How to Calculate Flat Plate Thickness of Flat Bottom Storage Tank?

Design of Bottom Plate :

Bottom Plate is assumed to be simply supported rectangular plate under uniform pressure ;

The bottom plate has been provided with stiffeners at a span of 666 mm X 375 mm

i.e. b₁ = 0.666m & a₁ = 0.375m.( a & b values will be as per your requirment)

Therefore, b₁ / a₁ = 0.666/ 0.375 = 1.7

Now, as per Table 6, page 118 of TPS(theory of Plates)

M_x = β' q₁ a₁² and (2.0)

M_y = β'₁ q₁ a₁² (3.0)

where,

M_x = Bending moment about 'X-axis'

M_y = Bending moment about 'Y-axis'

D.1.1 q₁ = (Hydrostatic Pressure + Unit weight of Plate ) in kg/cm²

= Pressure due to water column of 2000 mm + Weight of plate / Plate area

= [0.20 + 3000X2000x8x0.00000785/(300x200)] (considering 8mm thk. Plate)]

= 0.20 + 0.00628 = 0.20628kg/cm²

β' = 0.0555(interpolated from Table 6, page 118 of TPS)

β'₁ = 0.0493 (interpolated from Table 6, page 118 of TPS)

Therefore, putting the values in eqns. (2.0) & (3.0), we get

M_x = 0.0555 x 0.20628 x (37.5)² = 16.09 kg-cm and,

M_y = 0.0493 x 0.20628 x (37.5)² = 14.3 kg-cm

Resultant Bending Moment, M₁ = √( M_x² + M_y² )

= √( 16.09 ² + 14.3² ) = 21.52 kg-cm

Again, as per Cl. BSB-8, page BSB-6&7 of 'Elementary Strength of Material' by Birinder Singh ;

Section Modulus, Z₁ = b₄ x d² = M (4.0)

6 S_d

where

b₄ = 1 cm (Considering unit width of plate)

d = 't₁' in cm. (i.e. thickness of plate to be obtained)

S_d = Maximum Allowable Design Stress in kg/cm² = 153 MPa

= 153 X 10.19716/cm²

M = M₁ = 21.52 kg-cm

D.1.2 Therefore, putting the values in eqn. (4.0), we get

1 x t₁² = 21.52

6 153 X 10.19716

or, t₁ = √[21.52x6/(1560.16)] = 0.287 cm = 2.87 mm

(without corrosion allowance)

Thus, thickness of bottom plate with corrosion allowance =t₁+CA =2.87+2.0= 4.87mm

Hence, Thickness of Bottom Plate provided as 8.0 mm.

D.2 Stiffener Sizing Calculation for Bottom Plate :

Total load on bottom plate, W₁ = Total weight of water filled tank = 12376.8 kg

= 0.206 kg/cm²

D.2.1 Considering, Section of stiffener as ISMC 75 with unit weight of 6.8 kg/m

[as per table II, page 6 of SP-6(Part-I)];

Now, uniform load on stiffener section, w₁ = W₁xa₁ + unit wt. of section

= 0.206x0.375x100 +0.068 =7.793 kg/cm

Maximum length of un-stiffened section, l₁ = b₁ = 0.666m =66.6 cm

Therefore, Considering UDL on simply supported Beam;

Bending Moment on stiffener section, M₁ = wl²/8 (as per Cl. SFBM-12, page SFBM-23

of 'Elementary Strength of Material' by Birinder Singh)

= w₁xl₁²/8 =7.793X66.6²/8=4320.78 kg-cm

Now, Allowable Bending Stress, σ_bc = 152 MPa (Refer Sl. No. C.1)

= 152 x 10.19716 kg/cm²

Required section modulus, Z₁ = M₁/ σ_bc = 4320.78 = 2.787 cm³

152x10.19716

D.2.2 But, Section modulus of ISMC 75 = 20.27cm³ [as per table II, page 7

of SP-6(Part-I)]

> 2.787 cm³ and thus satisfactory.

Hence, Actual Stiffener Size selected as ISMC 75.

D.3 Deflection calculation of bottom plate :

W1_max = α q a⁴ = α q a⁴ (as per Eqn. No. 141, Page No. 117 of TPS) (5)

D EI

Where,

W1_max = Maximum deflection of plate in cm

q = Uniformly distributed load, kg/cm² /cm width of plate = q₁ = 0.20628 kg/cm

a = Smaller Side of the unstiffened area in cm = a₁ = 0.375 m = 37.5 cm

D = Flexural rigidity of the plate = EI [as per Eqn. 4, page 5 of TPS]

α = Numerical factor depending upon ratio b/a

E = Young's modulus in kg/cm² = 2x10⁶ kg/cm²

I = Moment of inertia in cm⁴ = (1/12)xbd³ [as per Cl. MOI-5, page MOI-4 of

'Elementary Strength of Material' by Birinder Singh]

= (1/12) x 1 x 0.8³ cm⁴ [Considering plate width,b = 1 cm & plate

depth,d = 0.8 cm]

Now,

a = a₁ = 0.375 m = 37.5 cm; b = b₁ = 0.666m = 66.6 cm

For b/a = 66.6/37.5 = 2, α = 0.00486 [as per Table 8, page 120 of TPS]

D.3.1 Therefore, putting the values in eqn. (10.0), we get

W1_max = 0.00486 x 0.20628x (37.5)⁴ = 0.00061cm = 0.0061mm

2 x 10⁶ x (1/12) x 37.5 x 0.8³

D.3.2 Now, As per Cl. 3.13.1.2 of IS-800;

Limiting vertical deflection, δ₁ = a₁/325 = 37.5/325 = 0.1154 cm. = 1.154 mm

Since, W1_max is less than δ₁ , the 8.0mm thk. bottom plate is safe under deflection.

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