PM Interaction Curves

steel for an under reoinforced section to assist in assignmnt 2.1fy=

550

pt pt= 0.15 percentfind xu/d

xu/d= 0.057 XuMax/d=

Mu for the pt and xu/d is

IS 456 Mu= 0.70074 bd^2b= 350 mm

D= 750d= 692 mm

Mu= 117.4 kNm

steel for an under reoinforced section 250 20

415 25fck= 500 30

550 3535 40

45

15 50scroll to reach target MuR 55

60min steel 0.15 percent 374 sqmm

bar selection ****only one dia*** no combo suggested here***

0.443 Ast= 363 mm2

Area dianumber 10 12 16 20 25 32

1 79 113 201 314 491 8042 157 226 402 628 982 16083 236 339 603 942 1473 2413

4 314 452 804 1257 1963 32175 393 565 1005 1571 2454 40216 471 679 1206 1885 2945 48257 550 792 1407 2199 3436 56308 628 905 1608 2513 3927 64349 707 1018 1810 2827 4418 7238

10 785 1131 2011 3142 4909 8042

Wu= 1200 kNRadius= 5.52 mbreadth 350 mm

vu= 05.Wu(1-8 theta /PI()Tu = WuR(1.20711sin(Q)-.5COS(Q)-4(Q)/pi()+.5

theta theta Tu Vu toa ve= Vu+ 1.6 *Tu/b0 0 0 600 600

0.01 1 -4.216155 584.7211 603.995 Vu is not enhanced greately just less than 10 knm0.02 1 -8.109125 569.4423 606.51250.03 2 -11.68695 554.1634 607.58950.04 2 -14.95772 538.8845 607.26270.05 3 -17.92953 523.6056 605.56920.06 3 -20.61051 508.3268 602.54620.07 4 -23.00885 493.0479 598.23120.08 5 -25.13272 477.769 592.66140.09 5 -26.99035 462.4901 585.8746

0.1 6 -28.58999 447.2113 577.90830.1 6 -28.58999 447.2113 577.9083

0.1664 10 -33.2746 345.7595 497.8720.2 11 -32.22882 294.4225 441.7543

0.25 14 -27.30614 218.0281 342.85620.3 17 -19.30705 141.6338 229.8946

0.35 20 -9.305559 65.23939 107.77910.4 23 1.619305 -11.15498 18.55752

0.45 26 12.38621 -87.54935 144.17210.5 29 21.91424 -163.9437 264.1231

0.55 32 29.12553 -240.3381 373.48340.619 35 33.29051 -345.7623 497.9475

0.65 37 32.31822 -393.1268 540.86730.7 40 26.1836 -469.5212 589.2177

0.75 43 13.50548 -545.9156 607.6549

0.78 45 2.331686 -591.7522 602.4114

WUload*Radius*(0.5*SIN(A30)-1.20711*COS(A30)-1.27324)Mu

0 0 -438.04510.05 2.864789 -282.5069

0.1 5.729578 -147.3430.15 8.594367 -32.89133

0.2 11.45916 60.562120.25 14.32394 132.7837

0.3 17.18873 183.5930.35 20.05352 212.8629

0.4 22.91831 220.52030.45 25.7831 206.546

0.5 28.64789 170.9751

0.55 31.51268 113.89630.6 34.37747 35.45238

0.65 37.24226 -64.160610.7 40.10705 -184.6937

0.75 42.97183 -325.84560.8 45.83662 -487.2636

0.785398 45 -438.05140.392699 220.751

Vu is not enhanced greately just less than 10 knm

AXIAL COMPRESSION fck = fck = fck = fck = fck = fck =fy= 500 15 20 25 30 35 40

p Pu/Ag

0.8 8.632 10.616 12.6 14.584 16.568 18.5521 9.29 11.27 13.25 15.23 17.21 19.19

1.5 10.935 12.905 14.875 16.845 18.815 20.7852 12.58 14.54 16.5 18.46 20.42 22.38

2.5 14.225 16.175 18.125 20.075 22.025 23.9753 15.87 17.81 19.75 21.69 23.63 25.57

3.5 17.515 19.445 21.375 23.305 25.235 27.1654 19.16 21.08 23 24.92 26.84 28.76

8 13 18 23 280

1

2

3

4

5AXIAL COMPRESSION

fck = 15 fck = 20 fck = 25 fck = 30 fck = 35 fck = 40Pu/Ag, N/sqmm

PE

RC

EN

T S

TE

EL

. %

Pu/Ag Ag= Ag= Ag= Ag= Ag= Ag=500 1000 1500 2000 2500 3000

sqcm7 350 700 1050 1400 1750 21008 400 800 1200 1600 2000 2400

10 500 1000 1500 2000 2500 300021 1050 2100 3150 4200 5250 6300

8 13 18 23 280

1

2

3

4

5AXIAL COMPRESSION


PE

RC

EN

T S

TE

EL

. %

7 9 11 13 15 17 19 21 230

2000400060008000

1000012000140001600018000

AXIAL COMPRESSION, Ag in sqcm

Ag= 500 Ag= 1000 Ag= 1500 Ag= 2000Ag= 2500 Ag= 3000 Ag= 4000 Ag= 5000Ag= 6000 Ag= 7000 Ag= 8000

Pu/Ag, N/sqmm

LO

AD

, P

u ,

kN

fyy250415500550

8 13 18 23 280

1

2

3

4

5AXIAL COMPRESSION


PE

RC

EN

T S

TE

EL

. %

Ag= Ag= Ag= Ag= Ag=4000 5000 6000 7000 8000

sqcm2800 3500 4200 4900 56003200 4000 4800 5600 64004000 5000 6000 7000 80008400 10500 12600 14700 16800

8 13 18 23 280

1

2

3

4

5AXIAL COMPRESSION


PE

RC

EN

T S

TE

EL

. %

7 9 11 13 15 17 19 21 230

2000400060008000

1000012000140001600018000

AXIAL COMPRESSION, Ag in sqcm

Ag= 500 Ag= 1000 Ag= 1500 Ag= 2000Ag= 2500 Ag= 3000 Ag= 4000 Ag= 5000Ag= 6000 Ag= 7000 Ag= 8000

Pu/Ag, N/sqmm

LO

AD

, P

u ,

kN

interaction curve for B1G ext

concrete fck= 30Breadth= 500DepthOverall=D=450+Q 450new depthoevrall= D= 500Overall Depth = finally 500

Xu/d ecu= g=

0 0.00350.075 0.0035

0.1 0.00350.15 0.0035

0.2 0.00350.225 0.0035

0.25 0.00350.275 0.0035

0.3 0.00350.325 0.0035

0.35 0.00350.375 0.0035

0.4 0.00350.425 0.0035

0.45 0.00350.475 0.0035

0.5 0.0035

Roll no. Q Queue=

0.0035-.75*ec min

16/(7*xu/D-3)sq

0.525 0.00350.55 0.0035

0.575 0.00350.6 0.0035

0.625 0.00350.65 0.0035

0.675 0.00350.7 0.0035

0.725 0.00350.75 0.0035

0.775 0.00350.8 0.0035

0.85 0.00350.9 0.0035

0.95 0.00351 0.0035

1 0.00350 1.000 1.05 0.00338 0.846

1.1 0.00328 0.724 1.2 0.00311 0.549 1.3 0.00298 0.430 1.4 0.00288 0.346 1.5 0.00280 0.284

2 0.00255 0.132 2.5 0.00241 0.076

3 0.00233 0.049 3.5 0.00228 0.035

4 0.00224 0.026 40 0.00202 0.000

16/(7*xu/D-3)sq

0 steel fy= 415

bar dia steel area

no mm sqmm mm

2 20 3217.00 56 0.1120

2 20 1608.00 185 0.3700

zero4RollNo 1608 314 0.6280

0 0 0.00002 20 3217.00 443 0.8860

9650.00ratio to dpeth

main rod dia 32trans dia 12clear cover = 40***eff*** cover 68 0.1360

432 0.8640

Cu Mc strain in steel, es

row 2

.416Xu 432 mm & 0.864 D/2

Cu, kN mm Mc, kNm

204 15.6 47.73 -0.03785 0.00350 -0.02581 -0.01377272 20.8 62.23 -0.02751 0.00350 -0.01848 -0.00945407 31.2 89.11 -0.01717 0.00350 -0.01115 -0.00513543 41.6 113.16 -0.01200 0.00350 -0.00749 -0.00297611 46.8 124.13 -0.01028 0.00350 -0.00627 -0.00226679 52.0 134.39 -0.00890 0.00350 -0.00529 -0.00168747 57.2 143.95 -0.00778 0.00350 -0.00449 -0.00121815 62.4 152.80 -0.00684 0.00350 -0.00383 -0.00082882 67.6 160.95 -0.00604 0.00350 -0.00326 -0.00048950 72.8 168.38 -0.00536 0.00350 -0.00278 -0.00020

1018 78.0 175.12 -0.00477 0.00350 -0.00236 0.000051086 83.2 181.14 -0.00425 0.00350 -0.00200 0.000261154 88.4 186.47 -0.00380 0.00350 -0.00167 0.000451222 93.6 191.08 -0.00339 0.00350 -0.00138 0.000621290 98.8 194.99 -0.00303 0.00350 -0.00113 0.000771358 104.0 198.20 -0.00270 0.00350 -0.00090 0.00091

at dd from comp face

face to centre of other side rod

area of stress blcok

distance of the centroid of

stress block from comp face

Mc= cu * z from

centroidrow 1 -

t side left

0.362*xu*DepthO

Cu*(.5 D -.416xu)

.447*(1-4*gee/21)

(0.5-8*gee/49)(D/(1-4gee/21) ecu/xu*(effdepth-

xu)

Ecu/Xu*(Xu-D/2)

1425 109.2 200.69 -0.00241 0.00350 -0.00069 0.001031493 114.4 202.48 -0.00214 0.00350 -0.00050 0.001151561 119.6 203.57 -0.00189 0.00350 -0.00032 0.001251629 124.8 203.95 -0.00167 0.00350 -0.00016 0.001341697 130.0 203.63 -0.00146 0.00350 -0.00002 0.001431765 135.2 202.59 -0.00127 0.00350 0.00012 0.001511833 140.4 200.86 -0.00109 0.00350 0.00024 0.001581900 145.6 198.41 -0.00093 0.00350 0.00036 0.001651968 150.8 195.26 -0.00078 0.00350 0.00047 0.001712036 156.0 191.41 -0.00063 0.00350 0.00057 0.001772104 161.2 186.85 -0.00050 0.00350 0.00066 0.001832172 166.4 181.58 -0.00038 0.00350 0.00075 0.001882308 176.8 168.93 -0.00015 0.00350 0.00091 0.001982443 187.2 153.45 0.00005 0.00350 0.00106 0.002062579 197.6 135.15 0.00024 0.00350 0.00119 0.002142715 208.0 114.03 0.00040 0.00350 0.00130 0.00221

2714 208.0 114.03 0.00048 0.001752813 215.7 96.42 0.00060 0.001772890 221.4 82.59 0.00070 0.001793002 229.2 62.57 0.00087 0.001813078 234.1 49.03 0.00100 0.001843132 237.4 39.46 0.00110 0.001853171 239.8 32.44 0.00119 0.001873268 245.4 15.08 0.00145 0.001913304 247.4 8.68 0.00158 0.001933321 248.3 5.63 0.00166 0.001943330 248.8 3.95 0.00172 0.001953336 249.1 2.92 0.00176 0.001963352 250.0 0.02 0.00198 0.00200

.447*(1-4*gee/21)

(0.5-8*gee/49)(D/(1-4gee/21)

Ecu*(Xu -d/2)*effdepth

Ecu/Xu*(Xu-D/2)

strain in steel, es stress in steel, fsi stress in concrete fci for deduction

row 2 row 2

IF(strain*200000>0.87*fyy,0.87*fyy,strain*200000) 0 if tensile, .447 fck if > 0.002, parabolic in bet

MPa MPa

-0.00173 -361.1 361.1 -361.1 -361.1 -345.3 0.00 13.41 0.00-0.00042 -361.1 361.1 -361.1 -361.1 -84.0 0.00 13.41 0.000.00089 -361.1 361.1 -361.1 -361.1 177.3 0.00 13.41 0.000.00154 -361.1 361.1 -361.1 -361.1 308.0 0.00 13.41 0.000.00176 -361.1 361.1 -361.1 -361.1 351.6 0.00 13.41 0.000.00193 -361.1 361.1 -361.1 -336.0 361.1 0.00 13.41 0.000.00207 -361.1 361.1 -361.1 -241.8 361.1 0.00 13.41 0.000.00219 -361.1 361.1 -361.1 -163.3 361.1 0.00 13.41 0.000.00229 -361.1 361.1 -361.1 -96.9 361.1 0.00 13.41 0.000.00238 -361.1 361.1 -361.1 -40.0 361.1 0.00 13.41 0.000.00245 -361.1 361.1 -361.1 9.3 361.1 0.00 13.41 0.000.00252 -361.1 361.1 -361.1 52.5 361.1 0.00 13.41 0.000.00258 -361.1 361.1 -334.4 90.6 361.1 0.00 13.41 0.000.00263 -361.1 361.1 -276.9 124.4 361.1 0.00 13.41 0.000.00267 -361.1 361.1 -225.5 154.7 361.1 0.00 13.41 0.000.00272 -361.1 361.1 -179.2 182.0 361.1 0.00 13.41 0.00

row 3 -c sode right

row 1 -t side left

row 3 -c sode right

row 1 -t side left

68 mm & 0.136

Ecu/Xu*(Xu-ddash)

-200.0 -100.0 0.0 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.00.0

1000.0

2000.0

3000.0

4000.0

5000.0

6000.0

7000.0UNIAXIAL BENDING OF A GIVEN SECTION with three rows of rods

scatter PM for Xu<=D for Xu>=D Mu, kNm

Pu

, kN

0.00275 -361.1 361.1 -137.3 206.7 361.1 0.00 13.41 0.000.00279 -361.1 361.1 -99.3 229.1 361.1 0.00 13.41 0.000.00282 -361.1 361.1 -64.5 249.6 361.1 0.00 13.41 0.000.00285 -333.7 361.1 -32.7 268.3 361.1 0.00 13.41 0.000.00287 -292.3 361.1 -3.4 285.6 361.1 0.00 13.41 0.000.00290 -254.2 361.1 23.7 301.5 361.1 0.00 13.41 1.540.00292 -218.8 361.1 48.7 316.3 361.1 0.00 13.41 3.070.00294 -186.0 361.1 72.0 330.0 361.1 0.00 13.41 4.390.00296 -155.4 361.1 93.7 342.8 361.1 0.00 13.41 5.540.00298 -126.9 361.1 113.9 354.7 361.1 0.00 13.41 6.550.00299 -100.3 361.1 132.8 361.1 361.1 0.00 13.41 7.420.00301 -75.2 361.1 150.5 361.1 361.1 0.00 13.41 8.190.00304 -29.6 361.1 182.8 361.1 361.1 0.00 13.41 9.460.00306 10.9 361.1 211.6 361.1 361.1 0.72 13.41 10.430.00309 47.2 361.1 237.3 361.1 361.1 2.98 13.41 11.190.00311 79.8 361.1 260.4 361.1 361.1 4.82 13.41 11.78

IF(strain*200000>0.87*fyy,0.87*fyy,strain*200000) 0 if tensile, .447 fck if > 0.002, parabolic in bet

0.00302 95.2 350.0 361.1 5.62 13.200.00294 119.7 354.0 361.1 6.83 13.230.00287 140.6 357.4 361.1 7.77 13.260.00276 174.2 361.1 361.1 9.14 13.300.00267 200.1 361.1 361.1 10.06 13.320.00260 220.7 361.1 361.1 10.72 13.340.00255 237.4 361.1 361.1 11.20 13.350.00237 289.2 361.1 361.1 12.38 13.380.00228 315.9 361.1 361.1 12.82 13.390.00223 332.3 361.1 361.1 13.03 13.400.00219 343.3 361.1 361.1 13.14 13.400.00216 351.2 361.1 361.1 13.21 13.400.00201 361.1 361.1 361.1 13.41 13.41

Ecu/Xu*(Xu-ddash)

UNIAXIAL BENDING

stress in concrete fci for deduction Cs( + comp - tens) from Tu Ms

As1 As2 As3

3217.00 1608.00 3217.00 for Xu<=D

0 if tensile, .447 fck if > 0.002, parabolic in bet fsi - fci * Asi

MPa N Tu, kN Ms, kNm-2903.6 0.0

0.00 0.00 -1161498 559005 -1110937 -1713 87.18 -1509.8 134.90.00 0.00 -1161498 559005 -270228 -873 240.19 -601.2 302.40.00 9.25 -1161498 559005 540709 -62 387.78 345.5 476.90.00 12.70 -1161498 559005 949978 347 462.27 890.5 575.40.00 13.21 -1161498 559005 1088447 486 487.47 1096.8 611.60.00 13.39 -1161498 559005 1118408 516 492.92 1194.7 627.30.00 13.41 -1161498 559005 1118358 516 492.91 1262.5 636.90.00 13.41 -1161498 559005 1118358 516 492.91 1330.4 645.70.00 13.41 -1161498 559005 1118358 516 492.91 1398.2 653.90.00 13.41 -1161498 559005 1118358 516 492.91 1466.1 661.30.62 13.41 -1161498 559005 1118358 516 492.91 1534.0 668.03.29 13.41 -1161498 559005 1118358 516 492.91 1601.9 674.15.39 13.41 -1161498 559005 1118358 516 492.91 1669.7 679.47.05 13.41 -1161498 559005 1118358 516 492.91 1737.6 684.08.37 13.41 -1161498 559005 1118358 516 492.91 1805.5 687.99.43 13.41 -1161498 559005 1118358 516 492.91 1873.4 691.1

Pu= Cu+Tu

Mu= Muc+Mus

row 3 -c sode right

Algebraic sum of

Asi

algebraic sum of

Asi*zi from centroid

sum of Asi*zi

sum of Cu and Tu

sum of Muc Mus

-200.0 -100.0 0.0 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.00.0

1000.0

2000.0

3000.0

4000.0

5000.0

6000.0

7000.0UNIAXIAL BENDING OF A GIVEN SECTION with three rows of rods

scatter PM for Xu<=D for Xu>=D Mu, kNm

Pu

, kN

10.28 13.41 -1161498 559005 1118358 516 492.91 1941.2 693.610.96 13.41 -1161498 559005 1118358 516 492.91 2009.1 695.411.51 13.41 -1161498 559005 1118358 516 492.91 2077.0 696.511.96 13.41 -1073406 559005 1118358 604 470.97 2233.0 674.912.31 13.41 -940393 559005 1118358 737 437.83 2433.8 641.512.60 13.41 -817613 559005 1118358 860 407.24 2624.5 609.812.82 13.41 -703927 559005 1118358 973 378.91 2806.1 579.813.00 13.41 -598362 559005 1118358 1079 352.61 2979.5 551.013.14 13.41 -500077 559005 1118358 1177 328.13 3145.7 523.413.24 13.41 -408345 559005 1118358 1269 305.27 3305.3 496.713.31 13.41 -322530 559005 1118358 1355 283.90 3459.0 470.713.36 13.41 -242079 559005 1118358 1435 263.85 3607.3 445.413.41 13.41 -95375 559005 1118358 1582 227.30 3889.7 396.213.41 13.41 32713 559005 1118358 1710 195.39 4153.6 348.813.41 13.41 142135 559005 1118358 1819 168.13 4398.7 303.313.41 13.41 241221 559005 1118358 1919 143.44 4633.6 257.5

0 if tensile, .447 fck if > 0.002, parabolic in bet fsi - fci * Asifor Xu>=D

13.41 288167 541574 1118358 1948 131.75 4662.0 245.813.41 363193 547991 1118358 2030 113.06 4842.1 209.513.41 427300 553455 1118358 2099 97.09 4989.1 179.713.41 531077 559190 1118358 2209 71.23 5210.7 133.813.41 611453 559150 1118358 2289 51.21 5366.9 100.213.41 675538 559122 1118358 2353 35.24 5484.6 74.713.41 727830 559101 1118358 2405 22.21 5576.2 54.613.41 890412 559050 1118358 2568 -18.29 5835.9 -3.213.41 975072 559031 1118358 2652 -39.38 5956.4 -30.713.41 1026999 559022 1118358 2704 -52.32 6025.3 -46.713.41 1062101 559017 1118358 2739 -61.07 6069.9 -57.113.41 1087415 559014 1118358 2765 -67.37 6100.9 -64.513.41 1118363 559005 1118358 2796 -75.08 6148.1 -75.1

last point axial tension 0.87*fyy*ast -2904 0

for Xu<=D

-0.387142 0-0.201307 0.035976-0.080163 0.0806450.046062 0.127170.118731 0.1534480.146244 0.1630930.159289 0.1672840.168332 0.169830.177382 0.172190.186432 0.1743620.195482 0.1763460.204532 0.1781410.213582 0.1797480.222632 0.1811680.231682 0.1823980.240732 0.1834410.249782 0.184295

NON DIMENSIONAL UNIAXIAL BENDING

Pu= Cu+Tu

Mu= Muc+Mus

sum of Cu and Tu

sum of Muc Mus

-0.05 0 0.05 0.1 0.15 0.2

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1non dimensional UNIAXIAL BENDING OF A GIVEN SECTION with three

rows of rods

for Xu<=D for Xu>=D Mu/(fck bD2), Nmm

Pu

/(fc

k B

D),

N

0.258832 0.1849610.267882 0.1854390.276932 0.1857290.297728 0.1799780.324513 0.1710540.349933 0.1626220.374141 0.1546050.397267 0.146940.419421 0.1395710.440702 0.1324490.461194 0.1255310.480971 0.1187820.518632 0.105661

0.55381 0.0930250.5865 0.080875

0.617811 0.06866

for Xu>=D0.621604 0.0655410.645613 0.055860.665212 0.0479140.694766 0.035680.715584 0.026730.731275 0.0199190.743487 0.0145730.778117 -0.0008570.794182 -0.0081880.803379 -0.0124510.809316 -0.0152320.813459 -0.0171880.819746 -0.020016

B1B2G external columns B1B2G INTERNAL COLUMNS

kN kNm kNm kN kNm

P M2 M3 P M2

en

ve

lop

e m

in

1233.801 0.8251 41.0969 47.27096

En

velo

p m

in ,

ma

x

3870.071 0.77124583.848 -4.3791 29.0894 33.82974 121.2332 88.65634540.587 0.9786 25.5655 29.42186 1414.868 -36.1931983.709 -0.132 12.8225 14.74666 1170.264 -27.52331972.462 0.773 20.8255 23.96582 353.5733 165.4724

4529.34 5.0701 13.6344 16.72856 2178.871 -74.53274572.601 3.1758 11.6427 13.87827 2727.61 -93.02241222.554 1.7745 4.9593 6.057292 2178.871 -74.53271961.215 1.6474 36.9318 42.5138 381.69 -133.11254518.094 10.5911 4.6613 13.3072 282.0593 210.80524561.354 10.5864 -4.6586 13.301 1414.425 -36.20521211.308 2.8191 -31.0624 35.86857 1081.538 -29.942

en

ve

lop

e m

in

5705.311 -4.3917 -2.2698 5.685121 121.2332 210.80525700.754 -8.0055 2.1596 9.5354285691.253 3.1658 1.2212 3.9021485686.696 -0.0067 -1.2786 1.470415677.194 8.7679 1.0598 10.15648

Loading combination case

Mu combined approx


-0.05 0 0.05 0.1 0.15 0.2

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1non dimensional UNIAXIAL BENDING OF A GIVEN SECTION with three

rows of rods


Pu

/(fc

k B

D),

N

en

ve

lop

e m

in5672.637 7.9924 -6.4071 11.780032028.562 -0.1473 17.3341 19.934932014.504 0.7752 -9.7928 11.296952002.716 -1.0369 -17.5911 20.264882000.445 1.7157 -37.1485 42.766311988.658 -0.5575 9.865 11.36285

1974.6 -0.1137 28.0066 32.20786

B1B2G INTERNAL COLUMNS L1L2L3L4 INTERNAL COLUMNS

kNm kN kNm kNm

M3 Floor LABEL P M2 M32.0675 2.537648 L1 C10 4521.46 -10.328 -7.4422 14.63955

67.6916 128.2757 L4 C11 553.4975 4.0863 -102.4623 117.925380.9708 101.9954 L4 C12 829.7523 -8.7641 57.6319 67.03864

-84.6713 102.3872 L4 C11 553.4975 4.0863 -102.4623 117.9253-17.886 191.4017 L1 C13 4479.625 2.4423 -27.9743 32.29282-3.4361 85.80364 L4 C12 784.1736 -3.3863 102.5463 117.9925

-4.367 107.0936 L4 C12 829.7523 -8.7641 57.6319 67.03864-3.4361 85.80364 L4 C12 784.1736 -3.3863 102.5463 117.99255.6366 153.2166 L1 C13 4517.114 -14.1029 7.0966 18.15593

-8.9384 242.6438 L2 C10 3066.262 10.4725 28.3426 34.74782-103.7115 126.3268 L4 C11 843.0998 -2.4722 -106.3775 122.3672103.6679 124.0911 L4 C11 575.9909 2.1861 105.0682 120.8546103.6679 270.1542

Mu combined approx


Mu combined approx

L1L2L3L4 EXTERNAL COLUMNS

kN kNm kNm

Floor LABEL P M2 M3L1 C1 2462.077 60.8996 2.7274 70.10474 4521.46L4 C20 504.3093 20.6661 34.262 46.01398 553.4975L1 C20 1081.136 5.822 29.7313 34.84037 829.7523L1 C21 896.6654 8.5747 -33.9125 40.22672 553.4975L2 C14 2103.377 76.6844 -12.2944 89.31325 4479.625L2 C1 1683.278 -77.3096 -3.8008 89.01342 784.1736L4 C1 1478.385 -93.9178 -21.0168 110.6767 829.7523L4 C1 1179.895 -76.484 -3.8519 88.06807 784.1736L2 C14 2131.493 -120.7283 2.9687 138.8795 4517.114L2 C1 1705.771 102.017 24.1423 120.5599 3066.262L1 C20 1118.625 13.5152 -65.6359 77.06486 843.0998L1 C21 926.6565 13.5237 66.5295 78.07361 575.9909


Mu combined approx

-200.0 -100.0 0.0 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0

-4000.0

-2000.0

0.0

2000.0

4000.0

6000.0

8000.0UNIAXIAL BENDING OF A GIVEN SECTION 300 x 512 with three rows of rods

3x 2x 20 mm - Mxx-Pu

for Xu<=D for Xu>=D Mu, kNm

Pu

, kN

-0.05 0 0.05 0.1 0.15 0.2

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1non dimensional UNIAXIAL BENDING OF A GIVEN SECTION with three rows

of rods


Pu

/(fc

k B

D),

N

concrete fck= 30

Breadth= 512DepthOverall=D=450 512new depthoevrall= D= 300Overall Depth = finally 300

Xu/d ecu= g=

0 0.00350.075 0.0035

0.1 0.00350.15 0.0035

0.2 0.00350.225 0.0035

0.25 0.00350.275 0.0035

0.3 0.00350.325 0.0035

0.35 0.00350.375 0.0035

0.4 0.00350.425 0.0035

0.45 0.0035

Roll no. Q Queue=

0.0035-.75*ec min

16/(7*xu/D-3)sq

0.475 0.00350.5 0.0035

0.525 0.00350.55 0.0035

0.575 0.00350.6 0.0035

0.625 0.00350.65 0.0035

0.675 0.00350.7 0.0035

0.725 0.00350.75 0.0035

0.775 0.00350.8 0.0035

0.85 0.00350.9 0.0035

0.95 0.00351 0.0035

1 0.00350 1.000 1.05 0.00338 0.846

1.1 0.00328 0.724 1.2 0.00311 0.549 1.3 0.00298 0.430 1.4 0.00288 0.346 1.5 0.00280 0.284

2 0.00255 0.132 2.5 0.00241 0.076

3 0.00233 0.049 3.5 0.00228 0.035

4 0.00224 0.026 40 0.00202 0.000

16/(7*xu/D-3)sq

62

steel fy= 500

bar dia steel area

no mm sqmm mm

zero4RollNo 3 20 942.48 58

20 0.00 1503 20 942.48 242

ratio to dpeth main rod dia 20trans dia 8clear cover = 40***eff*** cover 58 0.1933

242 0.8067

Cu Mc strain in steel, es stress in steel, fsi

row 2 row 2

.416Xu D/2

ecu/xu*(effCu, kN mm Mc, kNm MPa

125 9.4 17.60 -0.03414 -0.01983 -0.00552 -435.0 -435.0167 12.5 22.94 -0.02473 -0.01400 -0.00327 -435.0 -435.0250 18.7 32.85 -0.01532 -0.00817 -0.00101 -435.0 -435.0334 25.0 41.72 -0.01062 -0.00525 0.00012 -435.0 -435.0375 28.1 45.76 -0.00905 -0.00428 0.00049 -435.0 -435.0417 31.2 49.54 -0.00779 -0.00350 0.00079 -435.0 -435.0459 34.3 53.07 -0.00677 -0.00286 0.00104 -435.0 -435.0500 37.4 56.33 -0.00591 -0.00233 0.00124 -435.0 -435.0542 40.6 59.33 -0.00519 -0.00188 0.00142 -435.0 -376.9584 43.7 62.07 -0.00457 -0.00150 0.00157 -435.0 -300.0626 46.8 64.56 -0.00403 -0.00117 0.00170 -435.0 -233.3667 49.9 66.78 -0.00356 -0.00087 0.00181 -435.0 -175.0709 53.0 68.74 -0.00314 -0.00062 0.00191 -435.0 -123.5751 56.2 70.44 -0.00277 -0.00039 0.00200 -435.0 -77.8

b D interchanged rods count position adjusted but shet retained for minor

axis YY interac diag

at dd from comp face

face to centre of other side rod

area of stress blcok

distance of the centroid of

stress block from comp face

Mc= cu * z from

centroidrow 1 -

t side left

row 3 -c sode right

row 1 -t side left

0.362*xu*DepthO

Cu*(.5 D -.416xu)

242 mm & 0.80666666666666

7

58 mm & 0.19333333333333

3

.447*(1-4*gee/21)

(0.5-8*gee/49)(D/(1-4gee/21)

Ecu/Xu*(Xu-D/2)

Ecu/Xu*(Xu-ddash)

IF(strain*200000>0.87*fyy,0.87*fyy,strain*200000)

-50.0 0.0 50.0 100.0 150.0 200.0

-2000.0

-1000.0

0.0

1000.0

2000.0

3000.0

4000.0

UNIAXIAL BENDING OF A GIVEN SECTION with three rows of rods

for Xu<=D for Xu>=D

Mu, kNm

Pu

, kN

792 59.3 71.88 -0.00244 -0.00018 0.00208 -435.0 -36.8834 62.4 73.06 -0.00215 0.00000 0.00215 -429.3 0.0876 65.5 73.98 -0.00188 0.00017 0.00221 -375.6 33.3917 68.6 74.64 -0.00163 0.00032 0.00227 -326.7 63.6959 71.8 75.04 -0.00141 0.00046 0.00232 -282.0 91.3

1001 74.9 75.18 -0.00121 0.00058 0.00237 -241.1 116.71043 78.0 75.06 -0.00102 0.00070 0.00242 -203.5 140.01084 81.1 74.68 -0.00084 0.00081 0.00246 -168.7 161.51126 84.2 74.04 -0.00068 0.00091 0.00250 -136.5 181.51168 87.4 73.14 -0.00053 0.00100 0.00253 -106.7 200.01209 90.5 71.98 -0.00039 0.00109 0.00257 -78.9 217.21251 93.6 70.56 -0.00026 0.00117 0.00260 -52.9 233.31293 96.7 68.88 -0.00014 0.00124 0.00263 -28.6 248.41334 99.8 66.94 -0.00003 0.00131 0.00265 -5.8 262.51418 106.1 62.27 0.00018 0.00144 0.00270 35.7 288.21501 112.3 56.57 0.00036 0.00156 0.00275 72.6 311.11585 118.6 49.82 0.00053 0.00166 0.00279 105.6 331.61668 124.8 42.04 0.00068 0.00175 0.00282 135.3 350.0

1667 124.8 42.04 0.00068 0.00175 0.00282 135.3 350.01728 129.4 35.54 0.00078 0.00177 0.00276 156.6 354.01776 132.9 30.45 0.00087 0.00179 0.00270 174.8 357.41845 137.5 23.07 0.00102 0.00181 0.00261 204.0 363.01891 140.4 18.08 0.00113 0.00184 0.00254 226.4 367.21924 142.4 14.55 0.00122 0.00185 0.00248 244.3 370.61948 143.9 11.96 0.00129 0.00187 0.00244 258.8 373.32008 147.2 5.56 0.00152 0.00191 0.00230 303.8 381.82030 148.4 3.20 0.00163 0.00193 0.00223 327.0 386.22040 149.0 2.08 0.00171 0.00194 0.00218 341.2 388.92046 149.3 1.46 0.00175 0.00195 0.00215 350.8 390.72050 149.5 1.08 0.00179 0.00196 0.00213 357.7 392.02060 150.0 0.01 0.00198 0.00200 0.00201 396.2 399.3

.447*(1-4*gee/21)

(0.5-8*gee/49)(D/(1-4gee/21)

Ecu*(Xu -d/2)*effdepth

Ecu/Xu*(Xu-D/2)

Ecu/Xu*(Xu-ddash)


stress in steel, fsi Cs( + comp - tens) from Tu Ms

row 2 As1 As2 As3

942.48 0.00 942.48

fsi - fci * Asi

MPa MPa N Tu, kN Ms, kNm

435.0 0.00 0.00 0.00 -409978 0 409978 0 98.88435.0 0.00 0.00 0.00 -409978 0 409978 0 98.88

-202.2 0.00 0.00 0.00 -409978 0 -190590 -601 43.6323.3 0.00 0.00 1.52 -409978 0 20560 -389 63.0698.5 0.00 0.00 5.79 -409978 0 87393 -323 69.21

158.7 0.00 0.00 8.53 -409978 0 141502 -268 74.18207.9 0.00 0.00 10.32 -409978 0 186198 -224 78.30248.9 0.00 0.00 11.50 -409978 0 223737 -186 81.75283.6 0.00 0.00 12.27 -409978 0 255709 -154 84.69313.3 0.00 0.00 12.78 -409978 0 283264 -127 87.23339.1 0.00 0.00 13.10 -409978 0 307259 -103 89.43361.7 0.00 0.00 13.29 -409978 0 328340 -82 91.37381.6 0.00 0.00 13.38 -409978 0 347008 -63 93.09399.3 0.00 0.00 13.41 -409978 0 363654 -46 94.62

stress in concrete fci for deduction

row 3 -c sode right

row 1 -t side left

row 3 -c sode right

Algebraic sum of

Asi

algebraic sum of

Asi*zi from centroid


0 if tensile, .447 fck if > 0.002, parabolic in bet

sum of Asi*zi

-50.0 0.0 50.0 100.0 150.0 200.0

-2000.0

-1000.0

0.0

1000.0

2000.0

3000.0

4000.0


for Xu<=D for Xu>=D

Mu, kNm

Pu

, kN

415.1 0.00 0.00 13.41 -409978 0 378572 -31 95.99429.3 0.00 0.00 13.41 -404637 0 391999 -13 96.43435.0 0.00 2.14 13.41 -353953 0 397339 43 89.36435.0 0.00 3.93 13.41 -307876 0 397339 89 82.49435.0 0.00 5.42 13.41 -265806 0 397339 132 76.21435.0 0.00 6.68 13.41 -227242 0 397339 170 70.46435.0 0.00 7.74 13.41 -191763 0 397339 206 65.16435.0 0.00 8.64 13.41 -159013 0 397339 238 60.28435.0 0.00 9.41 13.41 -128689 0 397339 269 55.75435.0 0.00 10.06 13.41 -100531 0 397339 297 51.55435.0 0.00 10.61 13.41 -74315 0 397339 323 47.64435.0 0.00 11.08 13.41 -49847 0 397339 347 43.99435.0 0.00 11.48 13.41 -26957 0 397339 370 40.58435.0 0.00 11.83 13.41 -5498 0 397339 392 37.38435.0 2.29 12.36 13.41 31479 0 397339 429 31.86435.0 4.43 12.75 13.41 64246 0 397339 462 26.97435.0 6.15 13.02 13.41 93746 0 397339 491 22.57435.0 7.54 13.20 13.41 120443 0 397339 518 18.59

fsi - fci * Asi

435.0 7.54 13.20 13.41 120443 0 397339 518 18.59435.0 8.45 13.23 13.41 139659 0 397339 537 15.72435.0 9.16 13.26 13.41 156069 0 397339 553 13.27435.0 10.19 13.30 13.41 182616 0 397339 580 9.31435.0 10.89 13.32 13.41 203163 0 397339 601 6.24435.0 11.38 13.34 13.41 219536 0 397339 617 3.80435.0 11.74 13.35 13.41 232890 0 397339 630 1.81435.0 12.63 13.38 13.41 274378 0 397339 672 -4.38435.0 12.96 13.39 13.41 295962 0 397339 693 -7.60435.0 13.12 13.40 13.41 309194 0 397339 707 -9.57430.6 13.21 13.40 13.41 318136 0 393226 711 -11.29426.3 13.26 13.40 13.41 324583 0 389184 714 -12.62402.4 13.41 13.41 13.41 360752 0 366594 727 -20.10

last point axial tension 0.87*fyy*ast


0 if tensile, .447 fck if > 0.002, parabolic in bet

UNIAXIAL BENDING

for Xu<=D for Xu<=D

-820.0 0.0 -0.177942 0125.1 116.5 0.02715 0.084259166.8 121.8 0.0362 0.088125166.8 121.8 0.0362 0.088125166.8 121.8 0.0362 0.088125

52.7 115.0 0.011445 0.083164148.5 123.7 0.032237 0.089501234.9 131.4 0.050987 0.095024314.2 138.1 0.068183 0.099883387.9 144.0 0.084171 0.104183457.1 149.3 0.099201 0.108522.8 154.0 0.113459 0.111393585.6 158.2 0.127084 0.114403646.0 161.8 0.140185 0.117064704.3 165.1 0.152847 0.119403

NON DIMENSIONAL UNIAXIAL BENDING

Pu= Cu+Tu

Mu= Muc+Mus

Pu= Cu+Tu

Mu= Muc+Mus

sum of Cu and Tu

sum of Muc Mus

sum of Cu and Tu

sum of Muc Mus

-50.0 0.0 50.0 100.0 150.0 200.0

-2000.0

-1000.0

0.0

1000.0

2000.0

3000.0

4000.0


for Xu<=D for Xu>=D

Mu, kNm

Pu

, kN

-0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7non dimensional UNIAXIAL BENDING OF A GIVEN SECTION with three

rows of rods


Pu

/(fc

k B

D),

N

760.9 167.9 0.165135 0.121438821.4 169.5 0.178257 0.12261919.1 163.3 0.199465 0.118161

1006.9 157.1 0.218515 0.1136661090.7 151.3 0.236695 0.1094161171.0 145.6 0.254113 0.1053551248.1 140.2 0.270863 0.1014391322.6 135.0 0.28702 0.0976291394.6 129.8 0.302651 0.0938931464.5 124.7 0.317812 0.0902031532.4 119.6 0.332551 0.0865341598.6 114.6 0.346911 0.0828651663.2 109.5 0.360928 0.0791781726.3 104.3 0.374635 0.0754581846.7 94.1 0.40076 0.0680931962.9 83.5 0.42597 0.060432075.8 72.4 0.450472 0.0523672185.9 60.6 0.474366 0.043853

for Xu>=D for Xu>=D2185.2 60.6 0.474223 0.0438532265.0 51.3 0.491543 0.0370832329.0 43.7 0.505427 0.0316252424.5 32.4 0.526141 0.023422491.6 24.3 0.540707 0.0175932540.9 18.3 0.551409 0.0132722578.4 13.8 0.55955 0.0099582679.6 1.2 0.581513 0.0008522723.2 -4.4 0.590977 -0.0031842746.9 -7.5 0.596123 -0.0054242757.6 -9.8 0.598428 -0.0071122763.5 -11.5 0.599718 -0.0083512787.0 -20.1 0.604826 -0.01453

-820 0

-0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7non dimensional UNIAXIAL BENDING OF A GIVEN SECTION with three

rows of rods


Pu

/(fc

k B

D),

N

-50.0 0.0 50.0 100.0 150.0 200.0

-1500.0

-1000.0

-500.0

0.0

500.0

1000.0

1500.0

2000.0

2500.0

3000.0

3500.0UNIAXIAL BENDING OF A GIVEN SECTION 300 x 512 with three rows of rods

3x 2x 20 mm - Myy-Pu

for Xu<=D for Xu>=D Mu, kNm

Pu

, kN

PM Interaction Curves

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