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Design of Foundation for 20 MW Turbo Generator

Drawings & Documents

The following drawings and documents have been referred for design of Foundation :

Data Supplied by KORUS

1. Drawing # TFB – 00124 rev 4

2. Drawing # TGA – 00154 rev 2

3. Drawing # 11044217 rev 0

Soil Data: Soil data taken as provided by Mr. Verma (KORUS) (Safe Bearing Capacity of 400 kN/m2 @ -4.5 m level

Reference Books & Codes:

1. Foundations for Industrial Machines – Handbook for Practising Engineers by K G Bhatia ISBN # 978-81-906032-2-5

2. IS 2974 Part 3 (1992)

3. IS 456 (2000)

4. IS 1893 part IV (2015)

5. ISO 1940 Part 1

Machine Foundation Layout

Plan

Elevation

Machine weight:

➢ Turbine:

Turbine mass with rotor +Gearbox (including Base Frame) = (4.1+0.65) X 22= 104 t Rotor Mass = 0.65 X 22 = 14.3 t

Rated Speed = 6850 rpm

Alternator

Mass of Alternator with rotor = 5.875 X 8 = 47 t

Rotor Mass = 13.14 t

Rated Speed = 1500 rpm

Critical Speed > 2160 rpm

Total Machine Mass (Turbine + Gear box + Alternator) = 104+47=151 t

➢ Dynamic Loads (as given in the drawing #

Foundation size are as under:- (Reference drawing # TFB – 00124, rev 4) Foundation Layout

|Length of Base Raft |16 |m |

|Width of Base Raft |8 |m |

|Ground Level |0 |m |

|Top of Deck (Turbine Side) Level |7.94 |m |

|Top of Deck (Generator Side) Level |8.752 |m |

|Length of Top Deck |15 |m |

|Width of Top Deck |7 |m |

|Bottom of Top Deck Level |6.94 |m |

|Top of Base Raft Level |-2 |m |

|Bottom of Base Raft Level |-4.5 |m |

|Column Sizes | | |

|No of Columns |6 |# |

|Turbine Frame Columns |1.3X1.5 |m |

|Middle Frame Columns |1.5X1.5 |m |

|Alternator Side Columns |1.2X1.2 |m |

Concrete Material

|Concrete Grade |M30 | |

|Dynamic Elastic Modulus (considered for design) |3.2e7 |kN/m2 |

|Weight Density of Concrete |25 |kN/m3 |

|Poison’s ratio |0.15 | |

Soil Data

• Bottom of Base Raft Level - 4.5 m

• Safe Bearing Capacity at (-)4.5 m level 350 kN/m^2.

Z

Isometric View of TG Foundation

Foundation Sizing: As per Codal requirement / provisions and best practices.

Top Deck (Plan dimensions as given by M/c supplier)

o Length 15000 mm

o Width 7000 mm

Deck Thickness considered (from weight & Frequency considerations)

o Thickness at Turbine side 1000 mm thick

o Thickness at Generator side 1812 mm thick

Columns

o Column sizing is done from weight & Eccentricity considerations.

o Column Sizes considered are:

• Turbine side columns 1300 X 1500 (1500 across machine axis)

• Middle column 1500 x 1500

• Gen side columns 1200 X 1200

Base Raft

(Bottom of Base Raft taken to – 4.5 m level)

• Base Raft dimensions considered for design

• Length 16000 mm

• Width 8000 mm

• Depth 2500 mm

With these dimensions, foundation weights are as under:.

|Top Deck Mass |= 316.8 t |= 3107.8 kN |

|Column |=257.0 t |= 2521.1 kN |

|Raft |= 815.5 t |= 8000.0 kN |

|Total |= 1389.3 t |= 13628.9 kN |

• For dynamic analysis, columns are considered fixed at the base (Ref clause 9-IS 2974 part 3)

• Foundation is modelled as a space frame. Columns and beams are modelled using Beam elements. Deck slab is modelled using Plate elements. Machine is modelled using Rigid links.

• To appropriately simulate the machine, machine loads are applied at top of these rigid links (@ m/c center line level)..

Y X

STAAD Model of TG Foundation Axis System as shown above

Natural frequencies obtained are listed below.

• Natural frequencies are extracted up to 106 Hz (24th mode).

• Since 95.606 % mass participation is achieved up to 24th mode, hence higher modes could not be extracted using STAAD.Pro.

|Natural Frequencies |

|Mode |Freq (Hz) |Mode |Freq (Hz) |

|1 |5.56 |13 |45.51 |

|2 |5.60 |14 |46.32 |

|3 |6.77 |15 |58.85 |

|4 |35.61 |16 |59.47 |

|5 |38.47 |17 |59.52 |

|6 |39.87 |18 |60.70 |

|7 |40.13 |19 |94.92 |

|8 |40.86 |20 |102.21 |

|9 |42.42 |21 |103.21 |

|10 |42.89 |22 |104.14 |

|11 |43.05 |23 |105.71 |

|12 |43.73 |24 |105.76 |

None of the frequencies are within (+/-) 20% of operating speeds

Salient mode shapes i.e. Lateral along Z, Axial along X and Vertical along Y as well as torsional mode about Y are plotted and shown subsequently.

1st Mode (Lateral) Along Z

Mode 1 5.56 Hz

2nd Mode (Axial) Along X

Mode 2 5.60 Hz

3rd Mode Torsional About Y

Mode 3 6.77 Hz

4th Mode (Vertical) Along Y

Mode 4 35.61 Hz

➢ Dynamic Loads for dynamic response computations:

➢ Balance Grade for rotors not given in the drawing

➢ Dynamic forces given by the supplier are not in accordance with the balance grade for rotors. These are much on the higher side.

➢ Dynamic forces used for response analysis are computed using Balance Grade (as per ISO 1940).

➢ Balance Grade considered for Turbine & Alternator Rotor:

➢ Turbine (6850 rpm) G 2.5

➢ Alternator (1500 rpm) G 6.3

➢ Balance Grade considered for design (Refer Annexure C - IS 2974 part 3): (one grade higher than respective grades given as above)

➢ Turbine (6850 rpm) G 6.3

➢ Alternator (1500 rpm) G 16

|Dynamic Loads considered for analysis as given in Drawing |

|Turbine |Alternaor |

|Rotor Mass |14.30 |t |Rotor Mass |13.14 |t |

|Operating Speed |6850 |rpm |Operating Speed |1500 |rpm |

|Operating Speed |114.167 |Hz |Operating Speed |25 |Hz |

|Omega (w) |717.33 |rad/s |Omega (w) |157.08 |rad/s |

|GR (considered) |6.3 |mm/s |GR (considered) |16 |mm/s |

|ew | |6.3 |mm/s |ew | |16 |mm/s |

|e | |8.78E-03 |mm |e | |1.02E-01 |mm |

|e | |8.78E-06 |m |e | |1.02E-04 |m |

|Dyn Force |mew^2 | |Dyn Force |mew^2 | |

| | |64.62 |kN | | |33.02 |kN |

|Distributed at |22 |# points |Distributed at |8 |# points |

|Force per point |2.94 |kN |Force per point |4.13 |kN |

1. Unbalance Dynamic Loads of turbine are applied at Rotor Center line level at all the turbine support points.

2. For obtaining maximum effect, dynamic loads are considered applied both in phase as well as out of phase conditions.

Forces in phase: Forces on Turbine and Generator are in-phase

Forces out of phase: Forces on Turbine and Generator are considered in

opposite direction

3. These are defined as under:

i. FYIP - Forces applied along Y direction – In phase

ii. FYOP - Forces applied along Y direction – Out of Phase

iii. FZIP - Forces applied along Z direction – In phase

iv. FZOP - Forces applied along Z direction – Out of Phase

• Steady state response is evaluated for all the four dynamic load conditions.

• Response is obtained a) at foundation top b) at Machine Center Line Level.

Amplitudes have been evaluated at the following machine points

3

Turbine

7

Alternator

5

8

6

1

4

2

Machine Points

(Amplitudes at foundation top deck)

Response has been evaluated at the following points on top deck:

14

11 17

3.5 m

12 18

3.5 m

13

7.5 m

19

16 7.5 m

[pic]

Top Deck

Load Calculation

Machine Loads - Machine Load Distribution points on Top Deck Turbine load points

Alternator load points

Load points & Loading data

Calculation of Seismic Coefficient( Ah)

Seismic Design is done in accordance with the provisions of following Indian standards:

IS 1893 (Part 4)-2015

CRITERIA FOR EARTHQUAKE RESISTANT DESIGN OF

STRUCTURES

Part (4) INDUSTRIAL STRUCTURES INCLUDING STACK-LIKE STRUCTURES

Seismic Zone: The site falls in Zone III

Zone Factor: (Annexure A) Z = 0.16

Category: (Table 6 ) Category 2 Response Reduction Factor: (Table 4): R= 3 Importance Factor: ( Table 9) I =1.5

♦Time period of Structure corresponding to three principal modes along X, Y and Z directions ( See Dynamic Analysis Report)

First Mode frequency (About Z – direction) f1= 5.563 Hz T1=0.18 sec Second Mode frequency (Along in X –direction) f2= 5.599 Hz T2=0.18 sec 4th Mode About Y f4 = 35.607 Hz T4 =0.028 sec

Spectral Acceleration (Annex B)

In Y direction Sa/g = 2.5

In X direction Sa/g = 2.5

In Z direction Sa/g = 2.5

IS 1893(Part 4-2015), Cl. 7

Design Horizontal Seismic Coefficient

A ’ (Z / 2)×(Sa / g) ’

h (R/ I)

0.1

Loads and Load combinations Load Cases

LOAD CASE 1 DL M/C WT. STATIC

LOAD CASE 2 Live load

LOAD CASE 3 DYNAMIC FORCE (+) LOAD CASE 4 DYNAMIC FORCE (-) LOAD CASE 5 VACCUM

LOAD CASE 6 SHORT CIRCUIT (+) LOAD CASE 7 SHORT CIRCUIT (-) LOAD CASE 8 EQ.L (+X)

LOAD CASE 9 EQ.L (-X) LOAD CASE 10 EQ.L (+Z) LOAD CASE 11 EQ.L (-Z) LOAD CASE 12 EQ.L (-Y) LOAD CASE 13 EQ.L (+Y)

STAAD - Loading diagrams

STAAD - Loading diagrams

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STAAD - Loading diagrams

STAAD - Loading diagrams

STAAD - Loading diagrams

STAAD - Loading diagrams

[pic]

STAAD - Loading diagrams

[pic]

STAAD - Loading diagrams

Seismic(+Y)

Soil parameters

SBC value at -4.5m depth = 350 kN/m2

Soil Stiffness

|SBC of Soil |qo |= |350 |kN/m2 | |

|Allowable deflection |δ |= |25 |mm |( Assumed) |

|Importance factor |I |= |2 | | |

Emprical formula = 40. I.qo

K δ

K = 40x 2x 350

0.0

kN/m

kN/m kN/m

h 2

= 1000 kN/m

[pic]

[pic]

[pic]

[pic]

[pic]

Z column axial direction as per SP 16, for Puz :

|Column Design C2 | |

|Column size |1500 |x |1500 mm | | |

|Concrete grade Steel |fck fy |= |30 N/mm2 | | |

| | |= |500 N/mm2 | | |

|Effective Length for Bending |lex |= |8.2 m | | |

|Effective Length for Bending |ley |= |8.2 m | | |

|Unsupported Length |L |= |8.2 m | | |

| | | | | | |

|Factored Design Forces | | | | | |

|Axial force |P |= |3521 kN | | |

|Moment |My |= |1615 kNm | | |

|Moment |Mz |= |1194 kNm | | |

| |lex /D |= |5.5 < |12 | |

| |ley /b |= |5.5 < |12 |Short Column |

Assumed % of reinfo p = 1 %

p/fck = 0.033

Uniaxial moment capacity of the section about y-y axis

Bar Dia = 32 mm

Clear Cover d = 50 mm

Effective cover d' = 66 mm

d'/D = 0.044

Pu/fckbD = 0.052

Mu/fck

bD2 = 0.080 SP 16 Refering chart 47

Mux1 = 8100 kNm

Uniaxial moment capacity of the section about z-z axis

Bar Dia = 32 mm

cover d' = 66 mm d'/D = 0.044

Pu/fckbD = 0.052

Mu/fck

bD2 = 0.080 SP 16 Refering chart 47

Muy1 = 8100 kNm

Calculation of Puz

SP 16 Refering chart 26 , p=1% and fy=500 N/mm2

Puz/Ag = 13.5

Puz = 30375 kN

Pu/Puz = 0.12

IS 456-2000, Cl.39. Pu/Puz αn

=< 0.2 1.0

=> 0.8 2.0

for 0.12 1.0

uy uy1

|Column Design C3 | |

|Column size Concrete grade |1200 |x |1200 mm | | |

|Steel |fck fy |= |30 N/mm2 | | |

| | |= |500 N/mm2 | | |

|Effective Length for Bending |lex |= |8.2 m | | |

|Effective Length for Bending |ley |= |8.2 m | | |

|Unsupported Length |L |= |8.2 m | | |

| | | | | | |

|Factored Design Forces | | | | | |

|Axial force |P |= |1766 kN | | |

|Moment |My |= |680 kNm | | |

|Moment |Mz |= |524 kNm | | |

| |lex /D |= |6.83 < |12 | |

| |ley /b |= |6.83 < |12 |Short Column |

Assumed % of reinfo p = 1 %

p/fck = 0.033

Uniaxial moment capacity of the section about y-y axis

Bar Dia = 32 mm

Clear Cover d = 50 mm

Effective cover d' = 66 mm

d'/D = 0.055

Pu/fckbD = 0.041

Mu/f bD2 = 0.070 SP 16 Refering chart 47

Mux1 = 3628.8 kNm

Uniaxial moment capacity of the section about z-z axis

SP 16 Refering chart 47

Calculation of Puz

SP 16 Refering chart 26 , p=1% and fy=500 N/mm2

Puz/Ag = 13.5

Puz = 19440 kN

Pu/Puz = 0.09

IS 456-2000, Cl.39.6, Pu/Puz αn

=< 0.2 1.0

=> 0.8 2.0

for 0.09 1.0

uy uy1

Top Deck slab Design

Design Moments

Maximum Moment values in kNm/m

| | |Load C |Mx |Mxy |Mx +Mxy |

|Mx | | | | | |

| |+ve |210 |450 |250 |700 |

| |-ve |210 |-600 |-450 |1050 |

| | | |My |Mxy |Mx +Mxy |

|My | | | | | |

| |+ve |208 |550 |250 |800 |

| |-ve |210 |-600 |-450 |1050 |

[pic]

Top Deck_ Reinforcement Design - 1000 mm Thick

|Slab Thickness |D |= |1000 |mm | |

|Clear Cover |dcov |= |100 |mm | |

|Effective Depth |d |= |888 |mm | |

|Concrete Grade |fck |= |30 |N/mm2 | |

|Reinforcement Grade |Fy |= |500 |N/mm2 | |

| |Bar Dia |= |25 |mm | |

| |Bar Are |= |491 |mm2 | |

| |Spacing |= |200 |mm | |

| |No. of ba |= |6 |per m | |

|Reinforcement provided |Area |= |2946 |mm2 |ok |

|Minimum Reinforcement |Ast |= |0.85 bd/fy |

| | |= |1509 mm2 |

Xu 0.87 fy Ast 0.13

= =

d 0.36 fckb.d < 0.46 ( Limiting value, IS 456:Annex G1.1 1

|Moment Capac(itIyS 456:Annex G1.1 1 ) |Mu |= |0.87 fy Ast d [1 -(Astfy)/(bdfck)] |

| | |= |1074 kN.m per m |

|Maximum moment - Strength Level Loads |Raft Reinforcement |

| | |Load case |

|Bottom reinft : |T25 dia @ 200 mm c/c |Minimum % of reinft governing |

|Top reinft : |T25 dia @ 200 mm c/c |Minimum % of reinft governing |

|Middle layer R/t : |T20 dia @ 300 mm c/c |Minimum spacing as per Cl.26.3.3 (b) 2 |

Top Deck_ Reinforcement Design - 1800 mm Thick

|Slab Thickness |D |= |1800 |mm | |

|Clear Cover |dcov |= |100 |mm | |

|Effective Depth |d |= |1688 |mm | |

|Concrete Grade |fck |= |30 |N/mm2 | |

|Reinforcement Grade |Fy |= |500 |N/mm2 | |

| |Bar Dia |= |25 |mm | |

| |Bar Are |= |491 |mm2 | |

| |Spacing |= |200 |mm | |

| |No. of ba |= |6 |per m | |

|Reinforcement provided |Area |= |2946 |mm2 |ok |

|Minimum Reinforcement |Ast |= |0.85 bd/fy |

| | |= |2869 mm2 |

Xu 0.87 fy Ast 0.07

= =

d 0.36 fckb.d < 0.46 ( Limiting value, IS 456:Annex G1.1 1 )

|Moment Capac(itIyS 456:Annex G1.1 1 ) |Mu |= |= 0.87 fy Ast d [1 -(Astfy)/(bdfck)] |

| | |= |2100 kN.m per m |

|Maximum moment - Strength Level Loads |Raft Reinforcement |

| | |Load case |

|Bottom reinft : |T25 dia @ 200 mm c/c |Minimum % of reinft governing |

|Top reinft : |T25 dia @ 200 mm c/c |Minimum % of reinft governing |

|Middle layer R/t : |T20 dia @ 300 mm c/c |Minimum spacing as per Cl.26.3.3 (b) 2 |

Top Deck_ Reinforcement Design - 1400 mm Thick

|Slab Thickness |D |= |1400 |mm | |

|Clear Cover |dcov |= |100 |mm | |

|Effective Depth |d |= |1288 |mm | |

|Concrete Grade |fck |= |30 |N/mm2 | |

|Reinforcement Grade |Fy |= |500 |N/mm2 | |

| |Bar Dia |= |25 |mm | |

| |Bar Are |= |491 |mm2 | |

| |Spacing |= |200 |mm | |

| |No. of ba |= |6 |per m | |

|Reinforcement provided |Area |= |2946 |mm2 |ok |

|Minimum Reinforcement |Ast |= |0.85 bd/fy |

| | |= |2189 mm2 |

Xu 0.87 fy Ast 0.09

= =

d 0.36 fckb.d < 0.46 ( Limiting value, IS 456:Annex G1.1 1 )

|Moment Capac(itIyS 456:Annex G1.1 1 ) |Mu |= |= 0.87 fy Ast d [1 -(Astfy)/(bdfck)] |

| | |= |1587 kN.m per m |

|Maximum moment - Strength Level Loads |Raft Reinforcement |

| | |Load case |

|Bottom reinft : |T25 dia @ 200 mm c/c |Minimum % of reinft governing |

|Top reinft : |T25 dia @ 200 mm c/c |Minimum % of reinft governing |

|Middle layer R/t : |T20 dia @ 300 mm c/c |Minimum spacing as per Cl.26.3.3 (b) 2 |

Summary of design

Raft Design

|Thickness : |2500 mm |Clear Cover |= |100 |mm |

|Bottom reinft : |T32 dia @ 200 mm c/c | | | | |

|Top reinft : |T25 dia @ 200 mm c/c | | | | |

|Middle layer R/t : |T20 dia @ 300 mm c/c | | | | |

|Column Design | | | |

| |Size |Main Reinft |Ties |

|Column C1 1300 |X |1500 T32 - 26Nos. |T12@150 c/c |

|Column C2 1500 |X |1500 T32 - 28Nos. |T12@150 c/c |

|Column C3 1200 |X |1200 T32 - 20Nos. |T12@150 c/c |

| | | | |

|Deck Design | | | |

|Thickness : |1000 mm |Clear Cover |= |100 |mm |

|Bottom reinft : |T25 dia @ 200 mm c/c T25 dia @ 200 mm| | | | |

|Top reinft : |c/c T20 dia @ 300 mm c/c | | | | |

|Middle layer R/t : | | | | | |

|Thickness : |1800 mm |Clear Cover |= |100 |mm |

|Bottom reinft : |T25 dia @ 200 mm c/c T25 dia @ 200 mm| | | | |

|Top reinft : |c/c T20 dia @ 300 mm c/c | | | | |

|Middle layer R/t : | | | | | |

| | | | | | |

|Thickness : |1400 mm |Clear Cover |= |100 |mm |

|Bottom reinft : |T25 dia @ 200 mm c/c T25 dia @ 200 mm| | | | |

|Top reinft : |c/c | | | | |

|Middle layer R/t : |T20 dia @ 300 mm c/c | | | | |

Note: Opening portion area reinforcement to be distributed around the opening.

-----------------------

3

Y

X

Z

|Response in microns at 25 Hz of Operation |

|Frequency |

|Point |RESP along Y |RESP along Z |

| |FYIP |FYOP |FZIP |FZOP |

|1 |0.66 |0.79 |0.18 |0.03 |

|2 |0.04 |0.2 |0.18 |0.06 |

|3 |2.45 |2.5 |2.34 |1.9 |

|4 |1.83 |0.05 |2.34 |1.9 |

|5 |3 |3.03 |3.11 |2.57 |

|6 |2.75 |2.8 |3.11 |2.57 |

|7 |3.84 |3.85 |4.16 |3.48 |

|8 |3.6 |3.62 |4.16 |3.48 |

|Response microns at 114 Hz of Operation |

|Frequency |

|Point |RESP along Y |RESP along Z |

| |FYIP |FYOP |FZIP |FZOP |

|1 |0.1 |0.1 |0.24 |0.06 |

|2 |0.11 |0.11 |0.24 |0.03 |

|3 |0.05 |0.05 |0.18 |0.06 |

|4 |0.05 |0.05 |0.18 |0.06 |

|5 |0.03 |0.03 |0.16 |0.06 |

|6 |0.05 |0.03 |0.16 |0.06 |

|7 |0.01 |0.01 |0.13 |0.07 |

|8 |0.01 |0.01 |0.13 |0.07 |

Maximum amplitude obtained at machine location is 4.16 microns at 25 Hz and 0.24 microns at 114 Hz.

These are well within (much below) acceptable limits.

15

|Response in microns at 25 Hz of Operation |

|Frequency |

|Point |RESP along Y |RESP along Z |

| |FYIP |FYOP |FZIP |FZOP |

|11 |0.05 |0.04 |0.43 |0.43 |

|12 |0.23 |0.16 |0.42 |0.42 |

|13 |0.33 |0.29 |0.43 |0.43 |

|14 |2.41 |2.47 |3.03 |2.66 |

|15 |2.03 |2.1 |3.03 |2.66 |

|16 |1.5 |1.58 |3.03 |2.66 |

|17 |2.86 |2.86 |5.63 |4.9 |

|18 |3.7 |3.7 |5.59 |4.86 |

|19 |1.54 |1.53 |5.62 |4.89 |

|Response microns at 114 Hz of Operation |

|Frequency |

|Point |RESP along Y |RESP along Z |

| |FYIP |FYOP |FZIP |FZOP |

|11 |0.014 |0.001 |0.21 |0.06 |

|12 |0.08 |0.1 |0.21 |0.06 |

|13 |0.02 |0.02 |0.21 |0.06 |

|14 |0.05 |0.05 |0.14 |0.02 |

|15 |0.06 |0.06 |0.14 |0.02 |

|16 |0.06 |0.06 |0.14 |0.02 |

|17 |0.006 |0.01 |0.09 |0.06 |

|18 |0.01 |0.01 |0.09 |0.06 |

|19 |0.01 |0.02 |0.1 |0.06 |

Maximum amplitude at top deck is 5.63 microns at 25 Hz and 0.21 microns at 114 Hz

These are well within (much below) acceptable limits.

STAAD 3D model

Self weight

Turbine load _ Static

part

Turbine load _ Rotating part

Alternator load _

static

Live load _ 10 kN/m2

Dynamic force(+)

Dynamic force(-)

Vaccum pull

Short circuit (+)

Short circuit (-)

Seismic(-X)

Seismic(+X)

Seismic(+Z)

Seismic(-Z)

Seismic(-Y)

| |0.025 |

| |K |= |1120000 |

|No.of Nodes | |= |561 |

|Vertical Stiffness per node |kv |= |1996 |

| |kv |= |2000 |

|Lateral Stiffness per node | |= |kv |

| |k | | |

123456=?CDEFZC1 - 1.3 X1.5 M C2 - 1.5 X1.5 M C3 - 1.2 X 1.2 M

|Muy/Muy1 = |0.199 |

|Muz/Muz1 = |0.147 |

|[M /M ] αn + [Muz/Muz1] αn |= |< 1.0 | |

|0.200 + 0.147 |= |0.347 | |

| | |< 1.0 |OK |

|Minimum Reinforceme Ast | | | |

| |= |0.8%bD | |

| |= |18000 |mm2 |

|Reinforcement provid Area |= |1%bD |mm2 |

| | |22500 |mm2 |

|Bar Area |= | 804 |mm2 | |

|No. bars |= |28 |Nos | |

|Ast |= |22508 |mm2 |Ok |

|Hence, Provided reinforcement | | | | |

|Main bar |T32 - 28Nos. |

|Ties |T12@150 c/c |

ck

|Bar Dia |= |32 mm |

|cover d' |= |66 mm |

|d'/D |= |0.055 |

|Pu/fckbD |= |0.041 |

|2 |

|Mu/fckbD = 0.070 |

|Muy1 |= |3628.8 kNm |

|Muy/Muy1 = |0.187 |

|Muz/Muz1 = |0.144 |

|[M /M ] + [Muz/M |uz1] αn |= |< 1.0 | |

|0.190 + |0.144 |= |0.334 | |

| | | |< 1.0 |OK |

| |Ast | | | |

|Minimum Reinforceme | |= |0.8%bD | |

| | |= |11520 |mm2 |

|Reinforcement provid |Area |= |1%bD |mm2 |

| | | |14400 |mm2 |

|Bar Area |= | 804 |mm2 | |

|No. bars |= |20 |Nos | |

|Ast |= |16077 |mm2 |Ok |

|Hence, Provided reinforcement |

|Main bar |T32 - 20Nos. |

|Ties |T12@150 c/c |

-----------------------

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