Design of Rectangular Column Section by Limit-State Method N. Prabhakar
Design of Rectangular Column Section by Limit-State Method N. Prabhakar
Design of Rectangular Column Section by Limit-State Method N. Prabhakar
:
Design by:
Client: Date: 6-Oct-18
Project: AHMEDABAD METRO RAIL Page No.
Applied Ultimate Loads (See figures on next page) Effective Length Un- Braced /
Col. Axial Load Initial Moment Muix(kN.m) Initial Moment Muiy(kN.m) lex (m) ley (m) Supported Unbraced
Pu (kN) M uix1(+ or -) Muix2 (+ only) M uiy1(+ or -) Muiy2 (+ only)
* *
Mk. Length (m) Column
1 902 -77.01 181.3 39.23 202 6.540 6.540 5.450 Unbraced
2 815 1 19.2 160 482 8.640 6.540 5.450 Unbraced
3 1027 2.4 16.5 85.3 189 8.640 6.540 5.450 Unbraced
4 0 0 0 0 0
5 0 0 0 0 0
6 0 0 0 0 0
7 0 0 0 0 0
8 0 0 0 0 0
9 0 0 0 0 0
10 0 0 0 0 0
Note: * at Muix1 and Muiy1 indicates moment is +ve for single curvature bending, and -ve for double curvature bending.
Companys' Name: GEC MEGA Job No.: 0
0 Design by: 0
Client: 0 Date: 6-Oct-18
Project: AHMEDABAD METRO RAIL Page No. C/102
Pu
Muix2 or Initial Moments Muix & Muiy
Muiy2 Muix2>Muix1
+ Muiy2>Muiy1 +
+ Addn. Moments Max & May
Deflected due to slenderness
shape
- -
Muix1 or
Muiy1
Summary of Results:
0 0 40 40 -100 375
0 750 40 710 500 375
350 750 310 710
350 0 310 40
0 0 40 40
pi(fsi-fci)*y/(fck*D)
xu/D y1 y2 y3 y4 y5 y6
0.1 0.00967238 -0.0231935 -0.0077312 0.00773117 0.02319352 0.01932793
0.125 0.01381889 -0.0226675 -0.0077312 0.00773117 0.02319352 0.01932793
0.15 0.01571009 -0.0202757 -0.0077312 0.00773117 0.02319352 0.01932793
0.175 0.01640992 -0.0138612 -0.0077312 0.00773117 0.02319352 0.01932793
0.2 0.01683905 -0.0074637 -0.0076506 0.00773117 0.02319352 0.01932793
0.225 0.01708423 -0.0024879 -0.0074319 0.00773117 0.02319352 0.01932793
0.25 0.01728038 0.00066006 -0.0069779 0.00773117 0.02319352 0.01932793
0.275 0.01744086 0.00391696 -0.0062223 0.00769364 0.02319352 0.01932793
0.3 0.0175746 0.00663104 -0.0046994 0.00757879 0.02319352 0.01932793
0.325 0.01768165 0.00892757 -0.003381 0.0073701 0.02319352 0.01932793
0.35 0.01775264 0.01089602 -0.002251 0.0070384 0.02315476 0.01932793
0.375 0.01781417 0.01260202 -0.0012716 0.00660366 0.02287419 0.01932793
0.4 0.01786801 0.01409476 -0.0004147 0.00580512 0.02262869 0.01932793
0.425 0.01791551 0.01541189 6.3916E-05 0.0047319 0.02200528 0.01932793
0.45 0.01795774 0.01658267 0.00073603 0.00377793 0.02121608 0.01913839
0.475 0.01799552 0.01763021 0.0013374 0.00292438 0.02027566 0.01896208
0.5 0.01802952 0.018163 0.00187863 0.00215619 0.01899568 0.01872342
0.525 0.01806028 0.018606 0.00236831 0.00146115 0.01670452 0.0182685
0.55 0.01808825 0.01896774 0.00281348 0.0008293 0.01424892 0.01773356
0.575 0.01811379 0.01921569 0.00321993 0.0002524 0.01200686 0.01714892
0.6 0.01813719 0.01944298 0.00359252 -0.0002349 0.00995163 0.016404
0.625 0.01815257 0.01965208 0.0039353 -0.0006652 0.00806082 0.0153421
0.65 0.0181592 0.0198451 0.00425171 -0.001076 0.00631546 0.01355591
0.675 0.01816534 0.02002382 0.00454468 -0.0014646 0.00469938 0.01190203
0.7 0.01817103 0.0201312 0.00481673 -0.0018306 0.00319874 0.01036628
0.725 0.01817634 0.02022512 0.00507001 -0.0021749 0.00180159 0.00893645
0.75 0.01818129 0.02031278 0.00530641 -0.0024986 0.00049758 0.00760194
0.775 0.01818592 0.02039478 0.00552756 -0.0028032 -0.0006517 0.00635353
0.8 0.01819026 0.02047166 0.00573488 -0.0030899 -0.0016962 0.00518314
0.825 0.01819434 0.02054388 0.0059186 -0.0033602 -0.0026896 0.00408369
0.85 0.01819818 0.02061185 0.0060138 -0.0036153 -0.0036337 0.00304891
0.875 0.0182018 0.02067593 0.00610356 -0.0038564 -0.004531 0.00207326
0.9 0.01820521 0.02073646 0.00618833 -0.0040845 -0.005384 0.00115181
0.925 0.01820845 0.02079371 0.00626852 -0.0043005 -0.0061953 0.00028017
0.95 0.01821151 0.02084795 0.00632814 -0.0045055 -0.0069675 -0.0005019
0.975 0.01821442 0.02089941 0.00637674 -0.0047002 -0.0077029 -0.0012272
1 0.01821718 0.02094829 0.00642291 -0.0048854 -0.0084039 -0.0019208
1.025 0.01819268 0.0208855 0.00642012 -0.0049661 -0.0088993 -0.0025343
1.05 0.01817015 0.02082776 0.00641757 -0.0050403 -0.0093558 -0.0031002
1.075 0.01814909 0.02077449 0.00641521 -0.0051089 -0.0097777 -0.0036237
1.1 0.01809137 0.02072519 0.00641302 -0.0051724 -0.0101688 -0.0041094
1.125 0.0180378 0.02067942 0.00641099 -0.0052314 -0.0105323 -0.0045614
1.15 0.01798794 0.02063683 0.00640911 -0.0052863 -0.0108712 -0.0049829
1.175 0.01794142 0.02059709 0.00640734 -0.0053376 -0.0111877 -0.0053769
1.2 0.01789792 0.02055992 0.0064057 -0.0053856 -0.0114841 -0.0057462
1.225 0.01785714 0.02052509 0.00640415 -0.0054306 -0.0117622 -0.0060928
1.25 0.01781885 0.02049238 0.0064027 -0.0054729 -0.0120237 -0.0064189
1.275 0.01778282 0.0204616 0.00640134 -0.0055127 -0.0122699 -0.0067262
1.3 0.01774886 0.02043259 0.00640005 -0.0055503 -0.0125022 -0.0070162
1.325 0.01771679 0.0204052 0.00639884 -0.0055857 -0.0127218 -0.0072905
1.35 0.01768647 0.02037929 0.00639769 -0.0056193 -0.0129296 -0.0075502
1.375 0.01765509 0.02035475 0.0063966 -0.0056511 -0.0131266 -0.0077965
1.4 0.01761787 0.02033147 0.00639557 -0.0056813 -0.0133136 -0.0080304
1.425 0.01758251 0.02030936 0.00639459 -0.0057099 -0.0134913 -0.0082528
1.45 0.01754888 0.02028834 0.00639366 -0.0057372 -0.0136605 -0.0084645
1.475 0.01751686 0.02026832 0.00639277 -0.0057632 -0.0138217 -0.0086663
1.5 0.01748633 0.02024923 0.00639193 -0.0057879 -0.0139754 -0.0088589
1.525 0.0174572 0.02023101 0.00639112 -0.0058116 -0.0141222 -0.0090428
1.55 0.01742936 0.02021361 0.00639035 -0.0058342 -0.0142626 -0.0092187
1.575 0.01740274 0.02019696 0.00638961 -0.0058558 -0.0143969 -0.0093871
1.6 0.01737726 0.02018103 0.00638891 -0.0058765 -0.0145255 -0.0095484
1.625 0.01735284 0.02016576 0.00638823 -0.0058963 -0.0146488 -0.0097031
1.65 0.01732942 0.02015111 0.00638758 -0.0059134 -0.0147671 -0.0098515
1.675 0.01730694 0.02013706 0.00638696 -0.0059228 -0.0148808 -0.0099941
1.7 0.01728534 0.02012355 0.00638636 -0.0059318 -0.01499 -0.0101312
1.725 0.01726457 0.02011057 0.00638578 -0.0059405 -0.015095 -0.010263
1.75 0.0172446 0.02009808 0.00638523 -0.0059489 -0.0151961 -0.01039
1.775 0.01722536 0.02008605 0.0063847 -0.0059569 -0.0152935 -0.0105123
1.8 0.01720682 0.02007446 0.00638418 -0.0059647 -0.0153873 -0.0106302
1.825 0.01718895 0.02006329 0.00638369 -0.0059722 -0.0154779 -0.010744
1.85 0.01717171 0.02005251 0.00638321 -0.0059794 -0.0155653 -0.0108538
1.875 0.01715506 0.0200421 0.00638275 -0.0059864 -0.0156497 -0.0109599
1.9 0.01713898 0.02002664 0.0063823 -0.0059931 -0.0157312 -0.0110624
1.925 0.01712344 0.02001065 0.00638187 -0.0059997 -0.01581 -0.0111615
1.95 0.01710841 0.01999519 0.00638146 -0.006006 -0.0158863 -0.0112575
1.975 0.01709386 0.01998022 0.00638105 -0.0060121 -0.0159602 -0.0113503
2 0.01707978 0.01996574 0.00638066 -0.006018 -0.0160317 -0.0114403
2.5 0.01686949 0.01974942 0.00637484 -0.0061064 -0.0171016 -0.0127877
3.0 0.01674098 0.01961723 0.00637128 -0.0061607 -0.0177461 -0.0136153
3.5 0.01662461 0.01952808 0.00636888 -0.0061973 -0.0179744 -0.0141751
4.0 0.01652194 0.01946389 0.00636715 -0.0062237 -0.0181392 -0.0145791
pi(fsi-fci)*x/(fck*b)
xu/b x1 x2 x3 x4 x5 x6
0.1 -0.0512618 0 0 0 0 0.0743382
0.125 -0.0170873 0 0 0 0 0.0743382
0.15 0.0030269 0 0 0 0 0.0743382
0.175 0.0193005 0 0 0 0 0.0743382
0.2 0.0315057 0 0 0 0 0.0743382
0.225 0.0409986 0 0 0 0 0.0743382
0.25 0.048593 0 0 0 0 0.0743382
0.275 0.0548065 0 0 0 0 0.0743382
0.3 0.0584514 0 0 0 0 0.0743382
0.325 0.0606601 0 0 0 0 0.0743382
0.35 0.0619753 0 0 0 0 0.0743382
0.375 0.0631151 0 0 0 0 0.0743382
0.4 0.0641124 0 0 0 0 0.07403648
0.425 0.0646943 0 0 0 0 0.07325346
0.45 0.0651697 0 0 0 0 0.07255745
0.475 0.0655951 0 0 0 0 0.07085484
0.5 0.065978 0 0 0 0 0.06864688
0.525 0.0663244 0 0 0 0 0.06635386
0.55 0.0666394 0 0 0 0 0.06324529
0.575 0.0669269 0 0 0 0 0.05869108
0.6 0.0671905 0 0 0 0 0.05126183
0.625 0.067433 0 0 0 0 0.04442692
0.65 0.0676568 0 0 0 0 0.03811777
0.675 0.067864 0 0 0 0 0.03227597
0.7 0.0680258 0 0 0 0 0.02685144
0.725 0.068157 0 0 0 0 0.02180101
0.75 0.0682794 0 0 0 0 0.01708728
0.775 0.0683939 0 0 0 0 0.01267766
0.8 0.0685013 0 0 0 0 0.00854364
0.825 0.0686021 0 0 0 0 0.00466017
0.85 0.068697 0 0 0 0 0.00100513
0.875 0.0687865 0 0 0 0 -0.0022318
0.9 0.068871 0 0 0 0 -0.0052326
0.925 0.068951 0 0 0 0 -0.0080948
0.95 0.0690267 0 0 0 0 -0.0108254
0.975 0.0690986 0 0 0 0 -0.0134313
1 0.0691668 0 0 0 0 -0.0159197
1.025 0.0689436 0 0 0 0 -0.0179451
1.05 0.0687384 0 0 0 0 -0.0198123
1.075 0.0685491 0 0 0 0 -0.021539
1.1 0.0683738 0 0 0 0 -0.0231405
1.125 0.0682111 0 0 0 0 -0.02463
1.15 0.0680597 0 0 0 0 -0.0260187
1.175 0.0679098 0 0 0 0 -0.0273166
1.2 0.0677293 0 0 0 0 -0.0285322
1.225 0.0675602 0 0 0 0 -0.0296733
1.25 0.0674013 0 0 0 0 -0.0307463
1.275 0.0672519 0 0 0 0 -0.0317573
1.3 0.067111 0 0 0 0 -0.0327115
1.325 0.0669779 0 0 0 0 -0.0336134
1.35 0.0668521 0 0 0 0 -0.0344673
1.375 0.0667329 0 0 0 0 -0.035277
1.4 0.0666199 0 0 0 0 -0.0360457
1.425 0.0665125 0 0 0 0 -0.0367765
1.45 0.0664104 0 0 0 0 -0.0374721
1.475 0.0663132 0 0 0 0 -0.0381351
1.5 0.0662205 0 0 0 0 -0.0387676
1.525 0.066132 0 0 0 0 -0.0393718
1.55 0.0660475 0 0 0 0 -0.0399494
1.575 0.0659667 0 0 0 0 -0.0405022
1.6 0.0658893 0 0 0 0 -0.0410317
1.625 0.0658152 0 0 0 0 -0.0415394
1.65 0.065744 0 0 0 0 -0.0420267
1.675 0.0656758 0 0 0 0 -0.0424947
1.7 0.0656102 0 0 0 0 -0.0429445
1.725 0.0655472 0 0 0 0 -0.0433772
1.75 0.0654865 0 0 0 0 -0.0437937
1.775 0.0654281 0 0 0 0 -0.044195
1.8 0.0653718 0 0 0 0 -0.0445818
1.825 0.0653175 0 0 0 0 -0.0449549
1.85 0.0652652 0 0 0 0 -0.0453151
1.875 0.0652146 0 0 0 0 -0.045663
1.9 0.0651658 0 0 0 0 -0.0459992
1.925 0.0651186 0 0 0 0 -0.0463242
1.95 0.065073 0 0 0 0 -0.0466388
1.975 0.0650288 0 0 0 0 -0.0469432
2 0.064986 0 0 0 0 -0.0472381
2.5 0.0643475 0 0 0 0 -0.0516533
3.0 0.06378 0 0 0 0 -0.0543629
3.5 0.063347 0 0 0 0 -0.0561951
4.0 0.0630353 0 0 0 0 -0.0571883
Puz = 7668.66674 kN
Calculation of Pbx
xu/D= (.0035*d)/(.0055*D) = 0.5939394
Pb-conc = 1969911.36 N D= 750 mm b (mm) = 350
fy = 500 N/mm2 Es = 200000 N/mm2
Steel Strain
xu/D e1 e2 e3 e4 e5 e6
0.593939 0.00310714 0.0020857 0.0010643 4.286E-05 0.0009786 0.002
Steel Stress,fsi
xu/d fs1 fs2 fs3 fs4 fs5 fs6
0.593939 423.49959 379.1 212.73481 8.5665 195.60181 373.1
Concrete Stress, fci
0.593939 15.61 15.61 15.61 1.342834 0 0
Ast(fsi-fci)
xu/d y1 y2 y3 y4 y5 y6
0.593939 384426.884 685162.51 371571.52 13616.294 -368700.7 -351638.5
Pbx = 2704.34938 kN
Calculation of Pby
xu/B= (.0035*b)/(.0055*B) = 0.5454545
Pb-conc = 1809102.27 N D= 750 mm b (mm) = 350
fy = 500 N/mm2 Es = 200000 N/mm2
Steel Strain
xu/D e1 e2 e3 e4 e5 e6
0.545455 0.00258333 0.0035 0.0002917 0.0035 0.0035 0.002
Steel Stress,fsi
xu/B= fs1 fs2 fs3 fs4 fs5 fs6
0.545455 405.057516 427.84476 58.299808 427.84476 427.84476 373.1
Concrete Stress, fci
0.545455 15.61 15.61 9.7803395 15.61 15.61 0
Ast(fsi-fci)
xu/d y1 y2 y3 y4 y5 y6
0.545455 1712879.64 0 30485.681 0 0 -1640980
Pby = 1911.48809 kN
00
80
00
75
00
70
00
65
00
60
00
Pu (kN)
55
00
50
00
45
00
40
00
35
00
30
00
25
00
20
00
15 1027
00 815 902
10
0
50
0 0
0 100 200 300 400 500 600 700 800 900 1000
Mux (kN.m)
Indicates applied load values of Pu & Muy.
fck=M35, fy=500, p=3.59% Any value to the right of red line (permissible)
Pu & Muy Chart requires revision of section. See Chart for
Applied Loads
Pu & Mux also.
00
80
00
75
00
70
00
65
00
60
00
Pu (kN)
55
00
50
00
45
00
40
00
35
00
30
00
25
00
20
00
15 1027
00 902 815
10
0
50
0 0
0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600 625 650
Muy (kN.m)
NOTES:
This Spreadsheet is intended to be used by qualified Civil and Structural Engineers who are
familiar with the provisions of IS:456-2000, and those who will evaluate the significance and
limitations of its contents and take responsibility for its use and application.
DISCLAIMER
No liability, including that for negligence, for any loss resulting from such usage or information
is accepted by the author of this Spreadsheet.
N. PRABHAKAR
BE CEng(I) MIStructE (UK) MIE (Ind)
Chartered Structural Engineer
Structural Consultant
Flat E-8 Star Residency
Location: Evershine City
Vasai (E) Pin 401 208
Thane Dist, Maharashtra, India
11.4.2004
Revision History of BIAXCOLUMN
Date Revision