case 1(d). Select thickness (ta)

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TYPE-3: Tank with Top Edge Stiffener and one

horizontal stiffener

Calculate uniform load on entire span of top edge stiffener R1 & horizontal stiffener R2

•

Calculate moment of Inertia required for stiffeners and select stiffener size

•

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TYPE-4: Tank with Top Edge Stiffener and one or more

vertical stiffeners

•

Calculate R1 and size top edge stiffener. Use length of tank “L” as stiffener length [Do not use stiffener spacing “l” as length of stiffener]

•

Calculate moment of Inertia required for stiffener and select stiffener. Use height of tank as vertical stiffener length and uniformly increasing loading on the vertical stiffener

•

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TYPE-5: Top Tank with Top Edge Stiffener, one

horizontal primary stiffener and one or more vertical

secondary stiffener

Same as type-3 and calculate secondary vertical stiffener size considering uniformly increasing load both ends fixed (Roark’s case 2(d) Table-8; Wa = 0 & Wl = p). Alternatively, use same size as primary horizontal stiffener without calculation

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TYPE-6: Tank with Top Edge Stiffener, one or more

vertical primary stiffeners and one or more horizontal

secondary stiffener

Same as type-4 and calculate secondary horizontal stiffener size considering uniform load on entire span both ends fixed (Roark’s case 2(d) Table-8; Wa=Wl). Alternatively, use same size as primary horizontal stiffener without any calculation

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TYPE-7: Top Tank with Top Edge Stiffener and 2 or more

horizontal stiffeners

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Similar to type-3, however the loads on horizontal stiffeners are calculated using reference [6].

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Calculate load (uniform load on entire span) on each stiffener R1, R2, R3 etc. Refer Attachment for sample calculation.

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Calculate moment of Inertia required for each stiffener, select stiffener

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Recheck plate thickness & deflection Roark’s Case 1(d). Select thickness (ta)

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TYPE-8: Tank with Top Edge Stiffener, 2 or more

horizontal primary stiffeners and one or more vertical

secondary stiffener

Same as Type-7 and calculate secondary vertical stiffener

considering uniformly increasing load both ends fixed (Roark’s case 2(d) Table-8). Alternatively, use same size as primary stiffener without calculation.

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TYPE-9 Open Top Tank with Tie-rod supports

(For very large rectangular tanks, internal tie-rods can

be considered to reduce plate and stiffener size and

weight, if permitted for service or process requirements.

Internal baffles or partition plates can be considered as

tie rods/stiffeners)

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Top plate for Rectangular Tank

(common for all types of tanks)

►Design top plate, if applicable, [4 edges simply supported, uniform load over entire plate - Roark’s Case 1 (a)] Loads to be considered self weight, maintenance load, snow load etc. Use 2000 kg/m2, as a default uniformly distributed load on entire surface of top plate and add internal pressure if any.

►Provide stiffener for top plate by connecting all vertical stiffeners, as a default. This is mainly required for transfer of load from

vertical stiffener, unless special stiffener arrangement is designed.

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Bottom plate and Base Frame for Rectangular Tank

(common for all types of tanks)

• Provide base frame covering all 4 sides of the tank

• Consider simply supported both ends for sizing the long side frame member and load half of the maximum design weight UDL (uniformly distributed along the entire length), provide same size for short side (no calculation is required for short side-conservative)

• Provide stiffeners for tank bottom plate (connecting long side members of base frame) load may be calculated (W = p x spacing) kg/mm (uniformly distributed load/unit length). Stiffener size can be of smaller than outer base frame member size

• If required, provide additional stiffeners in perpendicular direction (smaller in size than outer base frame member size) in order to reduce the bottom plate thickness.

• Check bottom plate thickness for maximum un-stiffened area - Roark case 1(a) Table-26

• Minimum thickness shall be 0.25” (6 mm) plus corrosion allowance, if entire surface of the bottom plate is supported.

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Additional points for advanced design (Future)

► Combined effect of plate and stiffeners (limits 10 times plate thickness)

► Selection of primary stiffeners (vertical or horizontal) based on tank size and dimensions, relation between tank length-L and Height-H

► Bolted rectangular tanks, bolted top plate

► Consideration of design pressure, usually a small pressure like 0.05 bar

► Loading: seismic, transportation, wave etc.

► Top plate loading 2000 kg/sq.m

► Nozzle loading

► Lifting lugs, lifting analysis

► Spacing of horizontal stiffeners (unequal, increasing spacing from bottom to top)

► Weight estimation, optimization of weight, plate thickness, stiffener size/spacing etc.

► Types of loading UDL, uniformly increasing loading

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Practical tips

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Preferred type of welded joints (corner weld joining shell plates)

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Stiffener arrangements

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Do not extrapolate the design procedure of one type to other type without proper consideration

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Un-stiffened tanks may not be larger than 30 ft3 (0.85 m3)

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Un-stiffened tank size (any side) may not exceed 3 ft (0.9 m)

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For using Roark’s formula 2(d) in table 8 (both ends fixed), the tank shall have adequate stiffeners and all tank corners shall have

stiffener/framed structure. Stiffeners shall be continuous and interconnected at the ends

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Do not use Roark’s formula 8(d) in table 11 (rectangular tank fixed all edges, uniformly decreasing load parallel to side b), unless stiffeners and frame are very rigid

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References:

1. Eugene F.Megyesy, Pressure Vessel Handbook, Pressure Vessel

Publishing Inc., 12th Edition 2001 (Check for latest edition)

2. Kanti K Mahajan, Design of Process Equipment, Pressure Vessel Handbook Publishing, Inc. Third Edition 1990 (Check for latest edition)

3. Kanti K Mahajan, A method for designing rectangular storage tanks, Chemical Engineering, March 28, 1977 pp 107-112

4. Warren C. Young, Richard G. Budynas. Roark’s Formulas for Stress & Strain, 7th Edition

5. Omer W. Blodgett, Design of welded Structures, The James F.Lincln Arc Welding Foundation, Fifteenth Printing March-1996

6. M.Starczewski, Non-Circular Pressure Vessels – Some guidance notes for designers, British Engine Technical Report 1981 Volume XIV pp 62-88

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Rectangular Tank Design