Analysis and Design of Reinforced Concrete Reservoir

Analysis and design of reinforced concrete reservoir for a capacity of 115 m3

Translated and Presented By: Civilax.com

Analysis and design of reinforced concrete reservoir

for a capacity of 115 m3

DESIGN OF A SUPPORTED FOR RESERVOIR CAPACITY 115 m3

1. General Information.

1.1.

Geometry.

Type: a reservoir for storing water for human consumption shall be deemed, under section 2.1.1 ACI 350.3-01 circular tank is classified as reinforced concrete slab with free wall-no-Flexible 2.2 (1). Volume

:

Storage equal to 115 cubic meters.

Radio

:

Interior (D) of 7.00 m.

Alturas

:

Effective water storage height (Hl) equal to

3.00 m. Depth

buried

(He)

equal

to 1.00

meters.

Height

Total

of

wall

(HW)

equal

to 4.00

m. Arrow design for the dome (Fc) equal to

Light over 10 thus 7.00 / 10 =

0.70 meters. Thickness of walls

:

tw = 0.20 meters.

Thickness of the Dome

:

Ce = 0.10 meters with a widening 0.15

meters at 1 meter from the dome-wall junction. Thickness of Foundation:

Hz = 0.25 meters.

Flown Foundation

v = 0.50 meters.

:


for a capacity of 115 m3 1.2.

Materials. Strength of Concrete

:

f'c = 210 Kg / cm2at 28 days.

It's Concrete

:

According to ACI 350M-01 section 8.5.1 =

:

15100 √ f ' c= 218819.79 Kg / cm2. 4200 Kg / cm2.

steel fy

1.3.

Used regulations. 

Code Requirements for Environmental Engineering Concrete Structures (ACI 350M-01) And Commentary (ACI 350RM-01), ACI Committee 350 Reported By.



Seismic Design of Liquid-Containing Concrete Structures (ACI 350.3-01) and Commentary (350.3R-01), Reported by ACI Committee 350.



Design Considerations for Environmental Engineering Concrete Structures (ACI 350.4R-04), Reported by ACI Committee 350.



Concrete Structures for Containment of Hazardous Materials (ACI 350.2R04), Reported by ACI Committee 350.



Tightness Testing of Environmental Engineering Concrete Structures (ACI 350.1-01) and Commentary (350.1R-01), Reported by ACI Committee 350.



Environmental Engineering Concrete Structures (ACI 350.R-89), Reported by ACI Committee 350.



Building Code Requirements for Structural Concrete (ACI 318M-08) and Commentary, ACI Committee 318 Reported by.



Technical Standard for Buildings "Earthquake-resistant Design" E-030.

2. Analysis (according Methodology Appendix A of ACI 350.3-01).

2.1.

Static Seismic Analysis.

The results presented were evaluated in Excel spreadsheets and Sap2000 program.

Calculation of Effective Mass, according to ACI 350.3-01 Section 9.5.2:

M uro weight (W w) + Dome weight (W r) M uro weight (W w) Dome weight (W r) Interior diam eter (D) Effective Liquid height (Hl) Effective loop coefficient M (є) (for Dead Weight) Effective loop M (W e) (by Dead Weight)

5466.34 kg 4330.55 kg 1135.79 kg 7.00 m 3.00 m 0.66 3985.34 kg


for a capacity of 115 m3 Calculation of Effective Mass of the stored liquid, impulsive component (Wi) and convective component (Wc) as ACI 350.3-01 Section 9.3.1:

M Total Liquid handle acenado Alm (W l) D / Hl W i / W l W c / W l Equivalent Weight rapporteur Com Im pulsiva W i Equivalent Weight rapporteur Com Convective W c

115000.00 kg 2.33 0.48 0.49 54946.11 kg 56665.44 kg

Calculating the combined natural vibration frequency (wi) of the structure and the liquid stored impulsive component as ACI 350.3-01 section 9.3.4



Hl / D Coef. For det. Frequency Fund. Tank‐liquid (Cw) M uro thickness (tw) Inner rim radius R Coef. For det. Frequency Fund. Tank‐liquid (Cl) Resistance to pressure Com Concrete (f'c) M odule of elasticity of concrete (Ec) Concrete density (ρc) Freq. Circ. The m ode vibration compulsive im (wi) Fund period. Rocking Tank + Com p. Im compulsive (Ti)

0.43 0.156 0.20 m 3.50 m 0.373 210.00 kg / cm 21458.90 M Pa 2.40 kN. S2 / m 371.92 ra d / 0.0169 s

Calculate the frequency of vibration of the convective component (wc) as ACI 350.3-01 Section 9.3.4:



Acceleration due to gravity (g) ʎ Freq. circular vibration prim er m convective period (wc) N atural period of prim er m convective period (Tc)

9.81 m / s2 10,426 3.94 rad / s 1.59 s

Parameters for Calculating Seismic Force as ACI 350.3-01 NTE section 4.2 and E-030: The area factor corresponding to the Seismic Zone ACI 350.3 is similar to the values specified in the NTE E-030 Section 2.1. Being in the high hazard area shall be taken as Zone 3 with an acceleration of 0.30 g (NTE as E030), which is equivalent to Zone 4 ACI 350.3-01.

As for the parameter value of the soil, according to NTE 030 E-Type S3 corresponds to a value of 1.4, this time also the value is very similar to that proposed by ACI 350.3-01.

The NTE E-030, ranks as reservoirs Essential Building (A) that corresponds to the factor 1.5. NTE is seen that the E-030 does not have categories for major reservoirs such as ACI 350.3-01, which categorizaríamos this model in the second type corresponding to reservoirs intended to remain in use for emergency purposes in seismic events. For this model we use the highest value of 1.5.



The Sharpe ratio Response Modification or seismic force reduction if we used the NTE E-030 would have a value of 6, as in the previous parameter, we

see

that

the

ACI

350.3-01

delivery

values

for

different

types

of

reservoirs, and more NTE restrictive than the E-030. AL factors needed for impulsive and convective components will use the values Rwi Rwc = 2.75 and = 1.00 (type b).



Calculating spectral amplification factors Ci and Cc, as ACI 350.3-01 section 4.2:

Coefficient representing the characteristics of the soil (S) Spectral amplification factor Am for m ov. Horizontal Ci Spectral amplification factor Am for m ov. Horizontal Cc

1.40 1.96 1.37

Calculation of the maximum displacement of the liquid contents (dmax) as ACI 350.3-01 Section 7.1:



Factor zone (Z) Im importance factor (I) Margin Shift M axim um ent V ertical liquid content (dm ax)

0.40 1.50 4.04 m

Calculate the height of the center of gravity location of impulsive and convective components as ACI 350.3-01 Section 9.3.2:

hi / Hl Height at center of G ravedad of Com p. Im pulsiva (hi) hc / Hl Height at center of G ravedad of Com p. Convective (hc)

0.375 1.13 m 0.58 1.75 m

Calculation of dynamic lateral forces, according to ACI 350.3-01 Section 4.1.1:



Factor zone (Z) Im importance factor (I) Coefficient representing the characteristics of the soil (S) Coef. From MENDMENT Im pulsivas Response Forces (Rwi) Coef. From MENDMENT Convective Response Forces (Rwc) Effective Weight Tank M uro (є.W w) Dome Tank weight (W r) Equivalent Weight rapporteur Com Im pulsiva W i Equivalent Weight rapporteur Com Convective W c Spectral amplification factor Am for m ov. Horizontal Ci Spectral amplification factor Am for m ov. Horizontal Cc Inertial Force Lateral Acceleration of M uro (Pw) Lateral Acceleration Inertial Force Dome (Pr) Lateral Force pulsiva Im (Pi) Convective Lateral Force (Pc)

0.40 1.50 1.40 2.75 1.00 2849.55 kg 1135.79 kg 54946.11 kg 56665.44 kg 1.96 1.37 1709.73 681.47 32967.67 kg 65390.96 kg

2.2.

Horizontal Dynamic Spectral Analysis.

Initial Parameters and Formulation of Inelastic Spectra:

The following values specified in the static analysis will be taken:

Factor zone (Z) Im importance factor (I) Coefficient representing the characteristics of the soil (S) Coef. From MENDMENT Im pulsivas Response Forces (Rwi) Coef. From MENDMENT Convective Response Forces (Rwc) Spectral amplification factor Am for m ov. Horizontal Ci Spectral amplification factor Am for m ov. Horizontal Cc

0.40 1.50 1.40 2.75 1.00 1.96 1.37

The Design Spectrum for assessing inertial forces produced by the wall + dome + impulsive component, will be as follows.

ANÁLISISYDISEÑODEUNRESERVORIOAPOYADAOFCONCRETOARMADO PARAUNACAPACIDADDE115m3


The Spectrum Design for Convective Component shall:

For both parameters records were taken Static Analysis.


Modeling the Impulsive and convective mass:

Criteria developed by Housner, GW which can be found in "Dynamic Pressure on Fluid Containers", Technical Information (TID) Document 7024, Chapter 6, and Appendix F, U.S. Atomic Energy Commission, 1963. This model gives good approximation take compared to more sophisticated models such as that presented Graham and Rodriguez (1952).

A three dimensional model is built and a hub are assigned to map the impulsive component weight (W = 54.95 Tn) to a hi (1.13 m) tall. Knots hi level were modeled to have the same displacement and Wi simulate the mass moving with the tank walls. The first mode of vibration obtained was 0.1955s, 0.0169s compared to that obtained in the calculation of Ti. The convective component was modeled with Wc = 56.67 tons weight, a

height hc (1.75 m). This weight will be attached to the walls of tank

24 springs, which have a stiffness of 11.35 t / m; This causes the weight to interact with the walls of the tank. The first vibration mode which is obtained without considering the contribution of the tank walls, was 1.29s 1.59s compared to that obtained in the Tc calculation.

2.3.

Push Soil Dynamics.

The soil mass involved in an earthquake is calculated by the method of Pseudo force. The weight for the calculation of the mass of soil is considered

acting

for

a

length

equal

to

the

diameter

divided

by

the

reservoir area of each tributary of the wall section. Will be modeled to a height of 0.3 H of the base of the wall.


According Monobe-Okabe:

Density of Soil (γ) Depth of the reservoir is buried (hz) M uro inclination (θ) Soil Friction Angle (φ) Friction angle between M uro and Soil (δ) Incline Soil Slope (β) to m ax ψ K ae Weight per m handle soil Weight interacting ZISCi / Rwi (Pb)

1100.00 kg / m 1.00 m 0.00 º 17.00 º 12.75 º 0.00 º 0.20 g 11.31 º 0.73 2804.49 kg 1682.69 kg

2.4.

Uploads Dead Weight, Live Loads, Pressure Water and Soil Active Push. The

loads

by

weight own

be

the

that provide

the

walls

reservoir and the roof. As overhead design for minimum of 50 kg/m2 on the dome of the reservoir will be assigned. Water pressure is modeled using all the contour of the walls of the reservoir as the thrust forces from

the


active soil. Ture in both until they are, 3.00 m for water and 1.00 m to the ground.

2.5.

Summary of Structural Analysis

Calculation of Total Shear and Moment in the Base, as ACI 350.3-01 Section 4.1.2 and 4.1.3: The base shear is equal to the sum of the inertial forces of the reservoir, plus the forces promoting convective impulsive components, plus the force produced by the mass of soil; the combination of these forces will be in the discretion of the square root of the sum of squares.

AL IS AN IS AT E S T ICO

Total in base shear (V) Height to center of M uro ravedad G (hw) Height to center of the Dome ravedad G (hr) Height at center of G ravedad of Com p. Im pulsiva (hi) Height at center of G ravedad of Com p. Convective (hc) Height at the location of the thrust force em soil (hz / 3) M om ent by M uro acceleration (Pw) M om ent by accelerating the Dome (Pr) M om ent by Lateral Force pulsiva Im (Pi) M om ent by Lateral Force Convective (Pc) M om ent by Lateral Force Ground loop M (Pb) Total M om ent at the base (M b)

75153.54 kg 2.00 m 4.31 m 1.13 m 1.75 m 0.33 m 3419.46 kg ‐ m 2933.81 kg ‐ m 37088.63 kg ‐ m 114377.44 kg ‐ m 560.90 kg ‐ m 122549.76 kg ‐ m

AL IS IS AN DIN ÁM ICO

Total shear at the base to 80% of Static Analysis Total shear at the base to Dynamic Analysis ico (V) Factor to scale the design spectrum

60122.83 kg 77938.30 kg 9.81

De sp z to m e n t M a x im or

Right shift toward ent analysis Height at which the point is located Drift Drift m axim um

0.0083 cm 4.00 m 0.0000571 0.007


3. Design Parties Reservoir.

3.1.

Majorization Load Factors and Strength Reduction. According to ACI 350M-01 and ACI 318M-08. In both codes are working with the recently published ACI 318M-

. 08 The following load combinations are indicated by the load factors majorization: U = 1.4 (D + F)

U = 1.2 (D + F) + 1.6 (L + H) + Lr 0.5 U = 1.2 D + 1.6 L + Lr U = 1.2 D + E + L U = 0.9 D + E D = Dead Weight uploads, Dead Loads. L = Loads Vivas. Lr = Roof Loads.

H = Soil Pressure Loads.

F = Fluid Pressure Loads.

The reduction factors of resistance to: Controlled Voltage = 0.9

Controlled compression spiral wire members = 0.75 Compression Controlled, other types of reinforcement = 0.65 Shear and Torsion = 0.75

Seismic shear zones = 0.60

Boards and diagonal reinforcement beams = 0.85


3.2.

Design Dome Reservoir.

Shells and Folded Plates ACI 318M-08: the considerations listed in Chapter 19 shall take. According to section 9.2.11, the design strength will be equal to 0.40 f'c.

The minimum amount to be provided pursuant to Section 7.12, equal to 0.0018. The reinforcement is provided to resist tensile stresses. Design efforts for the action associated with membrane (normal and shear forces) and the effort associated with the flexural (bending moments, torsion and shear) should be verified. The reinforcement is provided in two directions and in a single layer. They first analyze the section of the dome of 0.10 m.



The initial data are shown in the table below:

Cú ñ design the pu's ode, e sp e so r = 1 0 cm

Yielding steel (fy) Resistance to pressure Com Concrete (f'c) M odule of elasticity of concrete (Ec) Thickness of the Dome Thickness prom edio Dome, ent area ensancham Com Resistance Design of Concrete pressure (f'dc) (19.2.11) M inim um amount to ρ (7.12) Drive Reduction Factor (φ)

4200.00 kg / cm 2 210.00 kg / cm 2 218819.79 kg / cm 2 0.10 m 0.125 m 84.00 kg / cm 2 0.0018 0.90

In both directions (radial and tangential) are worked with minimum amounts. Review before the moments and shear effects was performed.


Radial reinforcement (M em brane Actions) Effort Radial Drive S11 Elem ent length to assess Radial Force Drive N DES1 Steel area required Area of steel required to m inim um Steel used area Diam eter bar Bar area Bar Number Number of bars to use Separation Separation m axim um U sing separation Rods are placed φ3 / [email protected] m Isio REV A M O N M EN TO YOU AND CO rtan M om ent M 11 (Radial) Cant Efectico Ρ amount necessary Area of steel required Rods are placed φ3 / [email protected] m Shear V 13 (Radial) Shear resisting the proposed section No need for shear reinforcement Tangential Reinforcement (M em brane Actions) Tangential Effort Drive S22 Elem ent length to assess Tangential Force Drive N DES2 Steel area required Area of steel required to m inim um Steel used area Diam eter bar Bar area Bar Number Number of bars to use Separation Separation m axim um U sing separation Rods are placed φ3 / [email protected] m Isio REV A M O N M EN TO YOU AND CO rtan M om ent M 22 (Tangential) Cant Efectico Ρ amount necessary Area of steel required Rods are placed φ3 / [email protected] m Shear V 23 (Tangential) Shear resisting the proposed section No need for shear reinforcement

5.85 t / m 2 0.50 m 165.00 Kg 0.044 cm2 0.900 cm2 0.900 cm2 3/8 0.710 cm2 1.27 2.00 0.250 m 0.450 m 0.250 m

10.00 kg ‐ m 0.065 m 0.00013 0.0000041 cm2 0.79 Kg 1184.02 Kg

1.21 t / m 2 0.40 m 0.59 Kg 0.000 cm2 0.720 cm2 0.720 cm2 3/8 0.710 cm2 1.01 1.00 0.400 m 0.450 m 0.400 m

8.48 kg ‐ m 0.065 m 0.00013 0.0000051 cm2 15.47 Kg 947.22 Kg

The next step will be to design the widening area of the dome section shall be calculated to an average thickness of 12.5 cm.



Cú ñ design the pu's ode, e sp e so r = 1 5cm

Yielding steel (fy) Resistance to pressure Com Concrete (f'c) M odule of elasticity of concrete (Ec) Thickness prom edio Dome, ent area ensancham Com Resistance Design of Concrete pressure (f'dc) (19.2.11) M inim um amount to ρ (7.12) Drive Reduction Factor (φ)

4200.00 kg / cm 2 210.00 kg / cm 2 218819.79 kg / cm 2 0.125 m 84.00 kg / cm 2 0.0018 0.90


Radial reinforcement (M em brane Actions) Effort Radial Drive S11 Elem ent length to assess Radial Force Drive N des1 Steel area required Area of steel required to m inim um Steel used area Diam eter bar Bar area Bar Number Number of bars to use Separation Separation m axim um U sing separation Rods are placed φ3 / [email protected] m Isio REV A M O N M EN TO YOU AND CO rtan M om ent M 11 (Radial) Cant Efectico Ρ amount necessary Area of steel required Rods are placed φ3 / [email protected] m Shear V 13 (Radial) Shear resisting the proposed section No need for shear reinforcement Tangential Reinforcement (M em brane Actions) Tangential Effort Drive S22 Elem ent length to assess Tangential Force Drive N DES2 Steel area required Area of steel required to m inim um Steel used area Diam eter bar Bar area Bar Number Number of bars to use Separation Separation m axim um U sing separation Rods are placed φ3 / [email protected] m Isio REV A M O N M EN TO YOU AND CO rtan M om ent M 22 (Tangential) Cant Efectico Ρ amount necessary Area of steel required Rods are placed φ3 / [email protected] m Shear V 23 (Tangential) Shear resisting the proposed section No need for shear reinforcement

42.29 tons / 0.50 m 1479.56 Kg 0.391 cm2 1.125 cm2 1.125 cm2 3/8 0.710 cm2 1.58 2.00 0.250 m 0.450 m 0.250 m

6.39 kg ‐ m 0.065 m 0.00008 0.0000026 cm2 3.34 Kg 1184.02 Kg

44.82 tons / 0.90 m 1285.20 Kg 0.340 cm2 2,025 cm2 2,025 cm2 3/8 0.710 cm2 2.85 3.00 0.300 m 0.450 m 0.200 m

45.74 kg ‐ m 0.065 m 0.00032 0.0268371 cm2 36.63 Kg 2131.24 Kg

3.3.

Reservoir Design Wall (Walls).

Earthquake Resistant Structures Forces ACI 318M-08: the considerations listed in Chapter 21 shall be taken.


According to Table 1613.5.2 of the Standard IBC 2006, we classify the site in category "D", and according to Table R21.1.1 of ACI 318 Chapter 21-M-08, must comply with section 21.9.

The wall of a reservoir works to resist efforts membrane in the radial direction, in the tangential direction is more important to the effects produced by the moments and shear. The design is given for both the outside and inside.

Design ñ u ro M odel E x te rio r e sp e so r = 2 0 cm

Yielding steel (fy) Thickness of the M iddle prom uro Resistance to pressure Com Concrete (f'c) M odule of elasticity of concrete (Ec) M inim um amount to ρ (21.9.2.1) Drive Reduction Factor (φ)

4200.00 kg / cm 2 0.200 m 210.00 kg / cm 2 218819.79 kg / cm 2 0.0025 0.90




Radial reinforcement (horizontal) in the Exterior (Equity M em brane) Effort Radial Drive S11 79.93 tons / Elem ent length to assess 0.50 m Radial Force Drive N des1 3265.00 Kg Steel area required 0.864 cm2 Area of steel required to m inim um 2,500 cm2 Steel used area 2,500 cm2 Diam eter bar 3/8 Bar area 0.710 cm2 Bar Number 3.52 Number of bars to use 3.00 Separation 0.167 m Separation m axim um 0.450 m U sing separation 0.150 m Rods are placed φ3 / [email protected] m Isio REV A M O N M EN TO YOU AND CO rtan M om ent M 11 (Radial) 91.17 kg ‐ m Cant Efectico 0.065 m Ρ amount necessary 0.00116 Area of steel required 0.376 cm2 Rods are placed φ3 / [email protected] m Shear V 13 (Radial) 39.23 Kg Shear resisting the proposed section 1872.10 Kg No need for shear reinforcement Tangential reinforcement (vertical) in the Exterior (M em brane Actions) Tangential Effort Drive S22 128.75 tons / Elem ent length to assess 0.90 m Tangential Force Drive N DES2 5581.93 Kg Steel area required 1,477 cm2 Area of steel required to m inim um 4,500 cm2 Steel used area 4,500 cm2 Diam eter bar 3/8 Bar area 0.710 cm2 Bar Number 6.34 Number of bars to use 7.00 Separation 0.129 m Separation m axim um 0.450 m U sing separation 0.125 m Rods are placed φ3 / [email protected] m Isio REV A M O N M EN TO YOU AND CO rtan M om ent M 22 (Tangential) 813.74 kg ‐ m Cant Efectico 0.065 m Ρ amount necessary 0.00610 Area of steel required 3.57 cm2 Rods are placed φ3 / [email protected] m Shear V 23 (Tangential) 36.63 Kg Shear resisting the proposed section 3369.79 Kg No need for shear reinforcement




Radial reinforcement (horizontal) in the Inner Face (M em brane Actions) Effort Radial Drive S11 38.61 tons / Elem ent length to assess 0.50 m Radial Force Drive N des1 3027.67 Kg Steel area required 0.801 cm2 Area of steel required to m inim um 2,500 cm2 Steel used area 2,500 cm2 Diam eter bar 3/8 Bar area 0.710 cm2 Bar Number 3.52 Number of bars to use 4.00 Separation 0.125 m Separation m axim um 0.450 m U sing separation 0.125 m Rods are placed φ3 / [email protected] m Isio REV A M O N M EN TO YOU AND CO rtan M om ent M 11 (Radial) 95.40 kg ‐ m Cant Efectico 0.065 m Ρ amount necessary 0.00121 Area of steel required 0.394 cm2 Rods are placed φ3 / [email protected] m Shear V 13 (Radial) 40.38 Kg Shear resisting the proposed section 1872.10 Kg No need for shear reinforcement Tangential reinforcement (vertical) in the Inner Face (M em brane Actions) Tangential Effort Drive S22 129.32 tons / Elem ent length to assess 0.90 m Tangential Force Drive N DES2 5533.21 Kg Steel area required 1,464 cm2 Area of steel required to m inim um 4,500 cm2 Steel used area 4,500 cm2 Diam eter bar 3/8 Bar area 0.710 cm2 Bar Number 6.34 Number of bars to use 7.00 Separation 0.129 m Separation m axim um 0.450 m U sing separation 0.125 m Rods are placed φ3 / [email protected] m Isio REV A M O N M EN TO YOU AND CO rtan M om ent M 22 (Tangential) 813.74 kg ‐ m Cant Efectico 0.065 m Ρ amount necessary 0.00610 Area of steel required 3.57 cm2 Rods are placed φ3 / [email protected] m Shear V 23 (Tangential) 2116.54 Kg Shear resisting the proposed section 3369.79 Kg No need for shear reinforcement


Sap2000 Comments to use: It will work with the impulsive spectrum, for the weight of the convective component will have to scale the values as this weight needs another spectrum and would be evaluated in a separate model (separate the impulsive component and the inertial forces of the reservoir), but to work it in the same model we will: Rwc / Rwc = 1.65 / 0.6 = 2.75, so the weight will be 55,678 x Wc 2.75 = 155.83 corresponding to a value for the springs of 51.78 t / m. Spectra values vary for impulsive and convective components, but working with the peak values.

Analysis and Design of Reinforced Concrete Reservoir

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