Ejemlo Posta WeldedSteelTankCalcs_071713_PRINT (1)

AWWA D100 Moin - Costa Rica

Engineer: T. Tovey, PE Check: S. Goto, PE

Define Units

References 1) AWWA D100-11, IBC 2009 and ASCE 7-05 2) Basis of Seismic Provisions for welded Steel Oil Storage Tanks by Wozniak & Mitchell. 3) Steel Plate Engineering Data Vol. 1, Useful Information on the Design of Plate Structures, Steel Tanks for Liquid Storage 1982, SPFA 4) Structural Engineering Handbook, by Gaylord, 3rd Edition Chapter 27, Steel Water Tanks, by Bob Wozniak 5) ACI 318, Chapter 9 and AISC Manual of Steel Construction cone roof slope s =3/4":12"

tank diameter "D" water depth "h"

height of tank shell ="Hs"

ring wall depth "Df"

Dimensions and Design Criteria π 2 Diameter D  33.0  ft , water height h p  40  ft resulting in V   D  h p  255923.1  gal 4 R 

D 2

G  1.0

R  16.5  ft

diameter of tank and radius, ft.

specific gravity of water

Roof Snow load: pg  0  psf

Assumed snow load for Costa Rica

However, AWWA D100-11 minimum pressure for live load or snow load is 25 psf; therefore use: LL  25  psf

2/28/2013

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AWWA D100 Moin - Costa Rica

Engineer: T. Tovey, PE Check: S. Goto, PE

Wind Loads: Design wind load: from Drawing 003-S-0001 m Vdes  42   93.951  mph s

V 

Vdes mph

Cf  .60

force coef. per AWWA D100, Table 2

G'  1.0

wind gust factor (Sec. 3.1.4)

 93.951

I  1.15

wind importance factor (Sec. 3.1.4)

Soil and Seismic Factors:

Allowable bearing pressure:

f brg  200  kPa  4177.087  psf

Site Class, Sms and Sm1 values from project Geotech, Nason McCullough on 2-14-13: Soil underneath tank is to be 'vibro-compacted soil': Seismic parameters: SMS  1.0

SM1  1.0

Seismic Use Group: III

Site Class = D

IE  1.5

From Table 24 for Importance factor I  1.5 E

Design response spectra; U  .67 scaling factor This U scaling factor value should be .67 for 5% dampening Refer to IBC and to the AWWA D100 STD and eq 16-39 and 16-40 of IBC 2009. (Eqn. 13-7) SDS  U  SMS SDS  0.670 SD1  U  SM1

SD1  0.670

(Eqn. 13-8)

A v  0.14  SDS

A v  0.094

vertical acceleration per AWWA D100, Section 13.5.4.3

Tc  2  π 

D

 3.68  h p  3.68  g  tanh  D 

Tc  3.318 s

Eqn. 13-22 impulsive first mode slosh period

TL  16  sec region dependent transition period per Nason McCullough on 2-14-13 Ts 

SD1 SDS

Sai  SDS 2/28/2013

Ts  1 Sai  0.67

Section 13.2.7.3.1 Section 13.2.9.2 Ground-supported flat-bottom tanks.

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AWWA D100 Moin - Costa Rica

Engineer: T. Tovey, PE Check: S. Goto, PE

Check above formulas for application of design response spectrum for convective component Sac = design spectral response acceleration for the convective component, 0.5% damped, at the first mode sloshing wave period TC stated as a multiple (decimal) of g Tc  3.318 s K  1.5 K  SD1 Tc

TL  16 s

"1" means true

T c  TL  1

damping scaling factor, Section 13.2.7.3.2

 sec  0.303 K  SD1 Tc

K  TL  SD1

AWWA Eq 13-12

Tc

 sec  SDS  1

2

 sec  1.461

AWWA Eq 13-13

"1" means true

logic to pick design response spectrum for convective component Sac 

 K  SD1  min   sec SDS if Tc  TL  Tc    K  TL  SD1 Tc

2/28/2013

2

 sec otherwise

"Eq 13-12 Governs"

if Tc  TL

"Eq 13-13 Governs"

otherwise

 "Eq 13-12 Governs"

Sac  0.303

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AWWA D100 Moin - Costa Rica

Engineer: T. Tovey, PE Check: S. Goto, PE

Horizontal Design Accelerations; AWWA Section 13.2.9 for ground supported flat bottom tanks section 13.2.9.2 : GENERAL PROCEDURE uses equations 13-9, 13-10, 13-11 and equations 13-12 and 13-13 Select Response Modification Factors: Table 28 Response modification factors Ri and Rc Response Modification Factor Rc (convective component) -

Structure

Ri (impulsive component)

Cross-braced, column-supported elevated tank 3.0* Pedestal-type elevated tank 3.0 Ground-supported flat-bottom tank Mechanically-anchored 3.0 1.5 Self-anchored 2.5 1.5 * The response modification factor Ri for cross-braced, column-supported elevated tanks only applies to tanks with tension-only diagonal bracing. Tanks that utilize tension-compression diagonal bracing are beyond the scope of this standard.

Tank will be Ground supported, flat bottom, mechanically anchored: AWWA D100, Table 28: Ri  3

Rc  1.5

Determine Design Impulsive Acceleration: per AWWA Eq 13-17 Sai  IE

A i 

1.4  Ri

AWWA Eq 13-17; site specific procedure is based on 5 percent damped, Sai

 0.239

Determine Design Convective Acceleration: per AWWA Eq 13-18 A c 

Sac  IE 1.4  Rc

AWWA Eq. 13-18 design convective acceleration - site specific procedure

 0.216

ss  19.33

Maximum design tensile stress from Table 34

Input Table: First column is the design shell thickness. Second column is to determine height of

tank. Third column is needed for Chapter 14 tank steel strengths if different strength steels are used at different shell courses.

.3125  .3125  .375 tt    .375   .5   .5 2/28/2013

5 ss  8 8 8 8 8

 0.313 ss  0.313   ss   0.375 ss  0.375   0.5 ss    0.5 ss  

5 19.33 



8 19.33  8 19.33 



8 19.33  8 19.33 

n  rows ( tt)

n6

number of shell courses



8 19.33 

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AWWA D100 Moin - Costa Rica

  2 w  submatrix  tt 1 n 1 1   ft 1 t  submatrix tt 1 n 1 1  in

Hs 



Engineer: T. Tovey, PE Check: S. Goto, PE

shell course thk. shell course width total shell height of tank

w Hs  45 ft

Summary of Allowable stresses for chosen weld joint efficiency; E  1 Allow.

Allow. Shell

Shell

Stress times

5.0

Stress, ksi 19.33

E, ksi 19.33

0.3125

8.0

19.33

19.33

3

0.375

8.0

19.33

19.33

4

0.375

8.0

19.33

19.33

5

0.5

8.0

19.33

19.33

6

0.5

8.0

19.33

19.33

Shell Course

Shell Thickness

Shell

(in)

Width (ft)

1

0.3125

2

(from top)

Static & Dynamic Analysis Prgm

Static & Dynamic Shell Summary; Req'd

Shell

Shell

Course

Dynamic

Shell

Thick., in Shell

(from top)

Req'd

Static

Static Thick., in.

Stress, ksi

Shell Thick., in

Dynamic

Impulsive

Shell

Hoop Force, Hoop Force,

Stress, ksi Ni, lbs/in

Convective Nc, lbs/in

Hydrostatic Hoop Force, Nh, lbs/in

1

0.31

0.19

2.28

0.02

3.30

131

132

429

2

0.31

0.19

5.93

0.06

7.57

280

54

1115

3

0.38

0.19

9.59

0.09

11.70

353

22

1802

4

0.38

0.19

13.24

0.11

15.57

362

9

2488

5

0.50

0.19

16.89

0.14

19.43

362

4

3175

6

0.50

0.20

19.33

0.17

21.95

362

3

3861

The tank manufacturer will design the roofing system and rafter spacing. Estimated roof wt. estimated_roof_unitwt  15  psf W r  estimated_roof_unitwt  h' 

 D  12  2 

.75

2/28/2013



π 4

2

D

W r  13  kip

total roof DL

h'  12.375  in roof rise

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AWWA D100 Moin - Costa Rica

Engineer: T. Tovey, PE Check: S. Goto, PE

Sloshing of Water in Tank: 13.5.4.4 The freeboard provided shall meet the requirements of Table 29, unless otherwise specified. The sloshing wave height shall be determined by the equation; note SD1  0.67 and SDS  0.67

Sloshing calculations: A c  0.216 Tc  3.318 s

A f 

Convective and impulsive design accelerations

A i  0.239

Since Tc is less than T.L, equation 13-55 applies for Seismic Use Group III

K  SD1 Tc

 0.303

Convective design acceleration for sloshing

sec

Eqn 13-52

d  .5  D  A f  4.998 ft

Minimum freeboard for Seismic Use Group III is: per AWWA D100, Table 29 (min freeboard =d)

Freeboard  5  ft

Detailed Prgm. to Analyze Each Shell Course (not currently in AWWA). Determine convective & impulsive water weights and moment arms around tank base; calc moments for both tank shell (EBP=excluding bottom pressure) & slab foundation (IBP=including bottom pressure); determine shell wt., roof wt., shears, moments and slosh height; D  33  ft and hTank  ft p  40 Moments & Shears Prgm

Summary of Tank Moments & Shears; Shell Course (from top)

Accum. Sum of

Shell

Slab

M oment,

M oment,

432

kip*ft 20

kip*ft 20

67

67

Shear, kips

1

Shell wts., 7

2

17

434

3

30

437

646

662

4

43

440

1462

3045

5

60

444

4550

6525

6

76

448

8047

10076

M slab  max ( g')  kip  ft Fy  36000 2/28/2013

M slab  10076  kip  ft

ASTM A36 yield stress

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AWWA D100 Moin - Costa Rica

Engineer: T. Tovey, PE Check: S. Goto, PE

The following program determines the vertical shell buckling stress and required shell thickness of each shell course (not in AWWA D100) Vertical Buckling Prgm.

The following program determines effective shell stress and required shell thickness of each shell course based upon principle dynamic hoop stress (tension) and vertical stress (compression) using Henky Von Mises Eqs. σe =

σx2  σx σy  σy2 (not req'd by AWWA)

Effective Stress Prgm.

The following programs determine greater of static, dynamic, vertical buckling, effective stress (not req'd by AWWA) or 1/4" min. shell thickness for each shell course (this departs from AWWA); pick greatest for req'd design; compare existing shell thickness to required design shell thickness..."OK" if exst. is greater than design; determine order of equations used to solve for max. wall thickness Shell Thickness Summary Prgms

Shell Summary Table; Shell Course

Shell Thick

(from the top)

(in)

Req'd Shell

Shell Course

Req'd Shell

Wt (kips)

Thickness (in)

Course Wt ( Status

Governing Condition

kips)

1

0.31

6.6

0.25

5.3

OK

1/4" min.

2

0.31

10.6

0.25

8.5

OK

1/4" min.

3

0.38

12.7

0.25

8.5

OK

1/4" min.

4

0.38

12.7

0.25

8.5

OK

1/4" min.

5

0.50

16.9

0.25

8.5

OK

1/4" min.

6

0.50

16.9

0.29

9.8

OK

Vert. Buckling

Tank Wind Base Shear and Overturning Moments;

Pw  q z GC f  30C f

V  93.951 mph

q z  0.00256 K z IV 2

AWWA Eq. 3-1

AWWA Eq. 3-2

Wind Pressure Prgm

Tank Base Wind Shears and Overturning Moments Summary; D i st ance t o G r o und , ft 4 6 .0 4 5.0 4 0 .0 3 2 .0 2 4 .0 16 . 0 8 .0

2/28/2013

Kz

qz, p sf

Exp o sur e D Pw , F, ar m, p sf kip s ft

1.2 7 1.2 7 1.2 7 1.2 7 1.2 7 1.2 7 1.2 7

3 3 .0 3 3 .0 3 3 .0 3 3 .0 3 3 .0 3 3 .0 3 3 .0

19 .8 19 .8 19 .8 19 .8 19 .8 19 .8 19 .8

0 .3 3 .3 5. 2 5. 2 5. 2 5. 2 5. 2 2 9 .7

4 5.3 4 2 .5 3 6 .0 2 8 .0 2 0 .0 12 .0 4 .0

M o ment , ki p * f t 15. 3 13 8 .9 18 8 .2 14 6 .4 10 4 .6 6 2 .7 2 0 .9 6 76 . 9

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AWWA D100 Moin - Costa Rica

Kz

qz, p sf

Exp o sur e D Pw , F, ar m, p sf kip s ft

1.2 7 1.2 7 1.2 7 1.2 7 1.2 7 1.2 7 1.2 7

3 3 .0 3 3 .0 3 3 .0 3 3 .0 3 3 .0 3 3 .0 3 3 .0

19 .8 19 .8 19 .8 19 .8 19 .8 19 .8 19 .8

D i st ance t o G r o und , ft 4 6 .0 4 5.0 4 0 .0 3 2 .0 2 4 .0 16 . 0 8 .0

0 .3 3 .3 5. 2 5. 2 5. 2 5. 2 5. 2

4 5.3 4 2 .5 3 6 .0 2 8 .0 2 0 .0 12 .0 4 .0

2 9 .7

Engineer: T. Tovey, PE Check: S. Goto, PE

M o ment , ki p * f t 15. 3 13 8 .9 18 8 .2 14 6 .4 10 4 .6 6 2 .7 2 0 .9 6 76 . 9

Exposure D: values from table above Vw  26.5  kips

M w  536.4  kip  ft Pw

Check AWWA Eq 3-36 for Intermediate Wind Girders; P   19.802 aw psf D tank dia. D  D  33 tt  .3125 top shell course thickness ft h' 

10.625  106  tt

D Paw     tt 

Conclusion:

1.5

h'  154.52

allowable height, ft., of tt  0.313 plate between intermediate wind girders or boundaries

tt  0.313 " shell course height Hs  45  ft is less than h'  154.52 ft total

height calculated; therefore intermediate wind girders are not req'd for this shell area. Intermediate Wind Girder Prgm

Check tank stability for Seismic overturning to determine seismic loads would require anchor bolts. Hs  45  ft and D  33 The equations apply to self anchored tanks only (where J