20100419043934!El_Chaguite_Tank_Design.xls

8/14/2019 20100419043934!El_Chaguite_Tank_Design.xls

1/37

Reinforced Brick and Mortar Design

Created by: Ann Polaneczky, Ryan Mahoney & Rajesh

Last Revision: 6/9/2009

Checked by:

This design is based on:

Circular Storage Tanks and Silos by A. Ghali

Design of Concrete Structures by A. Nilson et. al.

Concrete Slabs Analysis and Design by R. J. Cope & L. A. Clark

Reinforced Concrete Slabs by R. Park & W. Gamble

See reference tables for formulas and assumed constants

Symbol Value

Bricks

Brick Length BrickL 10.00Brick Width BrickW 5.00

Brick Height BrickH 2.50

Tank

Tank Wall Thickness hb 10.00

Inner Diameter of Tank DINNER 13.00

Diameter of Tank D 13.83

Radius of Tank r 6.92

Inner Radius rINNER 6.50

Outer Radius rOUTER 7.33

Height of Water in Tank hWATER 6.50

Height of Tank hTANK 7.00

Circumference C 46.08

Mortar Thickness tMORTAR 1.33

Mortar Thickness at Rebar Location tREBAR MORTAR 2.00

Unit Weight Water wWATER 62.40

Unit Weight Mortar wMORTAR 120.00

Unit Weight Concrete wCONCRETE 150.00

Seismic Loads

Max Ground Acceleration a 2.45

Acceleration due to gravity g 9.81


2/37

Seismic Ratio S=a/g 0.25

Materials

Yield strength of Steel fy 40000.00

Tensile Strength of Masonry f'm 300.00

Modulus of Elasticity, Steel Es 29000000.00Modulus of Elasticity, Masonry Em 165000.00

N Es/Em 175.76

Compressive Strength of Concrete f'c 3000.00

Modulus of Elasticity, Concrete Ec 3122018.578


3/37

Punjabi

Units Notes

inin

in

in 2 Bricks wide

ft BrickL

Diameter to middle of tank wall

ft Radius to middle of tank wall

ft

ft

ft

ft

ft

in

in

pcf

pcf

pcf

m/s2

REF: Global Seismic Hazard Assessment Program Map: Central

America - Carribean

m/s2

These dimensions were taken during assessment


4/37

d=2r

psi

psi

psipsi

psi

psi


5/37

BrickH

BrickW

l


6/37

hb

hb


7/37

Tank Wall Design

Horizontal Reinforcement

Symbol Value Units

3.67

hTOP/hBOTTOM 1.00

Force Due to Water Pressure qHYDROSTATIC 405.60 lb/ft^2

N= coeff. X qr coefficient 1.00

@ x=0, (x/l)=0 & coeff. =

NHYDROSTATIC PER FOOT= 2804.56 lb/ft

NHYDROSTATIC= 2103.42 lb/9" section

Horizontal Rebar spacing HRebarSPACING

9.00 in

Weight of Water in 9" Section of Tank WWATER(9") 6211.87 lbs

Seismic Load qSEISMIC 112.15 lb-ft

coeff = 1.00 @ any (x/l)

NSEISMIC= 775.69 lbs / 9" section

NTOTAL 2879.11 lbs/9" sectionFactor of Safety FS 2.50

Ns 7197.78 NTOTAL*FS

Area of Steel As 0.18 in2/9" section

SEISMIC FORCES - Assuming Rigid Water

HYDROSTATIC FORCES

TOTAL LOADING


8/37

Notes

l^2 / dhb

* thickness of our walls does not vary.

q=(unit weight of water * pressure head) = w*l

coefficient from Table 11.1 of A.Ghali

Vertical distance between hoops (3 brick layers)

w**(rINNER)^2*HrebarSPACING

Weight of 9" section*S/DINNER

REF: Table 11.3 Circular Storage Tanks and Silos by A. Ghali

NSEISMIC+ NHYDROSTATIC

2 No. 3 bars at 9" O.C. (every 3rd Brick layer)

Hoop Force


9/37

D

siesmic loading = load per 9" of water


10/37

Tank Wall Design

Bending Moment on Vertical Wall

Fixed End at bottom, Free End at top

Symbol Value Units

HYDROSTATIC COMPONENT

Dimensionless Parameter (Tank Shape) 3.67hTOP/hBOTTOM 1.00

Force Due to Water Pressure qHYDROSTATIC 405.60 lb/ft 2

Max Negative Coefficient: -0.02655

Max Positive Coefficient: 0.00763

Hydrostatic Neg. Moment = NMomentHYDROSTATIC -454.91 lb-ft/ft

Hydrostatic Pos. Moment = PMomentHYDROSTATIC 130.75 lb-ft/ft

SEISMIC COMPONENT

Weight of Water in 9" Section of Tank WWATER(1') 7033.79 lbs/ft

Force due to Seismic Load qSEISMIC 126.99

Max Negative Coefficient: -0.03640

Max Positive Coefficient: 0.00739

Seismic Moment = coefficient*qh*l^2

Seismic Neg. Moment = NMomentSEISMIC -195.28 lb-ft/ft

Seismic Pos. Moment = PMomentSEISMIC 39.63 lb-ft/ft

TOTAL BENDING MOMENT

Total Negative Moment NMomentTOTAL -650.19 lb-ft/ft

Total Positive Moment PMomentTOTAL 170.39 lb-ft/ft

FACTORED BENDING MOMENT

Factor Of Safety FS 2.5

Negative Factored Moment NMFACTORED -1625.48 lb-ft/ft

Positive Factored Moment PMFACTORED 425.96 lb-ft/ft


11/37

Notes

l^2 / dhb

* thickness of our walls does not vary.

q=(unit weight of water * pressure head) = w*l

Coefficient from Table 11.23 of A. Ghali


Coefficient*qHYDROSTATIC*hWATER

Coefficient*qHYDROSTATIC*hWATER

w**(rINNER)^2*(9/12)

weight of 1' section*S/D



Coefficient*qSEISMIC*hWATER

Coefficient*qSEISMIC*hWATER

NMomentHYDROSTATIC+ NMomentSEISMIC

PMomentHYDROSTATIC+ PMomentSEISMIC


12/37

Tank Wall Design

Vertical Reinforcement

Symbol Value Units

Design of Vertical Rebar

Base of Section b 12.00 in

Effective Depth d 5.00 in

Trial & Error:

Area of Steel As 0.20 in2

Spacing 18.00 in

Area of Steel per ft AsPER FT 0.133 in2

= As/bd 0.0033

N 9.29

k = sqrt((pn)^2 + 2pn) - pn k 0.22

j = 1 - k/3 j 0.93

M = As*fy*j*d M 2059.40 lb-ft

Factored Moment NMFACTORED 1625.48 lb-ft

Straight Development Length needed for rebar with standard tank = 0.02*fy/sqrt(f'c)*(diameter of bar)

Diameter of #4 Rebar #4 db 0.5 in

Diameter of #3 Rebar #3 db

0.375 in

#4 Rebar Development Length ldh(#4) 7.303 in

#3 Rebar Development Length ldh(#3) 5.477 in

if we provide >2" of cover we can multiply this by 0.7 (ACI Code)

ldh(#4) 5.112 in

ldh(#3) 3.834 in

However ACI states the development length cannot be less than 6"


13/37

Notes

No. 4 Rebar

Eq. 3.11 of A. Nilson et. al.

Es/Ec



(Eq. 3.7 of A. Nilson et. al.)

M MUST BE > NMFACTORED


14/37

Tank Wall Design

Checking for Cracking in Walls

Symbol Value

Critical Stress vs Total Stress

Base of Section b 12

Height of Section h 10Inertia I 1000

NMomentHYDROSTATIC 454.91

NMomentHYDROSTATIC 5458.90

c 5

27.29

Unit Weight of Mortar wMORTAR 120.00

Unit Weight of Concrete wCONCRETE 150.00

Tank Wall Height hTANK 7.00

Outer Radius rOUTER 7.33

Wall Stress StressWALL 5.83

Roof Stress StressROOF 2.29

Compressive Stress StressCOMP 8.13

Total Stress StressTOTAL 19.17

Critical Stress StressCRITICAL 20


15/37

Units Notes

in

inin^3 I = bh^3/12

lb-ft/ft Higher value from wall moment calculation

lb-in/ft

in

psi Stress = Mc/I

pcf

pcf

ft

ft

psi

psi

psi from weight of wall + weight of roof

psi

psi Critical stress must be > Total Stress


16/37

Foundation Design

Rebar at bottom of Foundation:

1 Foot Section

15 ' 17 ' diamet

foundationh = 9" d = 6" 15 ' to outs

17 ' of tank wall

pmin = 0.001

therefore As= pbh = 0.096 0.108

Use No. 3 rebar at 12" O.C.

Rebar at Top of Foundation:

12"

9"

6"

Design Moment for Foundation = M factored from vertical rebar calc

1625.48 lb-ft/ft

because d for the foundation is larger than d for the walls (6">5") calc is not necessary with stronger

concrete in foundation (instead of brick and mortar in walls) and no.4

rebar @ 12" O.C. (instead of 18" to prevent cracking)

Use No. 4 rebar at 12" O.C.


17/37

er

ide

ls


18/37

Roof Design

Elastic Method - Load Combination

Symbol Value Units

Load Combination

Roof Thickness tROOF 0.5 ft.

Factor of Safety FS 1.4

Weight of Slab (DL) wSLAB 105 psf

Weight chlorination tank (DL) wCl. Tank 2380 lbs

Weight person wPERSON 200 lbs

Concentrated Load from People p 1020 lbs

Bending Moment at Center Due to Distributed Load, q

Base of Section b 12 in

Effective Depth of Section d 4 in

Bending Moment due to Distributed Load

MCENTER= 0.2 * q * a^2 MCENTER, q 1129.33 lb-ft/ft

Bending Moment at Center Due to Concetrated Load, p

MCENTER, p 1360 lb-ft/ft

Total Bending Moment

MuTOTAL 2489.33

MnTOTAL 2765.926


19/37

Notes

1700*1.4(FOS)

Wt of 3 people * 1.7(FOS)

Eq from Concrete Slabs Analysis and Design by R. J. Cope & L. A. Clark

where a=radius and q=wSLAB

MCENTER= 0.4*p

Mu=0.9*Mn

Mn=Mn/0.9


20/37

Roof Design

Roof Reinforcement

Symbol Value Units

Design of Roof Rebar

Base of Section b 12.00 in

Effective Depth d 3.50 in

Trial & Error:

Area of Steel As 0.20 in2

Spacing 8.00 in

Area of Steel per ft AsPER FT 0.300 in2

= As/bd 0.0048

N 9.29

k = sqrt((pn)^2 + 2pn) - pn k 0.26

j = 1 - k/3 j 0.91

M = As*fy*j*d M 3200.79 lb-ft

Factored Moment MnTOTAL 2765.93 lb-ft


21/37

Notes

No. 4 Rebar




(Eq. 3.7 of A. Nilson et. al.)

M MUST BE > MnTOTAL


22/37

Tank Material QuantitiesCalculated By: Rajesh Punjabi & Ryan Mahoney

Last Revision 6/9/2009

Checked By:

Summary

Bricks 2235 Bricks

Cement 61 94lb-bags

Sand 11.96 cu.yds

Gravel 7.49 cu.yds

Water 1.20 cu.yds

#3 Rebar 1979 ft

#4 Rebar 775 ft


23/37

Brick and Mortar Quantities

Calculated By: Rajesh Punjabi & Ryan Mahoney

Last Revision 6/9/2009

Checked By:

Symbol Value Units Notes

Given

Brick Length BrickL 10.00 in 0.833 feet

Brick Width BrickW 5.00 in 0.417 feet

Brick Height BrickH 2.50 in 0.208 feet

Mortar Thickness 1 inches

Tank Diameter (int.) 12.667 feet

Height of Tank hTANK 7.00 feet

Gallons of Water 6598.4 gallons

Brick Data

Brick Volume 125 cu.in. 0.072 cf

Brick Length w/ mortar 11 inches 0.9167 feet

Brick Depth w/ mortar 6 inches 0.50 feet

Brick Height w/ mortar 3.5 inches 0.2917 feet

Inner Wall of Bricks

Thickness of interior grout 2 inches

Diameter inside bricks 13.00 feet

Circumference (int.) 40.8 feet

No. bricks per course 45 bricks

Outer Wall of Bricks

Gap between walls 2 inches (I assumed this from y

Diameter inside bricks 14.2 feet Watch units!

Circumference 44.5 feet Gap should have been

No. bricks per course 49 bricks

Brick Quantity Summary

Bricks per course 93 bricks/course

No. of courses 24 coursesTotal bricks required 2235 bricks

Wall Thickness Summary

Tank interior diameter 12.67 feet

Thickness of interior mortar 2 inches

Thickness of inner bricks 5 inches

Thickness of middle mortar 2 inches This appears


24/37

Thickness of outer bricks 5 inches 2"

Thickness of exterior mortar 1 inches

Wall thickness 15 inches 1.25 feet

Tank Diameter (exterior) 15.17 feet

Tank Radius (exterior) 7.58 feet

Floor Summary

Thickness of Interior Mortar on floor 2 inches

Bulk Volume Summary

Volume of walls and water 1265 cu.ft

Volume of water 861 cu.ft 6441.3 Gal

Volume of walls 404 cu.ft

Volume of bricks 162 cu.ft

Volume of mortar 242 cu.ft 8.9601 cu.yds

Average Circumfrence 42.674347

Will we need additional mortar for the interior floor of the tank?

Will we need additional bricks and mortar for the valve boxes on the side of


25/37

our formula for outer row circumference, which seemed to add 1.5 inches to 13 feet to get 14.5 feet?)

2" as referenced below. I also changed cell C28 to reference C27, not C21

as 1.5 inches under "outer wall of bricks" calc. Which is right?


26/37

6 inches - ht of outlet (bottom of pipe)

63.0097 cu. Ft

471.3126 gallons 5969.959

I'm not sure what this is for, but it looks like it might be referenced later, so I left it here.

Also, I think it might be calculated wrong? It's the average of the circumferences of the

interior edges of each brick course.

he tank and the chlorination box on the roof?


27/37


28/37

Mortar Mix

Standard Mix Amount Units % by Volume Total Amount

Mortar in Walls 8.96

Sand 4 100.00% 8.96

Cement 1 25.00% 2.24

Note: For regular masonry, the volume of mortar equals the volume of sand with a 4:1 ratio of sand:cement

per A Handbook of Gravity-flow Water Systems by Thomas D. Jordan Jr.


29/37

Units

cubic yds.

cubic yds.

cubic yds.


30/37

Concrete Quantites

Symbol Value Units Notes

Concrete Foundation Dimensions:

Diameter 17.17 ft

Radius 8.58 ft

Depth 0.75 ft

Foundation Volume: 173.60 ft^3 6.43 yd^3

Concrete Roof Dimensions:

Diameter 15.50 ft

Radius 7.75 ft

Depth 0.50 ft

Roof Volume 94.35 ft^3 3.49 yd^3

Total Concrete NeededTotal Concrete Volume 267.95 ft^3 9.92 yd^3

Unit weight of sand 110.00 pcf

Unit weight of gravel 110.00 pcf

Unit weight of water 62.40 pcf

Unit weight of concrete 145.00 pcf

Concrete Mix: Volume Volume

sand: 10 gal 1.336806 cubic ftgravel: 25 gal 3.342014 cubic ft

water: 4 gal 0.534722 cubic ft

cement: 1 bag 1 cubic ft

Total: 4.42784 cubic ft

For 1 Cubic Yard of Concrete:

Volume

sand: 0.302 cubic yd

gravel: 0.755 cubic yd

water: 0.121 cubic yd

cement: 0.226 cubic yd


31/37

Weight

147.05 lbs367.62 lbs

33.37 lbs

94 lbs

642.04 lbs


32/37

Concrete Mix

Total Amount Units

Foundation 6.43 cubic yds.

Sand 1.94 cubic yds.

Gravel 4.85 cubic yds.Water 0.78 cubic yds.

Cement 39.21 94-lb bag

Roof 3.49 cubic yds.

Sand 1.06 cubic yds.

Gravel 2.64 cubic yds.

Water 0.42 cubic yds.

Cement 21.31 94-lb bag

Total Concrete 9.92 cubic yds.

Sand 3.00 cubic yds.Gravel 7.49 cubic yds.

Water 1.20 cubic yds.

Cement 61 94-lb bag


33/37

Rebar Quantities

Rebar Lengths (ft.) x 4 (each side & dir.)

Roof - No. 3 Rebar

8.5 34

10 40

11 44

11.5 46

12.5 50

13 52

13.5 54

14 56

14 56

14.5 58

14.5 58

15 6015 60

Triple bars sides of roof Hatch 156

Diagonal rebar around roof Hatch 16

Subtotal 824 ft

Top of Foundation - No. 3 Rebar

9.5 38

12 48

13.5 54

15 60

16 64

16.5 66

16.5 66

16.5 66

Subtotal 462 ft

Bottom of Foundation - No. 4 Rebar

9.5 38

12 48

13.5 54

15 6016 64

16.5 66

16.5 66

16.5 66

Subtotal 462 ft

Horizontal Wall - No. 3 Rebar circumference (ft) Totals


34/37

Inner Rebar 42.4 339

Outer Rebar 44.2 354

Subtotal 693 ft

Vertical Wall - No. 4 Rebar

Subtotal 313 ft

Total No. 3 Rebar 1979 ft

Total No. 4 Rebar 775 ft


35/37


36/37

What about overlap?

So, how many bars should we buy?


37/37

Yield Line Theory - Load Combination:Weight of slab (distributed load) + Weight of 3 people (concentrated load)

MOMENT DUE TO - DISTRIBUTED LOAD

Thicknes of Roof (t)= 0.5 ft.

FOS = 1.4

Wslab = 150pcf * t * FOS = 105 psf

Mu = W * r^2 / 6 (Eq. 7.30 of R. Park)

Mu (slab) = 941.11 lb-ft/ft

MOMENT DUE TO - CONCENTRATED LOAD

FOS = 1.7

W per person: 200 lbs

Pu = 3*W*FOS = 1020 lbs

Mu = Pu / (2pi) (Eq. 7.34 of R. Park)

Mu(3ppl) = 162.338 lb-ft/ft

FACTORED MOMENT:

Mfactored = (Mu (slab) + Mu (3ppl))/0.9

Mfactored = 1226.055 lb-ft/ft

Design of Rebar in RoofGoal: M>Mfactored

b= 12 in

d= 3 in (assume that steel is in center of 6" section)

Trial & Error:

Area of rebar: 0.049 in^2 (No. 2 rebar)

# of Bars: 10

spacing= 4.607669 ft. (along circumfrence)

As per ft. = 0.010634 in^2

M = As*fy*(d-(As*fy/1.7*f'c*b) (Eq. 3.31 & 3.32 of A. Nilson et. al)

M = 1246.567 lb-ft/ft

Trial & Error:Area of rebar: 0.11 in^2 (No. 3 rebar)

# of Bars: 5

spacing= 9.215338 ft. (along circumfrence)

As per ft. = 0.011937 in^2

M = As*fy*(d-(As*fy/1.7*f'c*b) (Eq. 3.31 & 3.32 of A. Nilson et. al)

Documents

20100419043934!El_Chaguite_Tank_Design.xls