pilares kns1-coldsn.xls

8/11/2019 PILARES KNS1-COLDSN.xls

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b (mm)= 350

D (mm)= 450fck (MPa)= 20 50

LOAD COMB 1 2 3 4 5 6Pu (kN) = 500 1000 1500 1550 1200 1450 1 3 2 3 1

Mux (kN.m) = 155 45 52 60 75 50 1 20 0 0 0 20

Muy (kN.m) = 0 75 45 45 75 50 5 16 16

MuxL (kN.m) = 4 0 0

MuyL (kN.m) = 5 16 % 16

1 20 0 0 0 20

Pu/Puz = 0.25 0.49 0.74 0.76 0.59 0.72 1 3 2 3 1

AlphaN = 1.08 1.49 1.90 1.94 1.65 1.86

LHS = CHECK = REV.REINF REV.REINF REV.REINF REV.REINF REV.REINF REV.REINF

As (mm2)

MAX. BARS ON 'b'FACE = 5

REINF. INPUT

COLUMN NO.C1

COLUMN DESIGN RENEW THE LICENCE

Eff. Cover, d'(mm) =

181650

Minimum c/c distancebetween Longi. Rebars

(mm)

M A

X .

B A R S O N

' D ' F A C E =

5

Pu, Axial (kN)

20601.31


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155, 500

45, 1000

52, 150060, 1550

75, 1200

50, 1450

0

500

1000

1500

2000

2500

0 20 40 60 80 100 120 140 160 180

P u

( k N )

Mux (kN.m)

Pu-Mux : INTERACTION DIAGRAM


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0, 500

75, 1000

45, 150045, 1550

75, 1200

50, 1450

0

500

1000

1500

2000

2500

0 20 40 60 80 100 120 140 160

P u

( k N )

Muy (kN.m)

Pu-Muy : INTERACTION DIAGRAM


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b(mm)= 350D(mm)= 450fck(Mpa)= 20

steel row,no. Asi, mm2 di, mmRX1 628 50RX2 401.92 166.66667RX3 0 225RX4 401.92 283.33333

RX5 628 400di= from max. comp. Fibre

k ( xu/D >1) Pu Mu e,max es,1 es,2 es,3k>=1 5 2071 2 0.002188 0.002139 0.002025 0.001969

2.5 2046 8 0.002414 0.002307 0.002056 0.0019311.5 1947 26 0.002800 0.002593 0.002109 0.0018671.2 1832 46 0.003111 0.002823 0.002151 0.0018151.1 1759 57 0.003277 0.002946 0.002173 0.001787

1 1648 75 0.003500 0.003111 0.002204 0.001750k


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es,4 es,5 fs,1 fs,2 fs,3 fs,4 fs,5 a,1 a,2 a,3 a,4 a,50.001912 0.001799 332.89 328.70 326.60 324.30 317.22 175 58.3 0 -58 -1750.001806 0.001556 339.08 329.83 325.21 317.68 299.65 175 58.3 0 -58 -1750.001625 0.001141 347.50 331.77 321.47 306.20 228.15 175 58.3 0 -58 -1750.001479 0.000807 352.35 333.33 318.24 292.37 161.32 175 58.3 0 -58 -1750.001401 0.000629 353.42 334.16 316.51 280.22 125.77 175 58.3 0 -58 -175

0.001296 0.000389 354.87 335.28 314.19 259.26 77.78 175 58.3 0 -58 -1750.001051 0.000043 354.49 329.96 299.65 210.29 8.64 175 58.3 0 -58 -1750.000907 -0.000160 354.27 326.83 288.81 181.48 32.03 175 58.3 0 -58 -1750.000745 -0.000389 354.02 322.28 262.50 149.07 77.78 175 58.3 0 -58 -1750.000657 -0.000514 353.88 319.02 248.39 131.30 102.87 175 58.3 0 -58 -1750.000562 -0.000648 353.74 315.54 233.33 112.35 129.63 175 58.3 0 -58 -1750.000352 -0.000944 353.41 307.83 200.00 70.37 188.89 175 58.3 0 -58 -1750.000110 -0.001286 353.04 294.92 161.54 21.94 257.26 175 58.3 0 -58 -175-0.000173 -0.001685 352.60 267.90 116.67 34.57 310.14 175 58.3 0 -58 -175-0.000507 -0.002157 352.09 228.62 63.64 101.35 333.54 175 58.3 0 -58 -175-0.000907 -0.002722 350.83 181.48 0.00 181.48 350.83 175 58.3 0 -58 -175-0.001397 -0.003414 348.61 123.87 77.78 279.42 357.52 175 58.3 0 -58 -175-0.002377 -0.004796 344.16 8.64 233.33 341.66 360.90 175 58.3 0 -58 -175

-0.003846 -0.006870 335.28 164.20 340.07 360.90 360.90 175 58.3 0 -58 -175-0.007519 -0.012056 299.65 353.74 360.90 360.90 360.90 175 58.3 0 -58 -175-0.018537 -0.027611 77.78 360.90 360.90 360.90 360.90 175 58.3 0 -58 -175


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Pus,1 Pus,2 Pus,3 Pus,4 Pus,5 Pu,s Mu,s (Pu)conc (Mu)conc209 132 0 130 199 671 2 1401 1213 133 0 128 188 661 5 1385 3218 133 0 123 143 618 14 1329 12221 134 0 118 101 574 22 1258 24222 134 0 113 79 548 26 1211 31

223 135 0 104 49 511 32 1137 43223 133 0 85 5 445 41 1023 58222 131 0 73 -20 407 46 967 64222 130 0 60 -49 363 52 910 68222 128 0 53 -65 339 55 881 70222 127 0 45 -81 313 58 853 72222 124 0 28 -119 255 65 796 75222 119 0 9 -162 187 73 739 76221 108 0 -14 -195 120 80 682 77221 92 0 -41 -209 63 83 625 76220 73 0 -73 -220 0 86 569 75219 50 0 -112 -225 -68 87 512 72216 3 0 -137 -227 -144 86 426 66

211 -66 0 -145 -227 -227 81 341 58188 -142 0 -145 -227 -326 73 227 43-49 -145 0 -145 -227 -566 31 114 23


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D(mm)= 450b(mm)= 350

fck(Mpa)= 20

steel row,no. Asi, mm2 di, mmRY1 1029.92 50RY2 0 133.333333RY3 0 175RY4 0 216.666667RY5 1029.92 300

di= from max. comp. Fibre

k ( xu/D >1) Pu Mu e,max es,1 es,2k>=1 5 2071 2 0.002188 0.002125 0.002021

2.5 2044 7 0.002414 0.002276 0.0020461.5 1932 23 0.002800 0.002533 0.0020891.2 1803 41 0.003111 0.002741 0.0021231.1 1723 51 0.003277 0.002851 0.0021421 1605 66 0.003500 0.003000 0.002167

k


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es,3 es,4 es,5 fs,1 fs,2 fs,3 fs,4 fs,5 a,10.001969 0.001917 0.001813 332.3725 328.5247 326.6008 324.592 318.0906 1250.001931 0.001816 0.001586 337.9452 329.4535 325.2076 318.3147 302.5512 1250.001867 0.001644 0.001200 345.9714 331.0386 321.4713 307.6015 240 1250.001815 0.001506 0.000889 351.3047 332.3155 318.235 294.969 177.7778 1250.001787 0.001433 0.000723 352.5968 332.9947 316.5136 286.5248 144.6809 1250.001750 0.001333 0.000500 353.9 333.9116 314.1897 266.6667 100 1250.001556 0.001093 0.000167 353.4139 328.4392 299.6474 218.5185 33.33333 1250.001441 0.000951 -0.000029 353.1279 325.2201 288.8115 190.1961 5.882353 1250.001313 0.000792 -0.000250 352.8063 319.3908 262.5 158.3333 50 1250.001242 0.000704 -0.000371 352.6298 316.0353 248.3871 140.8602 74.19355 1250.001167 0.000611 -0.000500 352.4417 312.456 233.3333 122.2222 100 125

0.001000 0.000405 -0.000786 352.025 303.4068 200 80.95238 157.1429 1250.000808 0.000167 -0.001115 351.0483 289.5259 161.5385 33.33333 223.0769 1250.000583 -0.000111 -0.001500 349.3999 255.5556 116.6667 22.22222 294.3842 1250.000318 -0.000439 -0.001955 347.4519 215.1515 63.63636 87.87879 326.0761 1250.000000 -0.000833 -0.002500 345.1143 166.6667 0 166.6667 345.1143 125-0.000389 -0.001315 -0.003167 342.1203 107.4074 77.77778 262.963 355.3583 125-0.001167 -0.002278 -0.004500 333.9116 11.11111 233.3333 338.016 360.9 125-0.002333 -0.003722 -0.006500 319.3908 188.8889 340.0681 360.2194 360.9 125-0.005250 -0.007333 -0.011500 200 355.3583 360.9 360.9 360.9 125-0.014000 -0.018167 -0.026500 294.3842 360.9 360.9 360.9 360.9 125


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a,2 a,3 a,4 a,5 Pus,1 Pus,2 Pus,3 Pus,4 Pus,541.66667 0 -41.6667 -125 342 0 0 0 32841.66667 0 -41.6667 -125 348 0 0 0 31241.66667 0 -41.6667 -125 356 0 0 0 24741.66667 0 -41.6667 -125 362 0 0 0 18341.66667 0 -41.6667 -125 363 0 0 0 14941.66667 0 -41.6667 -125 364 0 0 0 10341.66667 0 -41.6667 -125 364 0 0 0 3441.66667 0 -41.6667 -125 364 0 0 0 -641.66667 0 -41.6667 -125 363 0 0 0 -5141.66667 0 -41.6667 -125 363 0 0 0 -7641.66667 0 -41.6667 -125 363 0 0 0 -103

41.66667 0 -41.6667 -125 363 0 0 0 -16241.66667 0 -41.6667 -125 362 0 0 0 -23041.66667 0 -41.6667 -125 360 0 0 0 -30341.66667 0 -41.6667 -125 358 0 0 0 -33641.66667 0 -41.6667 -125 355 0 0 0 -35541.66667 0 -41.6667 -125 352 0 0 0 -36641.66667 0 -41.6667 -125 344 0 0 0 -37241.66667 0 -41.6667 -125 329 0 0 0 -37241.66667 0 -41.6667 -125 206 0 0 0 -37241.66667 0 -41.6667 -125 -303 0 0 0 -372


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Pu,s Mu,s (Pu)conc (Mu)conc670 2 1401 1660 5 1385 3604 14 1329 10545 22 1258 18512 27 1211 24467 33 1137 33398 41 1023 45358 46 967 50312 52 910 53287 55 881 55260 58 853 56

201 66 796 58132 74 739 5957 83 682 6022 87 625 590 89 569 58

-14 90 512 56-28 89 426 51-43 88 341 45

-166 72 227 33-675 9 114 18


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b(mm)= 500 MuxL D(mm)= 500 MuylD(mm)= 500 cover b(mm)= 500

fck(Mpa)= 25 55 fck(Mpa)= 25

row,no. Asi, mm2 di, mm row,no. Asi, mm2 di, mmRX1 1923 55.0 RY1 2453 55.0 25 20 20 20

RX2 981 152.5 RY2 628 152.5 25

RX3 981 250.0 RY3 628 250.0 25RX4 981 347.5 RY4 628 347.5 25 %RX5 1923 445.0 RY5 2453 445.0 25 20 20 20

Asc / % 6790 2.72 Asc / % 6790 2.72di= from max. comp. Fibre di= from max. comp. Fibre

k ( xu/D >1) Pu Mu k ( xu/D >1) Pu Mu5.00 4990 8 k>=1 5.00 4989 92.50 4928 24 2.50 4924 271.50 4677 76 1.50 4646 871.20 4385 131 1.20 4332 1481.10 4206 164 1.10 4142 1841.00 3942 211 1.00 3863 236

0.900 3511 275 k


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Pu/Puz 0.73 0.73 0.83 0.83 0.91 0.91 AlphaN 1.88 1.88 2.00 2.00 2.00 2.00LHS 0.99 1.00 0.99 1.00 0.99 1.00

b(mm)= 500 MuxL D(mm)= 500 MuylD(mm)= 500 cover b(mm)= 500

fck(Mpa)= 25 55 fck(Mpa)= 25row,no. Asi, mm2 di, mm row,no. Asi, mm2 di, mm

1 1923 55.0 1 2453 55.0 25 20 20 20

2 981 152.5 2 628 152.5 25

3 981 250.0 3 628 250.0 254 981 347.5 4 628 347.5 25 %5 1923 445.0 5 2453 445.0 25 20 20 20

Asc / % 6790 2.72 Asc / % 6790 2.72di= from max. comp. Fibre di= from max. comp. Fibre

k ( xu/D >1) Pu Mu k ( xu/D >1) Pu Mu5.00 4990 8 k>=1 5.00 4989 92.50 4928 24 2.50 4924 271.50 4677 76 1.50 4646 871.20 4385 131 1.20 4332 1481.10 4206 164 1.10 4142 1841.00 3942 211 1.00 3863 236

0.900 3511 275 k


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Muy 123 196 90 145 65 104Muxl : Col. D 276.21 276.21 200.99 200.99 143.18 143.18Muyl : Col. I 292.11 292.11 210.30 210.30 150.78 150.78

Pu/Puz 0.73 0.73 0.83 0.83 0.90 0.90

AlphaN 1.88 1.88 2.00 2.00 2.00 2.00LHS 1.00 1.00 0.99 1.00 1.00 1.00

Pu, Axial

4320


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2525252525


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2525252525


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1. GENERAL :The design of rectangular RCC column for axial load and uniaxial bending is carried out using Pu-MuInteraction Diagrams using SP 16. For axial compression and biaxial bending the procedure is to use the

above mentioned Interaction diagrams to calculate limiting uniaxial bending moment( Muxl and Muyl)about each axes separately for given Pu and to satisfy inequality equation of IS-456

i.e. (Mux / Muxl) + (Muy / Muyl) < 1.

2. Design of Columns using 'SP 16' :

In SP 16, Pu-Mu interaction charts are presented for steel grade Fe 250, Fe 415 and Fe500 for d/D = 0.05, 0.1, 0.15 and 0.2 . The reinforcement arrangement is idealized as :1. Reinforcement on two opposite faces : Chart No. 27 to 382. Reinforcement on all four faces equally distributed : Chart No. 39 to 50.

Limitations of 'SP 16' :

1. The charts for case 1 can be used for uniaxial bending only. However small bending Momentin the other direction may be, There is no way to design a column for Biaxial Bending for thisarrangement of reinforcement.

. ,on the smaller (width- b) faces. These charts do not accommodate reinf. to be provided on larger(Depth-D) faces from detailing aspects. If a Column with D = 900mm, minimum four bars arerequired on each D-face, the charts can not account for these internal bars which may be of smaller diameter.

3. It is evident that larger diameter bars on the highly stressed face makes efficient use of reinforcement, even larger diameter bars in corner are used with advantage for biaxial bending,

it can not be accommodated by use of SP16.4. There would be confusion in arranging the reinforcement as equally distributed forrectangular section with large D/b ratio.

5. When the analysis and design is carried out using professional software, the intricacy of Column design is such that a designer would be confident only if he checks the design by his owndesign tools for different cases. The column design is carried for various load combinations at

junction with beam at top and bottom and at @ mid height section. More over most of thesoftware normally use the internal forces at the nodes instead of the beam face.

An effort is made to develop a spreadsheet for design of RCC columns to over come the above

mentioned limitations.

3. COLUMN DESIGN SPREADSHEET:

The formulation adopted is for Limit State of Collapse as per IS 456. The Pu-Mu has beencalculated considering concrete as well as each individual reinforcement bar separately.Concrete Grade M20, Steel Grade Fe 415 is considered.


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The column cross section accommodates up to maximum three internal equally spacedreinforcement bars on each face apart from the four corner bars. No. of bars on opposite facesare same, i.e. on any face no. of bars would be 2 to 5. At a time six load combinations areincluded but process can be repeated for any numbers in the same sheet.

Pu, Mux and Muy input values are Positive only.4. DESIGN PROCESS :

Give Input Data in white space, with red font. The last row will indicate whether the reinf.provided is adequate or otherwise modify grade of concrete or increase reinforcement.In case percentage of steel < 0.8 % and > 4 %, the user will be warranted to REVISE REINF.

5. WORKSHEETS IN THIS BOOK:

* The Worksheet 'Mux' shows data, steps and output calculation points for Interaction diagramPu-Mux diagram which is interpolated for Muxl.

* The Worksheet 'Muy' shows data, steps and output calculation points for Interaction diagramPu-Muy diagram which is interpolated for Muyl.* The worksheet 'Sample Problem' shows the design output for understanding the problem.

6. DISCLAIMER

* TO BE USED BY QUALIFIED STRUCTURAL ENGINEER FOR DESIGN AS PER OF IS - 456. CHECK BEFORE USE.

K. N. Sheth, Civil Engg. Dept., D.D. University, Nadiad - 387001Email : [email protected] , [email protected]

* NO LIABILITY OF DEVELOPER OF ANY TYPE UNTILL A LICENCE AGREEMENT IS SIGNED BETWEEN USER ANDDEVELOPER, AND THAT THE USER IS FORMALLY TRAINED FOR USE OF THIS SPREAD SHEET, INCL. ITS

ADVANTAGES AND ITS LIMITATIONS.


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pilares kns1-coldsn.xls

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