Gantry Girder Unprotected

Page 1 of 39

JOB NO. DATE 9-Apr-2023CUSTOMER DESIGNED BY

DESCRIPTION CHECKED BY

DESIGN OF CRANE BEAM

THE DESIGN DATA ARE AS FOLLOWS

CRANE CAPACITY = 30 KNSPAN BETWEEN CRANE RAILS = 18 MWEIGHT OF CRANE = 30 KNWEIGHT OF CRAB = 10 KNMINIMUM HOOK APPROACH = 0.5 MEND CARRIAGE WHEELCENTRES = 2.5 MSPAN OFCRANE GIRDER = 15 MSELF WEIGHT OF CRANE GIRDER = 25 KN 2520GRADE OF STEEL = S275

250

MODULUS OF ELASTICITY OF STEEL Es = 205000SIZE OF WELD = 6 mmTYPE OF CRANE RAIL =DIAMETER OD CRANE WHEEL = 200 mm

(1) MAXIMUM WHEEL LOADS, MOMENTS AND SHEAR

THE CRANE LOADS ARE SHOWN IN FIG.(a).THE MAXI. STATIC WHEEL LOADS @ A;

= 30/4+((30+10)x17.5)/18x2

= 26.95 KN

THE VERTICAL WHEEL LOAD, INCLUDING IMPACT

(THE MAXI.STATIC WHEEL LOADS SHALL BE INCREASED BY 25% FOR E.O.C.)

= 1.25 x26.95

= 33.69 KN

THE HORI. SURGE LOAD TRANSMITTED BY FRICTION TO THE RAILTHROUGH FOUR WHEELS:

(THE HORI. FORCE ACTING TRANSVERSE TO THE RAILS SHALL BE TAKENAS 10% OF THE COMBINED WT. OF THE CRAB AND THE LOAD LIFTED)

= 10%(30+10)/4

= 1 KN

LOAD FACTORS:(REFER BS5950-2000; TABLE 2 PARTIALFACTORS FOR LOADS)

DEAD LOAD - SELF WEIGHT ϒf = 1.4

VERT.& HORI. CRANE LOADS CONSIDERED SEPERATELY

ϒf = 1.6

VERT.& HORI. CRANE LOADS ACTING TOGETHER

ϒf = 1.4

THE CRANE LOADS IN A POSITION TO GIVE MAXI. VERT & HORI MOMENTS & MAXI VERT SHEAR.FIG.(b)

DESIGN A SIMPLY SUPPORTED BEAM TO CARRY AN ELECTRIC OVERHEAD CRANE.

N/mm2

N/mm2

Page 2 of 39



10 KNA B

26.95 kN/wheel 300.5 17.5

18

CRANE GIRDER CENTRESFIG.( a ) CRANE LOADS

33.69 33.69

C SELF WT.= 25A B

0.625 0.6255.625 2.5 6.875

15

FIG.(b) VERTICAL LOADS - MAXIMUM MOMENT

1 1

A C B

FIG.(c) HORIZONTAL LOADS - MAXIMUM MOMENTS

33.69 33.69 SELF WT.= 25

A B2.5 12.5

FIG.(d) LOADS CAUSING MAXI. VERTICAL SHEAR

CGLoads

Page 3 of 39



THE MAXI VERT MOMENTS DUE TO DEAD LOAD & CRANE LOADS ARE CALCULATED SEPERATELY:

DEAD LOAD;

25 kN / 2

12.5 KN

Mc = (12.5 x 6.875) - (25 x 6.875 x 6.875 / (15 x 2))

Mc = 46.55 KN m.

CRANE LOAD,INCLUDING IMPACT

33.69(5.625 + 0.625 + 2.5) / 15

30.89 KN

Mc = 30.89 x 6.875

Mc = 212.37 KN m.

CRANE LOAD WITH NO IMPACT

Mc = 212.37 x 26.95 / 33.69

Mc = 169.89 KN m.

THE MAXI HORI MOMENT DUE TO CRANE SURGE;

1(5.625 + 5.625 + 2.5) / 15

0.92 KN

Mc = 0.92 x 6.875

Mc = 6.33 KN m.

THE MAXI VERTICAL SHEAR;

12.5 KN

CRANE LOADS, INCLUDING IMPACT

33.69 + 33.69 x 12.5/15

61.77 KN

THE LOAD FACTORS ARE INTRODUCED TO CALCULATE THE DESIGN MOMENTS & SHEAR FORTHE VARIOUS LOAD COMBINATIONS:

(1) VERTICAL CRANE LOADS WITH IMPACT & NO HORI. CRANE LOAD.MAXIMUM MOMENT

Mc = (1.4 x 46.55) + (1.6 x 212.37)

Mc = 404.97 KN m.

MAXIMUM SHEAR

(1.4 x 12.5) + (1.6 x 61.77)

116.34 KN

(2) HORI. CRANE LOADS & VERT.CRANE LOADS WITH NO IMPACT.

MAXIMUM HORIZONTAL MOMENT,Mc = 1.6 x 6.33

Mc = 10.13 KN m.

MAXIMUM VERTICAL MOMENTMc = (1.4 x 46.55) + (1.6 x 169.89)

RB =

RB =

RB =

RB =

RB =

RB =

DEAD LOAD RA =

RA =

RA =

FA =

FA =

Page 4 of 39


DESCRIPTION CHECKED BYMc = 337 KN m.

Page 5 of 39



(3) VERT. CRANE LOAD WITH IMPACT & HORI. CRANE LOADS ACTING TOGETHER.

MAXIMUM VERTICAL MOMENTMc = (1.4 x 46.55) + (1.4 x 212.37)

Mc = 362.49 KN m.

MAXIMUM HORIZONTAL MOMENT,Mc = 1.4 x 6.33

Mc = 8.87 KN m.

(2) BUCKLING RESISTANCE MOMENT FOR THE X-X AXIS:

THE FOLLOWING TRIAL SECTION IS SELECTED:(REFERANCE: HANDBOOK OFSTRUCTURALSTEEL WORK 3rd edi.)

I-s/c GirderCHANNEL ISMC 250

FIG.(1) CRANE BEAMSECTIONAL PROPERTIES

Girder ISMC 250

AX 95.2 38.66D mm 760 250 X XBf mm 180 80Tf mm 10 14.7Tw mm 8 7.1

Ix 77642 381680

Iy 975.16 21910

Zx 2445 2181.02

Zy 173.84 384.38Cy cmr mm 10.2

REFERING TO FIG.(2), THE EQUAL AREA AXIS X-X & CENTROIDSOF THE TENSION & COMPRESSION AREAS ARE LOCATED ANDTHE PLASTIC MODULUS CALCULATED.

(1) LOCATE EQUAL AREA AXIS: FIG.(2) CRANE BEAM PLASTIC PROPERTIES

TOTAL AREA = 13438.26

C.G. FOR COMPRESSION AREA FROM TOP; (y)

6719.13 =(250 x 7.1) + (180 x 10) + 2 x 14.7( y - 7.1) + 8( y - 10-7.1)

y = 93.31 mm from top

(2) LOCATE CENTROIDS OF COMPRESSION & TENSION AREAS

COMPRESSION AREA TENSION AREAAREA MOMENTS @ TOP AREA MOMENTS @ BOTTOM

NO. AREA y Ay NO. AREA y Ay1 1775 3.55 6301.25 1 1800 5 9000

2 1800 12.1 21780 2 5310.32 341.895 1815571.86

3 2534.574 50.205 127248.288 3 -391.314 680.445 -266267.65

4 609.68 55.205 33657.3844

SUM 6719.26 188987 SUM 6719.01 1558304

ŷ = (188986.93 / 6719.26) ŷ = (1558304.21 / 6719.01)

ŷ = 28.13 mm ŷ = 231.93 mm

cm2

cm4

cm4

cm3

cm3

mm2

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250 14.7-13.31

7.1 663.79 673.7993.31 10

180 86.21 1076.21 180

14.7 8 28.13

(3) LEVER ARM, Z = ((760 + 7.1) - 28.13 - 231.93)

Z = 507.04 mm

(4) PLASTIC MODULUS, Sx ;

Sx = 6719.26 x 507.04

Sx = 3406933.6

15000 mm

(SQRT( ( 975.16 + 381680) / (95.2 + 38.66) )

534.67 mm

28.06

FACTORS MODIFYING SLENDERNESS:

1.0

THIS IS CONSERVATIVE: THE VALUE OF 0.81 IS CALCULATED FROM THE FORMULA IN

= 381680 + 1/2 x975.16

382167.58

½ Iy (UB)

487.58

η = 382167.58 / (382167.58 + 487.58)

η = 1

mm3

THE BENDING STRENGTH, pb TAKING TORSIONAL BUCKLING INTO ACCOUNT, IS DETERMINED:

EFFECTIVE LENGTH LE = SPAN =

MINI. RADIUS OF GYRATION ry =

ry =

SLENDERNESS RATIO, λ = LE / ry =

BUCKLING PARAMETER, μ =

APPENDIX B (BS-5950-1-2000) OF THE CODE

THE SLENDERNESS FACTOR ν IS CALCULATED FROM THE FORMULAE IN APPENDIA B:

Icf = Ix (Channnel) + ½ Iy (UB)

Icf = cm4

Itf =

Itf = cm4

X X

1

2

34

COMPRESSION AREA

TENSION AREA

XX

1

2

33

Iyc

Iyc Iytffffffffffffffffffffffffff

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THE DISTANCE BETWEEN THE SHEAR CENTRES OF THE FLANGES:

7.86

767.1 hz = 754.24

b 250200.3

5

17.1CRANE BEAM AREA A

AREA A = 3425.13TK. OF TOP FLANGE T = A/b

T = 13.71D/T = 55.96

DISTANCE TO CENTROID FROM TOP NO. AREA y A.y1 1775 3.55 6301.25

2 1800 12.1 21780SUM 3575 28081.25

CENTROIDAL DIST. FROM TOP = 7.86mm

hs = DIST. FROM CENTRE OF BOTTOM FLANGE TO CENTROID OF CHANNEL WEB & UB FLANGE

hs = 754.24 mm (Appro.) -----REFER ABOVE FIG.

J = 1/3 [ (10^ 3 x 180) + (8^3 x (760- 2 x 10)) + (17.1^3 x 200.3) + ( 2 x 14.7 x 80) ]

J = 520924.76

AREA (A); = 13386

THE TORSIONALINDEX (x);

x = 0.566 x 754.24(13386 / 520924.76)^ 0.5

x = 68.433

THIS COMPARES WITH D/T = 55.96 FROM THE S/C TABLE

80 mmD = OVERALL DEPTH = 767.1 mm

TORSION CONSTANT (J) = 1/3[ ∑b.t3 + hw.tw3 ]

mm4

mm2

THEMONOSYMMETRIC INDEX ψ FOR A T-SECTION WITH LIPPED FLANGES, WHERE

DL = DEPTH OF THE LIP =

1

2

0.8 2 @1b c

1 0.5DlDffffffff

f g

x 0.566hsAJfffff

f g0.5

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ψ = 0.8 ( 2 x 1 - 1 )( 1 + 0.5 x 80/767.1)

ψ = 0.842

ν = 0.77

FOR ν η λ/x λ0.77 1 0.42 28.06

REFERANCE BS5950-1-2000

1

21.61

THE SLENDERNESS FACTOR ν

1

4 1 @b c

0.05 xfffff

d e2

2

h

j

i

k

0.5

H

LLJ

I

MMK

0.5fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff

w

lt wqwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww

lt

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TOP FLANGE THICKNESS = 17.1 mm TOTAL

158.232

THE BUCKLING RESISTANCE; Mb = 3406933.6 x 158.232

Mb = 539.09 KN M.

(3) MOMENT CAPACITY FOR THE TOP SECTION FOR THE y-y AXIS:

Mcy = 265 x 30573280

Mcy = 8101.92 KN m 80 7.110

Zyy = 30573280 mm3

x = 125 mm(4) CHECK BEAM BENDING: y= 76.16 mm

Ixx = 219294816

(1) VERTICAL MOMENT, NO HORI. MOMENT Iyy = 3821660000

Zxx = 2879396.23

Mx = 404.97 < Mb = 539.09 KN M. Zyy = 30573280

(2) VERTICAL MOMENT NO IMPACT + HORIZONTAL MOMENT

(337 / 539.09 + 10.13 / 8101.92)

0.63 < 1

(3) VERTICAL MOMENT WITH IMPACT + HORIZONTAL MOMENT:

362.49 / 539.09 + 8.87 / 8101.92

0.674 < 1

THE CRANE GIRDER IS SATISFACTORY IN BENDING

(5) SHEAR CAPACITY (see scction 4.2.3, BS-5950-1-2000)

Pv = 0.6 x 760 x 8 x 265

Pv = 966.72 KN

MAXIMUM FACTORED SHEAR = 116.34 KN

FROM TABLE 17 BENDING STRENGTH pb (N/mm2) pg.52 FOR WELDED S/C FOR py = 265 N/mm2

pb = N/mm2

mm4

mm4

mm3

mm3

x

MxMbffffffffff

Mypy Zyffffffffffffffffff

MxMbffffffffff

Mypy Zyffffffffffffffffff

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(6) WELD BETWEEN CHANNEL AND UNIVERSAL BEAM:

THE DIMENSION FOR DETERMINING THE HORIZONTAL SHEAR ARE SHOWN IN FIGURE.THE LOCATION OF THE CENTROIDAL AXIX IS TAKEN FROM THE STRUCTURAL STEELWORK HANDBOOK.

250

13.55 x = 125 mm275.3 y = 491.8 mm

261.75 Ixx = 140751.73

Iyy = 382655.16767.1

491.8

HORIZONTAL SHEAR FORCE IN EACH WELD;

(116.34 x 38.66 x 100 x 261.75)/(140751.73 x 10000 )

0.09 KN / mm

SIZE OF WELD = 6 mmIN THE SIMPLE METHOD, THE STRENGTH OF A FILLET WELDIS CALCULATED USING THE THROAT THICKNESS.

220

STRENGTH OF WELD = 0.7 x 6 x 220/ 1000 = 0.924 KN/mm

PROVIDE 6 mm CONTINIOUS FILLET (WELD STRENGTH = 0.924 KN/mm )

cm4

cm4

FOR THE 900 FILLET WELD, THE THROAT THOCKNESS IS TAKEN AS 0.7 TIMES THE SIZE OR LEG LENGTH:

STRENGTH OF WELD = 0.7 LEG LENGTH x pw / 103 KN/mm

DESIGN STRENGTH OF FILLET WELDS pw (KN/mm2) = KN/mm2

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(7) WEB BEARING AND BUCKLING:

20.2

389.87380

760 719.6

8

20.2

9.87

STIFF BEARING WEB BUCKLING

LOAD DISPERSION AT SUPPORT WITH 1:2.5 DISPERSION

WEB BEARING:

10 + 10.2 = 20.2 mm

50.5

Rx = 116.34 KN (MAXI. SUPPORT REACTION)

116.34 x 1000 / ( 8 x 265 / 1.1 ) - 50.5

9.87 mm

WEB BEARING AT SUPPORT REQUIRES A MINIMUM STIFF BEARING OF 9.87 mm

60.37

BEARING CAPACITY = 60.37 x 8 x 265 / 1000

20.2 BEARING CAPACITY = 127.99 KN

9.87 HENCE 127.99 > 116.34 SATISFACTORY

WEB BEARING

AT POINT OF CONCENTRATED LOADS (WHEEL LOADS OR REACTION) THE WEB OF THE GIRDER MUST BE CHACKED FOR LOACAL BUCKLING. THE DISPERSION LENGTH UNDER WHEEL ( THE DIAM. OF WHEEL TO BE 200 AND ASSUMING AN ANGLE OF DISPERSION OF 45 DEGREE)

BUCKLING RESISTANCE : THE BUCKLING RESISTANCE Px OF THE WEB SHOULD BE TAKEN AS;

(REFERANCE- C.4.5.3.1, BS-5950-1-2000)

Px = (200 + 0.7 x 719.6) / ( 1.4 x 719.6) x (25 x 1.0 x 8)/ (SQRT (60.37 x 719.6) x 127.99

Px = 85.79 KN

45o

MINIMUM STIFF BEARING b1 = Rx / (t pyw/1.1) - n2

n2 = 2.5 d1 d1 =

n2 =

b1 =

b1 =

2.5

1

Px e 0.7d

1.4dfffffffffffffffffffffffffffffff 25t

b1 nK` a

dqwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwfffffffffffffffffffffffffffffffffffffffffffffB Pbw

Page 12 of 39



Page 13 of 39



(8) LOCAL COMPRESSION UNDER WHEELS:

THE LENGTH IN BEARING IS SHOWN IN FIG.

TAN 45 = (65 + 17.1) / x65

x = 82.1 mm82.1 17.1

164.2

LOCAL COMPRESSION UNDER WHEEL

BEARING CAPACITY = 250 x 8 x 164.2 / 1000

BEARING CAPACITY = 328.4 KN

FACTORED CRANE WHEEL LOAD = 33.69 x 1.6

FACTORED CRANE WHEEL LOAD = 53.904 KN ----- SATISFACTORY

(9) DEFLECTION:

THE VERTICAL DEFLECTION DUE TO THE STATIC WHEEL LOAD MUST NOT EXCEED:

SPAN / 600 = 15 x 1000 / 600 = 25 mm

THE HORIZONTAL DEFLECTION DUE TO CRANE SURGE MUST NOT EXCEED:

SPAN / 500 = 15 x 1000 / 500 = 30 mmTHE VERTICAL DEFLECTION AT THE CENTRE WITH THE LOADS IN POSITION FOR MAXIMUM MOMENT IS

16.312 mm SATISFACTORY

IF THE LOADS ARE PLACED EQUIDISTANT ABOUT THE CENTRE LINE OF BEAM a = c is 6.25 m.

26.95 26.95

6.25 2.5 6.25 16.426 mm

15 SATISFACTORY

THIS GIVES THE MAXIMUM DEFLECTION

THE HORIZONTAL DEFLECTION DUE TO DUE TO THE SURGE LOADS:

1 1

6.25 2.5 6.25 0.18 mm15

SATISFACTORY

A 25 Kg/m CRANE RAIL IS USED, AND THE HEIGHT HR IS 65 mm.

RAIL

δ=

δ=

δ=

Deflection at centre PL3

48EIffffffffffffffff 3 a c

` a

Lffffffffffffffffffffffffff@

4 a3 c3b c

L3

fffffffffffffffffffffffffffffffff

H

LJ

I

MK 5wL3

384EIffffffffffffffffffff

Page 14 of 39



FATIGUE RESISTANT DESIGN

CRANE CAPACITY = 30 KNSPAN BETWEEN CRANE RAILS = 18 MWEIGHT OF CRANE = 30 KNWEIGHT OF CRAB = 10 KNMINIMUM HOOK APPROACH = 0.5 MEND CARRIAGE WHEELCENTRES = 2.5 MSPAN OFCRANE GIRDER = 15 MSELF WEIGHT OF CRANE GIRDER = 25 KNGRADE OF STEEL = S275

250 N/mm2MODULUS OF ELASTICITY OF STEEL Es = 205000 N/mm2SECTION USED FOR THE GIRDER = GirderCRANE OPERATION (days/year) = 200 days/yearHOUR PER DAY = 8 hr/dayTRIPS PER HOUR @ THIS LOAD LEVEL = 3 cycles/hourDESIGN LIFE OF BUILDING = 50 years

THE GANTRY GIRDER RECEIVES A MAXIMUM OF 80 % OF THE TOTAL LOAD AS THE REACTIVE FORCE

IT IS ASSUMED THAT THIS FORCE IS APPLIED TO THE GIRDER AS A SINGLE CONCENTRATED LOAD.

NUMBER OF STRESS CYCLES (equal number of load cycles in this case)

N = (3cycles/hour) (8hr/day) (200days/year) (50years)

N = 240000 cycles

DETAIL CATEGORY AND FATIGUE STRENGTH

THE PROVIDED BEAM CORRESPONDS TO DETAIL CATEGORY = 118(AS PER TABLE 13.3(1) OF THE IS:800-2007 CODE.)

FROM FIG.13.1 IS:800-2007; READ THE CATEGORY 118 LINE AT N = 240000 CYCLES TO FIND THATUNCORRECTED FATIGUE STRENGTH IS = 330 Mpa.

THE FATIGUE STRENGTH OF THIS DETAIL CAN ALSO BE CALCULATED USING C.13.5 OF IS:800-2007

324.69 Mpa.

1.15(FROM C.2.4.3 BS:5950-2000 )

DESIGN FATIGUE STRENGTH = 324.69 / 1.15 = 282.34 Mpa.

CALCULATION OF ACTUAL STRESS RANGE:

0

30 x 1000 x 0.8 x 15 x 1000 / 4

M = 90000000 N mm

90000000 / (2445 x 1000 )

36.81 Mpa. < fy = 250 Mpa.

WHEN NSC ≤ 5 x 106 WHEN 5 x 106 ≤ NSC ≤ 108

f f =

ASSUMING FAIL-SAFE AND POOR ACCESSIBILITY FOR DETAIL, γmft =

fmin =

f max =

ff f

fn

5 x106

N SC

ffffffffffffffffffff3

vuut

wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww

ff f

fn

5 x106

N SC


vuut


M PL4fffffffff

fmax

MZffffffff

Page 15 of 39



THUS f = 36.81 - 0 Mpa.

SINCE THE ACTUAL STRESS RANGE ( 36.81 Mpa IS LESS THAN THE DESIGN FATIGUE STRENGTH (282.34 Mpa ) FOR THIS DETAIL, THE SIZE OF GIRDER IS SAFE.

SHEAR FORCE AT SUPPORT = 30 x 1000 x 0.8 / 2 = 12000 KN

12000 / (760 x 8)

SHEAR STRESS f = 1.98 Mpa.

AS PER C.13.3.2.3 IS:800-2007

27 / 1.15 23.48 Mpa.

HENCE 1.98 Mpa < 23.48 Mpa SAFE

HENCE FATIGUE ASSESSMENT IS NOT REQUIRED AT THE SUPPORT.HOWEVER, LET US FIND OUT THE FATIGUE STRENGTH IN SHEAR OF THE DETAIL USING C13.5 IS:800-2007

SHEAR STRESS;

216.59 Mpa.

DESIGN FATIGUE STRENGTH IN SHEAR =216.59 / 1.15 = 188.3391304 >> 1.98 Mpa.

HOWEVER, THE FOLLOWING POINTS HAVE TO BE BORNE IN MIND.1. THE NUMBER OF STRESS CYCLES WILL NOT ALWAYS BE EQUAL TO THE NUMBER OF LOADCYCLES. FOR EXAMPLE, IN A CONTINUOUS BEAM OR WHEN A MULTIPLE-AXLE VEHICLETRANSVERSES A MEMBER, MORE THAN ONE STRESS CYCLE COULD OCCUR.2. SINCE THE STRESS DUE TO THE DEAD LOAD IS ALWAYS PRESENT, THE CHANGE IN STRESS INTHE MEMBER COULD BE TAKEN EQUAL TO THE CHANGE IN STRESS PRODUCED BY THE MOVING(LIVE) LOAD.3. OF COURSE, WE CAN ALSO COMPARE THE NUMBER OF CYCLES PERMITTED AT THE ACTUALSTRESS RANGE OF 36.81 Mpa

FROM TABLE; log C FOR CATEGORY 118 AND N< 5 x 10^5 = 12.25

NUMERICAL VALUES FOR FATIGUE STRENGTH CURVES

NORMAL STRESS RANGE

(m = 3) (m = 5)160 12.901 17.036 118 64140 12.751 16.786 103 57125 12.601 16.536 92 51112 12.451 16.286 83 45100 12.301 16.036 74 4090 12.151 15.786 66 3680 12.001 15.536 59 3271 11.851 15.286 52 2963 11.701 15.036 46 2656 11.551 14.786 41 2350 11.401 14.536 37 2045 11.251 14.286 33 1840 11.101 14.036 29 1636 10.951 13.786 27 14

SHEAR STRESS = SF/(d.tw) =

τf =

log C for N < 108

ffn (N/mm2) N ≤ 5 x 106 N ≥ 5 x 106 fd (N/mm2) fL (N/mm2)

f 27

mft

fffffffffff

f fn

5 x106

N SC


vuut


Page 16 of 39



FROM EQUATION

log N = 12.25 - 3 x log 36.81

log N = 7.56

HENCE; N = 36307806 cycles

SINCE THE ACTUAL NUMBER OF CYCLES IS ONLY 240000,THIS ALSO SHOWS THAT THE SIZE OF THE GIRDER IS SUFFICIENT.

log N log c @m log ff

Page 17 of 39



REFERANCES: BS 5950-1:2000 STRUCTURAL USE OF STEELWORK IN BUILDINGIS 800:2007 CODE OF PRACTICE FOR GENERAL CONSTRUCTION IN STEEL (3rd REV.)STRUCTURAL STEELWORK:DESIGN TO LIMIT STATE THEORY BY DENNIS LAM, THIEN-CHEONG ANG - 3RD EDDESIGN OF STEEL STRUCTURES (L.S.M) BY N.SUBRAMANIAN

REFERANCE IS800-2007

Page 18 of 39



Page 19 of 39



NAME STAADNAME AX D Bf Tf Tw Ixcm^2 mm mm mm mm cm^4

UB127X76X13 UB127X76X13 16.5 127 76 7.6 4 473UB152X89X16 UB152X89X16 20.3 152.4 88.7 7.7 4.5 834

UB178X102X19 UB178X102X19 24.3 177.8 101.2 7.9 4.8 1356UB254X102X22 UB254X102X22 28 254 101.6 6.8 5.7 2841UB203X102X23 UB203X102X23 29.4 203.2 101.8 9.3 5.4 2105UB305X102X25 UB305X102X25 31.6 305.1 101.6 7 5.8 4455UB203X133X25 UB203X133X25 32 203.2 133.2 7.8 5.7 2340UB254X102X25 UB254X102X25 32 257.2 101.9 8.4 6 3415UB305X102X28 UB305X102X28 35.9 308.7 101.8 8.8 6 5366UB254X102X28 UB254X102X28 36.1 260.4 102.2 10 6.3 4005UB203X133X30 UB203X133X30 38.2 206.8 133.9 9.6 6.4 2896UB254X146X31 UB254X146X31 39.7 251.4 146.1 8.6 6 4413UB305X102X33 UB305X102X33 41.8 312.7 102.4 10.8 6.6 6501UB356X127X33 UB356X127X33 42.1 349 125.4 8.5 6 8249UB254X146X37 UB254X146X37 47.2 256 146.4 10.9 6.3 5537UB305X127X37 UB305X127X37 47.2 304.4 123.4 10.7 7.1 7171UB406X140X39 UB406X140X39 49.7 398 141.8 8.6 6.4 12510UB356X127X39 UB356X127X39 49.8 353.4 126 10.7 6.6 10170UB305X165X40 UB305X165X40 51.3 303.4 165 10.2 6 8503UB305X127X42 UB305X127X42 53.4 307.2 124.3 12.1 8 8196UB254X146X43 UB254X146X43 54.8 259.6 147.3 12.7 7.2 6544UB356X171X45 UB356X171X45 57.3 351.4 171.1 9.7 7 12070UB406X140X46 UB406X140X46 58.6 403.2 142.2 11.2 6.8 15690UB305X165X46 UB305X165X46 58.7 306.6 165.7 11.8 6.7 9899UB305X127X48 UB305X127X48 61.2 311 125.3 14 9 9575UB356X171X51 UB356X171X51 64.9 355 171.5 11.5 7.4 14140UB457X152X52 UB457X152X52 66.6 449.8 152.4 10.9 7.6 21370UB305X165X54 UB305X165X54 68.8 310.4 166.9 13.7 7.9 11700UB406X178X54 UB406X178X54 69 402.6 177.7 10.9 7.7 18720UB356X171X57 UB356X171X57 72.6 358 172.2 13 8.1 16040UB457X152X60 UB457X152X60 76.2 454.6 152.9 13.3 8.1 25500UB406X178X60 UB406X178X60 76.5 406.4 177.9 12.8 7.9 21600UB356X171X67 UB356X171X67 85.5 363.4 173.2 15.7 9.1 19460UB406X178X67 UB406X178X67 85.5 409.4 178.8 14.3 8.8 24330UB457X191X67 UB457X191X67 85.5 453.4 189.9 12.7 8.5 29380UB457X152X67 UB457X152X67 85.6 458 153.8 15 9 28930UB406X178X74 UB406X178X74 94.5 412.8 179.5 16 9.5 27310UB457X152X74 UB457X152X74 94.5 462 154.4 17 9.6 32670UB457X191X74 UB457X191X74 94.6 457 190.4 14.5 9 33320UB457X191X82 UB457X191X82 104 460 191.3 16 9.9 37050UB457X152X82 UB457X152X82 105 465.8 155.3 18.9 10.5 36590UB533X210X82 UB533X210X82 105 528.3 208.8 13.2 9.6 47540UB457X191X89 UB457X191X89 114 463.4 191.9 17.7 10.5 41020UB533X210X92 UB533X210X92 117 533.1 209.3 15.6 10.1 55230UB457X191X98 UB457X191X98 125 467.2 192.8 19.6 11.4 45730

UB533X210X101 UB533X210X101 129 536.7 210 17.4 10.8 61520UB610X229X101 UB610X229X101 129 602.6 227.6 14.8 10.5 75780UB533X210X109 UB533X210X109 139 539.5 210.8 18.8 11.6 66820

UB610X229X113 UB610X229X113 144 607.6 228.2 17.3 11.1 87320UB533X210X122 UB533X210X122 155 544.5 211.9 21.3 12.7 76040UB610X229X125 UB610X229X125 159 612.2 229 19.6 11.9 98610UB686X254X125 UB686X254X125 159 677.9 253 16.2 11.7 118000UB762X267X134 UB762X267X134 171 750 264.4 15.5 12 150700UB610X229X140 UB610X229X140 178 617.2 230.2 22.1 13.1 111800UB686X254X140 UB686X254X140 178 683.5 253.7 19 12.4 136300UB762X267X147 UB762X267X147 187 754 265.2 17.5 12.8 168500UB610X305X149 UB610X305X149 190 612.4 304.8 19.7 11.8 125900UB686X254X152 UB686X254X152 194 687.5 254.5 21 13.2 150400UB686X254X170 UB686X254X170 217 692.9 255.8 23.7 14.5 170300UB762X267X173 UB762X267X173 220 762.2 266.7 21.6 14.3 205300UB838X292X176 UB838X292X176 224 834.9 291.7 18.8 14 246000UB610X305X179 UB610X305X179 228 620.2 307.1 23.6 14.1 153000UB838X292X194 UB838X292X194 247 840.7 292.4 21.7 14.7 279200UB762X267X197 UB762X267X197 251 769.8 268 25.4 15.6 240000UB914X305X201 UB914X305X201 256 903 303.3 20.2 15.1 325300

UB1016X305X222 UB1016X305X222 283 970.3 300 21.1 16 408000UBM16X305X222 UBM16X305X222 283 970.3 300 21.1 16 408000UB914X305X224 UB914X305X224 286 910.4 304.1 23.9 15.9 376400UB838X292X226 UB838X292X226 289 850.9 293.8 26.8 16.1 339700UB610X305X238 UB610X305X238 303 635.8 311.4 31.4 18.4 209500

UB1016X305X249 UB1016X305X249 317 980.2 300 26 16.5 481300UBM16X305X249 UBM16X305X249 317 980.2 300 26 16.5 481300UB914X305X253 UB914X305X253 323 918.4 305.5 27.9 17.3 436300

UB1016X305X272 UB1016X305X272 347 990.1 300 31 16.5 554000UBM16X305X272 UBM16X305X272 347 990.1 300 31 16.5 554000UB914X305X289 UB914X305X289 368 926.6 307.7 32 19.5 504200

UB1016X305X314 UB1016X305X314 400 1000 300 35.9 19.1 644200UBM16X305X314 UBM16X305X314 400 1000 300 35.9 19.1 644200UB914X419X343 UB914X419X343 437 911.8 418.5 32 19.4 625800

UB1016X305X349 UB1016X305X349 445 1008.1 302 40 21.1 723100UBM16X305X349 UBM16X305X349 445 1008.1 302 40 21.1 723100UB914X419X388 UB914X419X388 494 921 420.5 36.6 21.4 719600

UB1016X305X393 UB1016X305X393 500 1016 303 43.9 24.4 807700UBM16X305X393 UBM16X305X393 500 1016 303 43.9 24.4 807700UB1016X305X437 UB1016X305X437 557 1025.9 305.4 49 26.9 909900UBM16X305X437 UBM16X305X437 557 1025.9 305.4 49 26.9 909900UB1016X305X487 UB1016X305X487 620 1036.1 308.5 54.1 30 1021400

Girder 760x180 95.2 760 180 10 8 77642

1.74E+05 173.84UBM16X305X349

plastic modulusDe Ct Iy Zx Zy NBFmm cm cm^4 cm^3 cm^3 mm96.6 1.3 56 84 23 76

121.8 1.6 90 123 31 89146.8 1.8 137 171 42 102225.2 3.5 119 259 37 102169.4 2.2 164 234 50 102275.9 4.4 123 342 39 102172.4 2.1 308 258 71 133225.2 3.3 149 306 46 102275.9 4.2 155 403 49 102225.2 3.2 179 353 55 102172.4 2.1 385 314 88 133219 2.7 448 393 94 146

275.9 4.1 194 481 60 102311.6 4.6 280 543 70 127219 2.6 571 483 119 146

265.2 3.8 336 539 85 127360.4 5.3 410 724 91 140311.6 4.4 358 659 89 127265.2 3 764 623 142 165265.2 3.9 389 614 98 127219 2.6 677 566 141 146

311.6 4.1 811 775 147 171360.4 5 538 888 118 140265.2 3.1 896 720 166 165265.2 3.9 461 711 116 127311.6 3.9 968 896 174 171407.6 6 645 1096 133 152265.2 3.2 1063 846 196 165360.4 4.8 1021 1055 178 178311.6 4 1108 1010 199 171407.6 5.8 795 1287 163 152360.4 4.6 1203 1199 209 178311.6 4 1362 1211 243 171360.4 4.7 1365 1346 237 178407.6 5.5 1452 1471 237 191407.6 5.9 913 1453 187 152360.4 4.8 1545 1501 267 178407.6 5.9 1047 1627 213 152407.6 5.4 1671 1653 272 191407.6 5.5 1871 1831 304 191407.6 6 1185 1811 240 152476.5 6.8 2007 2059 300 210407.6 5.5 2089 2014 338 191476.5 6.6 2389 2360 356 210407.6 5.5 2347 2232 379 191476.5 6.5 2692 2612 399 210547.6 7.8 2915 2881 400 229476.5 6.6 2943 2828 436 210

547.6 7.6 3434 3281 469 229476.5 6.7 3388 3196 500 210547.6 7.5 3932 3676 535 229615.1 8.9 4383 3994 542 254686 10.3 4788 4644 570 267

547.6 7.6 4505 4142 611 229615.1 8.6 5183 4558 638 254686 10.2 5455 5156 647 267540 6.5 9308 4594 937 305

615.1 8.6 5784 5000 710 254615.1 8.7 6630 5631 811 254686 10 6850 6198 807 267

761.7 11.4 7799 6808 842 292540 6.7 11410 5547 1144 305

761.7 11.1 9066 7640 974 292686 9.9 8175 7167 959 267

824.4 12.5 9423 8351 982 305868.1 13.8 9546 9807 1020 305868.1 13.8 9546 9807 1020 305824.4 12.1 11240 9535 1163 305761.7 10.8 11360 9155 1212 292540 7.1 15840 7486 1574 305

868.2 13.2 11750 11350 1245 305868.2 13.2 11750 11350 1245 305824.4 12 13300 10940 1371 305868.1 12.5 14000 12830 1470 305868.1 12.5 14000 12830 1470 305824.4 12.2 15600 12570 1601 305868.2 12.9 16230 14850 1713 305868.2 12.9 16230 14850 1713 305799.6 10.2 39160 15480 2890 419868.1 13.1 18460 16590 1941 305868.1 13.1 18460 16590 1941 305799.6 10.3 45440 17670 3341 419868.2 13.8 20500 18540 2168 305868.2 13.8 20500 18540 2168 305867.9 14 23450 20760 2469 305867.9 14 23450 20760 2469 305867.9 14.4 26720 23200 2800 305

975.16 2445 173.84

NAME STAADNAME AX D Bf Tf Tw Ixcm^2 mm mm mm mm cm^4

CH76X38 CH76X38 8.53 76.2 38.1 6.8 5.1 74.1CH100X50X10 CH100X50X10 13 100 50 8.5 5 208CH102X51 CH102X51 13.28 101.6 50.8 7.6 6.1 207.7CH125X65X15 CH125X65X15 18.8 125 65 9.5 5.5 483CH127X64 CH127X64 19 127 63.5 9.2 6.4 482CH152X76 CH152X76 22.8 152.4 76.2 9 6.4 852CH150X75X18 CH150X75X18 22.8 150 75 10 5.5 861CH180X75X20 CH180X75X20 25.9 180 75 10.5 6 1370CH178X76 CH178X76 26.6 177.8 76.2 10.3 6.6 1338CH200X75X23 CH200X75X23 29.9 200 75 12.5 6 1963CH203X76 CH203X76 30.4 203.2 76.2 11.2 7.1 1955CH152X89 CH152X89 30.4 152.4 88.9 11.6 7.1 1168CH150X90X24 CH150X90X24 30.4 150 90 12 6.5 1162CH230X75X26 CH230X75X26 32.7 230 75 12.5 6.5 2748CH180X90X26 CH180X90X26 33.2 180 90 12.5 6.5 1817CH229X76 CH229X76 33.2 228.6 76.2 11.2 7.6 2615CH178X89 CH178X89 34.1 177.8 88.9 12.3 7.6 1753CH260X75X28 CH260X75X28 35.1 260 75 12 7 3619CH254X76 CH254X76 35.9 254 76.2 10.9 8.1 3355CH200X90X30 CH200X90X30 37.9 200 90 14 7 2523CH203X89 CH203X89 37.9 203.2 88.9 12.9 8.1 2492CH230X90X32 CH230X90X32 41 230 90 14 7.5 3518CH229X89 CH229X89 41.6 228.6 88.9 13.3 8.6 3383CH260X90X35 CH260X90X35 44.4 260 90 14 8 4728CH254X89 CH254X89 45.4 254 88.9 13.6 9.1 4445CH300X90X41 CH300X90X41 52.7 300 90 15.5 9 7218CH305X89 CH305X89 53.3 304.8 88.9 13.7 10.2 7078CH300X100X46 CH300X100X46 58 300 100 16.5 9 8229CH305X102 CH305X102 58.9 304.8 101.6 14.8 10.2 8208CH380X100X54 CH380X100X54 68.7 380 100 17.5 9.5 15030CH381X102 CH381X102 70.1 381 101.6 16.3 10.4 14870CH430X100X64 CH430X100X64 82.1 430 100 19 11 21940ISMC 250 250x125 38.66 250 80 14.7 7.1 381680

plastic modulusIy Cy De Zx Zy

cm^4 cm mm cm^3 cm^310.7 1.2 45.8 23.4 7.832.3 1.7 65 48.9 17.529.1 1.5 65.7 48.8 15.780 2.3 82 89.9 33.2

67.2 1.9 84 89.4 29.3114 2.2 105.9 130 41.2131 2.6 106 132 47.2146 2.4 135 176 51.8134 2.2 128.8 176 48.1170 2.5 151 227 60.6152 2.1 152.5 226 53.5216 2.9 97 178 68.3253 3.3 102 179 76.9181 2.3 181 278 63.2277 3.2 131 232 83.5159 2 178 271 54.5241 2.8 121 230 75.4185 2.1 212 328 62162 1.9 203.8 316 53.9314 3.1 148 291 94.5265 2.7 145.2 287 81.7334 2.9 178 355 98.9285 2.5 169.8 348 86.3353 2.7 208 425 102302 2.4 194.7 414 89.6404 2.6 245 568 114326 2.2 245.4 559 92.9568 3.1 237 641 148499 2.7 239.2 638 128643 2.8 315 933 161579 2.5 312.4 931 144722 2.6 362 1222 176

21910 2181.02 384.38

Table 17 — Bending strength pb (N/mm2) for welded sections (BS 5950-1:2000)

λlt S 275 S 355 S 460235 245 255 265 275 315 325 335 345 355 400 410 430 440

25 235 245 255 265 275 315 325 335 345 355 400 410 430 44030 235 245 255 265 275 315 325 335 345 355 390 397 412 41935 235 245 255 265 272 300 307 314 321 328 358 365 378 38540 224 231 237 244 250 276 282 288 295 301 328 334 346 35245 206 212 218 224 230 253 259 265 270 276 300 306 316 32150 190 196 201 207 212 233 238 243 248 253 275 279 288 29355 175 180 185 190 195 214 219 223 227 232 251 255 263 26960 162 167 171 176 180 197 201 205 209 212 237 242 253 25865 150 154 158 162 166 183 188 194 199 204 227 232 242 24770 139 142 146 150 155 177 182 187 192 196 217 222 230 23475 130 135 140 145 151 170 175 179 184 188 207 210 218 22180 126 131 136 141 146 163 168 172 176 179 196 199 205 20885 122 127 131 136 140 156 160 164 167 171 185 187 190 19290 118 123 127 131 135 149 152 156 159 162 170 172 175 17695 114 118 122 125 129 142 144 146 148 150 157 158 161 162

100 110 113 117 120 123 132 134 136 137 139 145 146 148 149105 106 109 112 115 117 123 125 126 128 129 134 135 137 138110 101 104 106 107 109 115 116 117 119 120 124 125 127 128115 96 97 99 101 102 107 108 109 110 111 115 116 118 118120 90 91 93 94 96 100 101 102 103 104 107 108 109 110125 85 86 87 89 90 94 95 96 96 97 100 101 102 103130 80 81 82 83 84 88 89 90 90 91 94 94 95 96135 75 76 77 78 79 83 83 84 85 85 88 88 89 90140 71 72 73 74 75 78 78 79 80 80 82 83 84 84145 67 68 69 70 71 73 74 74 75 75 77 78 79 79150 64 64 65 66 67 69 70 70 71 71 73 73 74 74155 60 61 62 62 63 65 66 66 67 67 69 69 70 70160 57 58 59 59 60 62 62 63 63 63 65 65 66 66165 54 55 56 56 57 59 59 59 60 60 61 62 62 62170 52 52 53 53 54 56 56 56 57 57 58 58 59 59175 49 50 50 51 51 53 53 53 54 54 55 55 56 56180 47 47 48 48 49 50 51 51 51 51 52 53 53 53185 45 45 46 46 46 48 48 48 49 49 50 50 50 51190 43 43 44 44 44 46 46 46 46 47 48 48 48 48195 41 41 42 42 42 43 44 44 44 44 45 45 46 46200 39 39 40 40 40 42 42 42 42 42 43 43 44 44210 36 36 37 37 37 38 38 38 39 39 39 40 40 40220 33 33 34 34 34 35 35 35 35 36 36 36 37 37230 31 31 31 31 31 32 32 33 33 33 33 33 34 34240 28 29 29 29 29 30 30 30 30 30 31 31 31 31250 26 27 27 27 27 28 28 28 28 28 29 29 29 29L0 37.1 36.3 35.6 35 34.3 32.1 31.6 31.1 30.6 30.2 28.4 28.1 27.4 27.1

Steel grade and design strength py (N/mm2)

Table 17 — Bending strength pb (N/mm2) for welded sections (BS 5950-1:2000)

S 4604604604343983643323022812692562422282141951791641511401291201111049790858075716763605654514846444037343129

26.5

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