Calculation of Effective length factor for Columns as per BS 5950-1 Annex E

L1 = 3 m L2 = 0 m

No section C1

Ixx = 0.0

h1 = 0 m

B1 B2

No section No sectionIxx = 0.0 Ixx = 0.0

UB457x191x82 C2

Ixx = 37051.0

h2 = 8 m

B3 B4

UB305x165x40 No sectionIxx = 8503.0 cm4

UB457x191x82 C3

Ixx = 37051.0 cm4

h3 = 10 mStiffeness Coefficient K = I / LI = Moment of Inertia about X-axisL = Length of member

370510000 / 7890= 46959

0 / 0 370510000 / 9780= 0 = 37884

No Section No Section= 0 = 0

85030000 / 3300 No Section= 25766.66666667 = 0

= 1.000

= 0.767

Refer Figure E.2 of BS 5950-1

cm4

K1

K11 K12

cm4 cm4

cm4

KC

K21 K22

K2

KC = Ic / h2

KC =

K1 = I1 / h1 K2 = I2 / h3

K1 = K2 =

K11 = I11/ L1 K12 = I12/ L2

K11 = K12 =

K21 = I21/ L1 K22 = I22/ L2

K21 = K22 =

k1 = ( KC + K1 ) / ( KC + K1 + K11 + K12 )

k2 = ( KC + K2 ) / ( KC + K2 + K21 + K22 )

LE/L = 1-0.2 (k1 + k2) - 0.12 k1 k2 0.5

1-0.8 (k1 + k2) + 0.6 k1 k2

3.45LE/L

Calculation of Effective length factor for Columns as per BS 5950-1 Annex E

L1 = 3 m

No section C1

Iyy = 0.0

B1

UB457x191x82Ixx = 37051.0

UB457x191x82 C2

Iyy = 1871.0

B3

No section

UB457x191x82 C3

Iyy = 1871.0 cm4

Stiffeness Coefficient K = I / LI = Moment of Inertia about X-axisL = Length of member

18710000 / 7890= 2371

0 / 0 18710000 / 9780= 0 = 1913

370510000 / 2800 370510000 / 4400= 132325 = 84207

No Section No Section= 0 = 0

= 0.011 0.20895781151

cm4

K1

K11

cm4

cm4

KC

K21

K2

KC = Ic / h2

KC =

K1 = I1 / h1 K2 = I2 / h3

K1 = K2 =

K11 = I11/ L1 K12 = I12/ L2

K11 = K12 =

K21 = I21/ L1 K22 = I22/ L2

K21 = K22 =

k1 = ( KC + K1 ) / ( KC + K1 + K11 + K12 )

= 1.000 0.44304894553

Refer Figure E.2 of BS 5950-1

2.01 1.26800363089

k2 = ( KC + K2 ) / ( KC + K2 + K21 + K22 )

LE/L = 1-0.2 (k1 + k2) - 0.12 k1 k2 0.5

1-0.8 (k1 + k2) + 0.6 k1 k2

LE/L

Universal Beams to BS4 Part 1 1993Mass Depth Width Thickness ofper of of Web

DesignDesignmetre Section SectionM h b skg/m mm mm mm

Fixed

PinnedNo section 0 0 0 0 0

UB914914x4 388 921 420.5 21.4UB914914x4 343.3 911.8 418.5 19.4UB914914x3 289.1 926.6 307.7 19.5UB914914x3 253.4 918.4 305.5 17.3UB914914x3 224.2 910.4 304.1 15.9UB914914x3 200.9 903 303.3 15.1UB838838x2 226.5 850.9 293.8 16.1UB838838x2 193.8 840.7 292.4 14.7UB838838x2 175.9 834.9 291.7 14UB762762x2 196.8 769.8 268 15.6UB762762x2 173 762.2 266.7 14.3UB762762x2 146.9 754 265.2 12.8UB762762x2 133.9 750 264.4 12UB686686x2 170.2 692.9 255.8 14.5UB686686x2 152.4 687.5 254.5 13.2UB686686x2 140.1 683.5 253.7 12.4UB686686x2 125.2 677.9 253 11.7UB610610x3 238.1 635.8 311.4 18.4UB610610x3 179 620.2 307.1 14.1UB610610x3 149.2 612.4 304.8 11.8UB610610x2 139.9 617.2 230.2 13.1UB610610x2 125.1 612.2 229 11.9UB610610x2 113 607.6 228.2 11.1UB610610x2 101.2 602.6 227.6 10.5UB533533x2 122 544.5 211.9 12.7UB533533x2 109 539.5 210.8 11.6UB533533x2 101 536.7 210 10.8UB533533x2 92.1 533.1 209.3 10.1UB533533x2 82.2 528.3 208.8 9.6UB457457x1 98.3 467.2 192.8 11.4UB457457x1 89.3 463.4 191.9 10.5UB457457x1 82 460 191.3 9.9UB457457x1 74.3 457 190.4 9UB457457x1 67.1 453.4 189.9 8.5UB457457x1 82.1 465.8 155.3 10.5UB457457x1 74.2 462 154.4 9.6UB457457x1 67.2 458 153.8 9UB457457x1 59.8 454.6 152.9 8.1UB457457x1 52.3 449.8 152.4 7.6UB406406x1 74.2 412.8 179.5 9.5UB406406x1 67.1 409.4 178.8 8.8UB406406x1 60.1 406.4 177.9 7.9UB406406x1 54.1 402.6 177.7 7.7UB406406x1 46 403.2 142.2 6.8UB406406x1 39 398 141.8 6.4UB356356x1 67.1 363.4 173.2 9.1

UB356356x1 57 358 172.2 8.1UB356356x1 51 355 171.5 7.4UB356356x1 45 351.4 171.1 7UB356356x1 39.1 353.4 126 6.6UB356356x1 33.1 349 125.4 6UB305305x1 54 310.4 166.9 7.9UB305305x1 46.1 306.6 165.7 6.7UB305305x1 40.3 303.4 165 6UB305305x1 48.1 311 125.3 9UB305305x1 41.9 307.2 124.3 8UB305305x1 37 304.4 123.4 7.1UB305305x1 32.8 312.7 102.4 6.6UB305305x1 28.2 308.7 101.8 6UB305305x1 24.8 305.1 101.6 5.8UB254254x1 43 259.6 147.3 7.2UB254254x1 37 256 146.4 6.3UB254254x1 31.1 251.4 146.1 6UB254254x1 28.3 260.4 102.2 6.3UB254254x1 25.2 257.2 101.9 6UB254254x1 22 254 101.6 5.7UB203203x1 30 206.8 133.9 6.4UB203203x1 25.1 203.2 133.2 5.7UB203203x1 23.1 203.2 101.8 5.4UB178178x1 19 177.8 101.2 4.8UB152152x8 16 152.4 88.7 4.5UB127127x7 13 127 76 4UB1011016x 486.6 1036.1 308.5 30UB1011016x 436.9 1025.9 305.4 26.9UB1011016x 392.7 1016 303 24.4UB1011016x 349.4 1008.1 302 21.1UB1011016x 314.3 1000 300 19.1UB1011016x 272.3 990.1 300 16.5UB1011016x 248.7 980.2 300 16.5UB1011016x 222 970.3 300 16UC356356x4 633.9 474.6 424 47.6UC356356x4 551 455.6 418.5 42.1UC356356x4 467 436.6 412.2 35.8UC356356x4 393 419 407 30.6UC356356x4 339.9 406.4 403 26.6UC356356x4 287.1 393.6 399 22.6UC356356x4 235.1 381 394.8 18.4UC356356x3 201.9 374.6 374.7 16.5UC356356x3 177 368.2 372.6 14.4UC356356x3 152.9 362 370.5 12.3UC356356x3 129 355.6 368.6 10.4UC305305x3 282.9 365.3 322.2 26.8UC305305x3 240 352.5 318.4 23UC305305x3 198.1 339.9 314.5 19.1

UC305305x3 158.1 327.1 311.2 15.8UC305305x3 136.9 320.5 309.2 13.8UC305305x3 117.9 314.5 307.4 12UC305305x3 96.9 307.9 305.3 9.9UC254254x2 167.1 289.1 265.2 19.2UC254254x2 132 276.3 261.3 15.3UC254254x2 107.1 266.7 258.8 12.8UC254254x2 88.9 260.3 256.3 10.3UC254254x2 73.1 254.1 254.6 8.6UC203203x2 86.1 222.2 209.1 12.7UC203203x2 71 215.8 206.4 10UC203203x2 60 209.6 205.8 9.4UC203203x2 52 206.2 204.3 7.9UC203203x2 46.1 203.2 203.6 7.2UC152152x1 37 161.8 154.4 8UC152152x1 30 157.6 152.9 6.5UC152152x1 23 152.4 152.2 5.8

1 2 3 4 5 6 7

Calculation of Effective length factor for Columns as per BS 5950-1 Annex E

L2 = 4 m

h1 = 0 m

B2

UB457x191x82Ixx = 37051.0

h2 = 8 m

B4

No section

h3 = 10 m

18710000 / 9780

370510000 / 4400

K12

cm4

K22

[BS/EN Only Sections]Root Depth Second Moment

Flange Radius between of Areafillets Axis x-x Axis y-y

t r d Ix Iymm mm mm cm4 cm4

0 0 0 0 0 0 0 0 0

36.6 24.1 799.6 719635 4543832 24.1 799.6 625780 3915632 19.1 824.4 504187 15597

27.9 19.1 824.4 436305 1330123.9 19.1 824.4 376414 1123620.2 19.1 824.4 325254 942326.8 17.8 761.7 339704 1136021.7 17.8 761.7 279175 906618.8 17.8 761.7 246021 779925.4 16.5 686 239957 817521.6 16.5 686 205282 685017.5 16.5 686 168502 545515.5 16.5 686 150692 478823.7 15.2 615.1 170326 6630

21 15.2 615.1 150355 578419 15.2 615.1 136267 5183

16.2 15.2 615.1 117992 438331.4 16.5 540 209471 1583723.6 16.5 540 153024 1140819.7 16.5 540 125876 930822.1 12.7 547.6 111777 450519.6 12.7 547.6 98610 393217.3 12.7 547.6 87318 343414.8 12.7 547.6 75780 291521.3 12.7 476.5 76043 338818.8 12.7 476.5 66822 294317.4 12.7 476.5 61519 269215.6 12.7 476.5 55227 238913.2 12.7 476.5 47539 200719.6 10.2 407.6 45727 234717.7 10.2 407.6 41015 2089

16 10.2 407.6 37051 187114.5 10.2 407.6 33319 167112.7 10.2 407.6 29380 145218.9 10.2 407.6 36589 1185

17 10.2 407.6 32674 104715 10.2 407.6 28927 913

13.3 10.2 407.6 25500 79510.9 10.2 407.6 21369 645

16 10.2 360.4 27310 154514.3 10.2 360.4 24331 136512.8 10.2 360.4 21596 120310.9 10.2 360.4 18722 102111.2 10.2 360.4 15685 538

8.6 10.2 360.4 12508 41015.7 10.2 311.6 19463 1362

13 10.2 311.6 16038 110811.5 10.2 311.6 14136 968

9.7 10.2 311.6 12066 81110.7 10.2 311.6 10172 358

8.5 10.2 311.6 8249 28013.7 8.9 265.2 11696 106311.8 8.9 265.2 9899 89610.2 8.9 265.2 8503 764

14 8.9 265.2 9575 46112.1 8.9 265.2 8196 38910.7 8.9 265.2 7171 33610.8 7.6 275.9 6501 194

8.8 7.6 275.9 5366 1557 7.6 275.9 4455 123

12.7 7.6 219 6544 67710.9 7.6 219 5537 571

8.6 7.6 219 4413 44810 7.6 225.2 4005 179

8.4 7.6 225.2 3415 1496.8 7.6 225.2 2841 1199.6 7.6 172.4 2896 3857.8 7.6 172.4 2340 3089.3 7.6 169.4 2105 1647.9 7.6 146.8 1356 1377.7 7.6 121.8 834 89.87.6 7.6 96.6 473 55.7

54.1 30 867.9 1021420 2672149 30 867.9 909906 23447

43.9 30 868.2 807689 2049640 30 868.1 723131 18460

35.9 30 868.2 644212 1623231 30 868.1 553974 1400426 30 868.2 481306 11754

21.1 30 868.1 407961 954677 15.2 290.2 274845 98125

67.5 15.2 290.2 226938 8267158 15.2 290.2 183003 67834

49.2 15.2 290.2 146618 5536742.9 15.2 290.2 122543 4685336.5 15.2 290.2 99875 3867730.2 15.2 290.2 79085 30993

27 15.2 290.2 66261 2368823.8 15.2 290.2 57118 2052920.7 15.2 290.2 48589 1755317.5 15.2 290.2 40246 1461144.1 15.2 246.7 78872 2463537.7 15.2 246.7 64203 2031531.4 15.2 246.7 50904 16299

25 15.2 246.7 38747 1256921.7 15.2 246.7 32814 1070018.7 15.2 246.7 27672 905915.4 15.2 246.7 22249 730831.7 12.7 200.3 29998 987025.3 12.7 200.3 22529 753120.5 12.7 200.3 17510 592817.3 12.7 200.3 14268 485714.2 12.7 200.3 11407 390820.5 10.2 160.8 9449 312717.3 10.2 160.8 7618 253714.2 10.2 160.8 6125 206512.5 10.2 160.8 5259 1778

11 10.2 160.8 4568 154811.5 7.6 123.6 2210 706

9.4 7.6 123.6 1748 5606.8 7.6 123.6 1250 400

8 9 10 11 12 13 14 15 16

Radius Elastic Plasticof Gyration Modulus ModulusAxis x-x Axis y-y Axis x-x Axis y-y Axis x-xrx ry Zx Zy Sxcm cm cm3 cm3 cm3

0 0 0 0 0 0 0 0 0 0

38.2 9.59 15627 2161 1766537.8 9.46 13726 1871 15477

37 6.51 10883 1014 1257036.8 6.42 9501 871 1094236.3 6.27 8269 739 953535.7 6.07 7204 621 835134.3 6.27 7985 773 915533.6 6.06 6641 620 764033.1 5.9 5893 535 680830.9 5.71 6234 610 716730.5 5.58 5387 514 6198

30 5.4 4470 411 515629.7 5.3 4018 362 4644

28 5.53 4916 518 563127.8 5.46 4374 455 500027.6 5.39 3987 409 455827.2 5.24 3481 346 399426.3 7.23 6589 1017 748625.9 7.07 4935 743 554725.7 7 4111 611 4594

25 5.03 3622 391 414224.9 4.97 3221 343 367624.6 4.88 2874 301 328124.2 4.75 2515 256 288122.1 4.67 2793 320 319621.9 4.6 2477 279 282821.9 4.57 2292 256 261221.7 4.51 2072 228 236021.3 4.38 1800 192 205919.1 4.33 1957 243 2232

19 4.29 1770 218 201418.8 4.23 1611 196 183118.8 4.2 1458 176 165318.5 4.12 1296 153 147118.7 3.37 1571 153 181118.6 3.33 1414 136 162718.4 3.27 1263 119 145318.3 3.23 1122 104 128717.9 3.11 950 84.6 1096

17 4.04 1323 172 150116.9 3.99 1189 153 134616.8 3.97 1063 135 119916.5 3.85 930 115 105516.4 3.03 778 75.7 88815.9 2.87 629 57.8 72415.1 3.99 1071 157 1211

14.9 3.91 896 129 101014.8 3.86 796 113 89614.5 3.76 687 94.8 77514.3 2.68 576 56.8 659

14 2.58 473 44.7 54313 3.93 754 127 84613 3.9 646 108 720

12.9 3.86 560 92.6 62312.5 2.74 616 73.6 71112.4 2.7 534 62.6 61412.3 2.67 471 54.5 53912.5 2.15 416 37.9 48112.2 2.08 348 30.5 40311.9 1.97 292 24.2 34210.9 3.52 504 92 56610.8 3.48 433 78 48310.5 3.36 351 61.3 39310.5 2.22 308 34.9 35310.3 2.15 266 29.2 30610.1 2.06 224 23.5 2598.71 3.17 280 57.5 3148.56 3.1 230 46.2 2588.46 2.36 207 32.2 2347.48 2.37 153 27 1716.41 2.1 109 20.2 1235.35 1.84 74.6 14.7 84.240.6 6.57 19717 1732 2320040.4 6.49 17739 1535 2076240.2 6.4 15899 1353 1853940.3 6.44 14346 1223 1659240.1 6.37 12884 1082 14851

40 6.35 11190 934 1282639 6.09 9821 784 1135038 5.81 8409 636 9807

18.4 11 11582 4629 1423518 10.9 9962 3951 12076

17.5 10.7 8383 3291 1000217.1 10.5 6998 2721 822216.8 10.4 6031 2325 699916.5 10.3 5075 1939 581216.3 10.2 4151 1570 468716.1 9.6 3538 1264 397215.9 9.54 3103 1102 345515.8 9.49 2684 948 296515.6 9.43 2264 793 247914.8 8.27 4318 1529 510514.5 8.15 3643 1276 424714.2 8.04 2995 1037 3440

13.9 7.9 2369 808 268013.7 7.83 2048 692 229713.6 7.77 1760 589 195813.4 7.69 1445 479 159211.9 6.81 2075 744 242411.6 6.69 1631 576 186911.3 6.59 1313 458 148411.2 6.55 1096 379 122411.1 6.48 898 307 9929.28 5.34 850 299 9779.18 5.3 706 246 7998.96 5.2 584 201 6568.91 5.18 510 174 5678.82 5.13 450 152 4976.85 3.87 273 91.5 3096.76 3.83 222 73.3 2486.54 3.7 164 52.6 182

17 18 19 20 21 22 23 24 25 26

Buckling TorsionalParameterIndex

Axis y-ySy u xcm3    

0 0 0

3341 0.885 26.72890 0.883 30.11601 0.867 31.91371 0.866 36.21163 0.861 41.3

982 0.854 46.81212 0.87 35

974 0.862 41.6842 0.856 46.5959 0.869 33.2807 0.864 38.1647 0.858 45.2570 0.854 49.8811 0.872 31.8710 0.871 35.5638 0.868 38.7542 0.862 43.9

1574 0.886 21.31144 0.886 27.7

937 0.886 32.7611 0.875 30.6535 0.873 34.1469 0.87 38400 0.864 43.1500 0.877 27.6436 0.875 30.9399 0.874 33.2356 0.872 36.5300 0.864 41.6379 0.881 25.7338 0.88 28.3304 0.877 30.9272 0.877 33.9237 0.872 37.9240 0.873 27.4213 0.873 30.2187 0.869 33.6163 0.868 37.5133 0.859 43.9267 0.882 27.6237 0.88 30.5209 0.88 33.8178 0.871 38.3118 0.871 38.9

90.8 0.858 47.5243 0.886 24.4

199 0.882 28.8174 0.881 32.1147 0.874 36.8

89.1 0.871 35.270.3 0.863 42.2196 0.889 23.6166 0.891 27.1142 0.889 31116 0.873 23.3

98.4 0.872 26.585.4 0.872 29.7

60 0.866 31.648.5 0.859 37.438.8 0.846 43.4141 0.891 21.2119 0.89 24.3

94.1 0.88 29.654.8 0.874 27.5

46 0.866 31.537.3 0.856 36.488.2 0.881 21.570.9 0.877 25.649.8 0.888 22.541.6 0.888 22.631.2 0.89 19.622.6 0.895 16.32800 0.867 21.12469 0.868 23.12168 0.868 25.51941 0.872 27.91713 0.872 30.71470 0.873 351245 0.861 39.91020 0.85 45.77108 0.843 5.466058 0.841 6.055034 0.839 6.864154 0.837 7.873544 0.836 8.852949 0.835 10.22383 0.834 12.11920 0.844 13.41671 0.844 151435 0.844 171199 0.844 19.92342 0.855 7.651951 0.854 8.741581 0.854 10.2

1230 0.851 12.51053 0.851 14.2

895 0.85 16.2726 0.85 19.3

1137 0.851 8.49878 0.85 10.3697 0.848 12.4575 0.85 14.5465 0.849 17.3456 0.85 10.2374 0.853 11.9305 0.846 14.1264 0.848 15.8231 0.847 17.7140 0.848 13.3112 0.849 16

80.2 0.84 20.727 28 29