Crane Beam Design

DESIGN OF 'I' CRANE BEAM Location:‐ Overhead Gantry Crane Section Type: Rolled section Span L = 5900 mm    Ley       = 5900 mm Lex     = (BC1:2008)

Diagonal Brace

0

Braced length=

mm(both ends)

5900 mm 310 N/mm2 310 FPC available

Original strength = Design strength=

(Cl 4.7.5) (Cl 3.1.1: table 9)

I Section

310 Rolled section Pyd  =

310 N/mm2

TFW=

200 tTF= 14 tW= 9 H= 450

ŷ

tBF= 14

TBW= 200 Area A= ŷ= x=

9398 mm2 224 mm 100 mm

Ixx= 32259.9 cm4 Iyy= Zxx bottom= Zxx top = Zyy = Sxx= Syy= rxx= ryy= Torsional index x=

1869.23 1440.24 1427.36 186.923 1621.49 288.546 185.274 44.5978 35.6557

cm4 cm3 cm3 cm3 cm3 cm3 mm mm

 Section height H= Top flange width=  Top flange thick= Bot. Flange width=     Bot.Flange thk=              Web thick =

1.6 315 1.5 230 19.3

Deflection δx =

34.8 mm 230 506 632 51 462

Section Classification Outstand element of compression flange (compression due to bending)

ε= 0.94186 b/T= 6.82143 < 28ε ‐ Plastic Web of I section

F c= 0 r 1=

kNm crane (without impact) kN Dead  kN crane (without impact) mm kN kNm ultimate (without impact) kNm ultimate (with kNm ultimate kN ultimate (with impact)

Compression due  to bending

(Cl 3.5.2)

0

(Cl 3.5.5)

r 2= 0.05114 d/t= 46.8889 < 80ε/(1+r1) ‐ Plastic Therefore section is PLASTIC

mm mm mm mm mm mm

kNm Dead 

Mxx  = Mxx  = V = V = Deflection δy =

Max wheel load = Mxx= Mxx= Myy= Vmax =

450 200 14 200 14 9

Cl 3.6.2.4 200 mm 0.4beff 0

Top flange eff width= 200 mm 30TЄ = 395.58 mm >ACTUAL WIDTH 0.6beff Elastic NA

y = 225 mm

200 mm

Bot. flange eff width= 200 30TЄ = 395.58 mm >ACTUAL WIDTH

beff= 510.99 mm Aeff= 9398 mm2 y= 225 mm Ixx= 40905 cm4 Iyy= 1869.2 cm4 Eff.Zx top= 1818 cm3 Eff.ZX bot= 1818 cm3 Eff.Zy= 186.92 cm3 Torsional index x= 35.656

Sxx= 2044.3 cm3 rxx= 208.63 mm ryy= 44.598 mm

to be revised

Section Capacity Check Cl 4.8.3.2

(Cl 4.2.3) Max Shear Fv = 462.1 kN Shear Capacity Pv = 706.4 kN Adequate for Shear

Fc= 0 kN Mxx= 506.24 kNm (without impact) Mxx= 632.24 kNm (with impact) Myy= 50.624 kNm Mcx= 502.662 kNm Mcy= 89.4491 kNm

(Cl 4.2.5)

Fc / Ag.Py  Mxx/ Mcx Myy/ Mcy  1 Without impact Unity ratio =  1.10783

>1

NOT OK

Unity ratio =

 >1

NOT OK

With impact 1.3585

Member buckling check Cl 4.8.3.3.1 Table 26

mx = 0.95 my = 0.95 Pcx = 2809.7 kN Pcy = 962.04 kN Pc = 962.04 kN

Fc / Pc  mxMxx / Mcx  myMyy / Mcy  1 Without impact Unity ratio =  1.49442

 >1

NOT OK

Unity ratio = 1.73255

 >1

NOT OK

With impact

Lateral Torsional buckling check Cl 4.8.3.3.1 table 18 table 26 (Annex B.2.4)

mLT=

0.8

my =

0.9

λLT   = uvλ√βw λ= Ley/Ƴyy = 132.29 Iyc= 933.33 Iyt= 933.33 η= 0.5 ψ= ‐0.0024 v= 0.8781 γ= 0.9421 u= 0.8765 λLT   = 101.82

(Annex B.2.1)

Bc= Bt=

200 mm 200 mm

Tc=

14 mm

Tt=

14 mm

hc=

219.0 mm

ht=

217.0 mm

dc=

212.0 mm

dt=

210.0 mm

hs=

436 mm

Ix= x= βw=

32260 cm4 36 1

Pb  PE Py /[LT  (LT  PE Py ) 0.5 ] 2

PE  ( 2 E /  LT ) 2

PE= 195.18

 LT  [ Py  ( LT  1) PE ] / 2 (Annex B.2.2)

 Lo  0.4( 2 E / PY ) 0.5 λLo= 32.315

αLT= 7

ηLT= 0.4865 φLT = 300.06 N/mm2 Pb = 128.21 N/mm2 Mb = 207.89 kNm

Fc / PCY  m LT M

xx

/ M b  myM

Without impact Unity Ratio= 2.4575  >1 Without impact Unity Ratio= 2.9423  >1

yy

/ M cy  1

NOT OK NOT OK

Web Buckling Check Maximum Wheel load = 230 kN dep =300mm

a =2000mm

de =800mm

With Stiffener

a =2000mm d=

12

12

422 10

Maximum Support Reaction= 462.1 kN (Cl 4.4.4.2)

Susceptibility of Shear buckling

10

a = dep =

2000 mm 300 mm

Ts1 =

12 mm

Ts2 = de =

10 mm 800 mm

Limiting d/t = 70ε = 58.395 Actual d/t = 46.889 < 70ε Shear buckling no need to check (Cl 4.4.3.2)

Check web thickness for serviceability Minimum t required = d/250 = 1.7  mm < 9mm  Web thickness is adequate for serviciability

(Cl 4.4.3.3)

Check Flange Buckling in to Web Minimum t required = (d/250) x (Pyf/345) = 1.52  mm < 9mm  Flange Buckling Satisfied

(Cl 4.4.5.2) (Annex H.1)

Shear buckling resistance qw =

2 186 N/mm

Vw = dtqw = 706.43 kN Mcx = 378.448 kNm

Fv > 0.6Vw = Web under High Shear <   Mx Revise the Section

Web Shear Buckling capacity   Vb = Vw

= 706.43 kN

> Fv No web shear Buckling

Web check between stiffeners

Compression flange not  restrained against rotation

(Cl 4.5.3.2)

2 60.56 N/mm 2 Ped= 101.55 N/mm >  fed Satisfied

fed=

Compressive Strength

(Cl 4.4.5.4)

End Anchorage Check Condition‐1

Vw = Pv

Shear capacity is the governing criteria

Vw = 706.43 kN Condition‐2

Pv  = 1339.2 kN Condition‐1 does not Apply Fv ≤  Vcr Shear buckling resistance is adequate without tension field Vcr = 460.05 kN

Condition‐2 does not Apply

End Anchorage should be provided (Annex H.4.1)

Anchor force Hq =

7.5 kN

(Annex H.4.3)

Rtf =

5.6 kN

Vw,ep =

502.2 kN

Pv,ep  =

502.2 kN

Vcr,ep =

502.2 kN

 

Vcr,ep > Rtf End post capacity is Adequate Ftf= 1.5872 kN  

(Cl4.5.2)

Web Bearing Check 15tw

15tw Design strength of stiffener= 310 N/mm2 ε= 0.9419

 bs =100mm       tw  be =6mm  bs =100mm       ts

Check the stiffener at support Thickness of stiffener ts=

12 mm

Limiting outstand 19εts= 214.74 mm Effective outstand 13εts= 146.93 Provided otstand= 100 Distance to end from stiff bearing end  be= 6 (Fx‐Pbw)≤ check stiffened web

mm mm mm Ps 2 2112 mm

As,net= Ps=

(allowance 12mm for weld)

654.72 kN

Pbw= (b1+nk)tpyw = 191.394 kN (Fx‐Pbw)= 270.706 kN The bearing capacity of stiffened web is adequate check buckling resistance

Fx≤ Px Iy= 9137166 mm4 As= 5956.32 mm2 ry= 39.1667 mm 560 mm

Le= From table 24, strut curve c

λ= 14.2979 pc = 310 N/mm2 Px = 1846.46 kN Buckling resistance of stiffener adequate

Design Summary Catogory Section Capacity Check Member buckling check Lateral Torsional buckling check Web Buckling Check Web Bearing Check Overall Capacity Deflection Check

Vertical Lateral

L/600 L/500

Limiting  Ratio 1.00 1.00 1.00 1.00 1.00 1.00 9.8 11.8

Section Fail

Ratio 1.36 1.73 2.94 0.65 0.41 2.94

‐‐‐‐‐‐‐ Section Overstressed

19.30 34.80

‐‐‐‐‐‐‐ Deflection Fail