Crane Beam

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Section-Nymagasani 2-Power house-Crane beam design

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CRANE GANTRY GIRDER DESIGN (BS5950-1:2000) Crab Crane Bridge

Gantry Girder Safe Working Load, Wswl Crab weight, Wcrab

Crane bridge weight, Wcrane

Minimum hook approach, ah Span of crane bridge, L c

Elevation on Crane Bridge Bogie wheel centres, aw2

= = aw1 - aw2

Wheel centres, aw1

Bogie centres, aw1

2 Wheel End Carriage

4 Wheel End Carriage

Figure 1Gantry girder beam section details

1. CRANE & GIRDER DETAILS Crane details Self weight of crane bridge (excl. crab);

Wcrane = 58.6 kN

Self weight of crab;

Wcrab = 26.3 kN

Crane safe working load (SWL);

Wswl = 269.0 kN

Span of crane bridge;

Lc = 11250 mm

Minimum hook approach;

ah = 1000 mm 1

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Project- Nymagasani 2

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Section-Nymagasani 2-Power house-Crane beam design

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No. of wheels per end carriage;

Nw = 2

End carriage wheel centres;

aw1 = 3000 mm

Class of crane;

Q3

No. of rails resisting crane surge force;

Nr = 1

Self weight of crane rail;

wr = 0.5 kN/m

Height of crane rail;

hr = 100 mm

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Gantry girder details Span of gantry girder;

L = 4400 mm

Gantry girder section type;

Plain ‘I’ section

Gantry girder ‘I’ beam;

UB 610x305x238

Grade of steel;

S 275

2. LOADING, SHEAR FORCES & BENDING MOMENTS Unfactored self weight and crane rail UDL Beam and crane rail self weight udl;

wsw = (Massbm  gacc) + wr = 2.8 kN/m

Maximum unfactored static vertical wheel load From hook load;

Wh = W swl  (Lc - ah)/(Lc  Nw) = 122.5 kN

From crane self weight (incl. crab);

Ws = [W crane/2 + W crab  (Lc-ah)/Lc]/Nw = 26.6 kN

Total unfactored static vertical wheel load;

Wstat = Wh + W s = 149.2 kN

Maximum unfactored dynamic vertical wheel load From BS2573:Part 1:1983 - Table 4 Dynamic factor with crane stationary;

Fsta = 1.30;

Dynamic wheel load with crane stationary;

Wsta = (Fsta  W h) + W s = 185.9 kN

Dynamic factor with crane moving;

Fmov = 1.25;

Dynamic wheel load with crane moving;

W mov = Fmov  W stat = 186.4 kN

Max unfactored dynamic vertical wheel load;

Wdyn = max(W sta,W mov) = 186.4 kN

Unfactored transverse surge wheel load Number of rails resisting surge;

Nr = 1

Proportion of crab and SWL acting as surge load;

Fsur = 10 %

Unfactored transverse surge load per wheel;

Wsur = Fsur  (W crab + W swl)/(Nw  Nr) = 14.8 kN

Unfactored transverse crabbing wheel load Unfactored transverse crabbing load per wheel;

Wcra = max(Lc  W dyn/(40  aw1),W dyn/20) = 17.5 kN

Unfactored longitudinal braking load Proportion of static wheel load act’g as braking load; Fbra = 5 % Unfactored longitudinal braking load per rail;

Wbra = Fbra  W stat  Nw = 14.9 kN

Ultimate loads Loadcase 1 (1.4 Dead + 1.6 Vertical Crane) Vertical wheel load;

Wvult1 = 1.6  W dyn = 298.3 kN

Gantry girder self weight udl;

wswult = 1.4  wsw = 4.0 kN/m

Loadcase 2 (1.4 Dead + 1.4 Vertical Crane + 1.4 Horizontal Crane) Vertical wheel load;

Wvult2 = 1.4  W dyn = 261.0 kN

Gantry girder self weight udl;

wswult = 1.4  wsw = 4.0 kN/m 2

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Section-Nymagasani 2-Power house-Crane beam design

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Horizontal wheel load (surge);

Wsurult = 1.4  W sur = 20.7 kN

Horizontal wheel load (crabbing);

Wcrault = 1.4  W cra = 24.5 kN

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Maximum ultimate vertical shear force From loadcase 1;

Vv = W vult1  (2 - aw1/L) + wswult  L/2 = 402.0 kN

Ultimate horizontal shear forces (loadcase 2 only) Shear due to surge;

Vsur = W surult  (2 - aw1/L) = 27.2 kN

Shear due to crabbing;

Vcra = W crault = 24.5 kN

Maximum horizontal shear force;

Vh = max(Vsur,Vcra) = 27.2 kN

Ultimate vertical bending moments and co-existing shear forces Bending moment loadcase 1;

Mv1 = W vult1  L/4 + wswult  L2/8 = 337.7 kNm

Co-existing shear force;

Vv1 = W vult1/2 = 149.2 kN

Bending moment loadcase 2;

Mv2 = W vult2  L/4 + wswult  L2/8 = 296.7 kNm

Co-existing shear force;

Vv2 = W vult2/2 = 130.5 kN

Ultimate horizontal bending moments (loadcase 2 only) Surge moment;

Msur = W surult  L/4 = 22.7 kNm

Crabbing moment;

Mcra = W crault  L/4 = 26.9 kNm

Maximum horizontal moment;

Mh = max(Msur, Mcra) = 26.9 kNm

3. SECTION PROPERTIES Beam section properties Area;

Abm = 303.3 cm2

Second moment of area about major axis;

Ixxbm = 209471 cm4

Second moment of area about minor axis;

Iyybm = 15837 cm4

Torsion constant;

Jbm = 785.2 cm4

Section properties of top flange only Elastic modulus;

Ztf = Tbm  Bbm2/6 = 507.5 cm3

Plastic modulus;

Stf = Tbm  Bbm2/4 = 761.2 cm3

Steel design strength From BS5950-1:2000 - Table 9 Flange design strength (T = 31.4 mm);

pyf = 265 N/mm2

Web design strength (t = 18.4 mm);

pyw = 265 N/mm2

Overall design strength;

py = min(pyf,pyw) = 265 N/mm2

Section classification (cl. 3.5.2) Parameter epsilon;

= (275 N/mm2/py)1/2 = 1.019;

Flange (outstand element of comp. flange);

ratio1 = Bbm/(2  Tbm) = 4.959;

Web (neutral axis at mid-depth);

ratio2 = dbm/tbm = 29.348;

Flange classification;

Class 1 plastic

Web classification;

Class 1 plastic

Overall section classification;

Class 1 plastic

Shear buckling check (cl. 4.2.3) Ratio d upon t;

d_upon_t = dbm/tbm = 29.348; PASS - d/t <= 70 - The web is not susceptible to shear buckling 3

Project- Nymagasani 2

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Section-Nymagasani 2-Power house-Crane beam design

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4. DESIGN CHECKS Vertical shear capacity (cl. 4.2.3) Pvv = 0.6  py  tbm  Dbm = 1860.1 kN

Vertical shear capacity of beam web;

PASS - Vv <= Pvv - Vertical shear capacity adequate (UF1 = 0.216) Loadcase 1 - Vv1 <= 0.6Pvv - Beam is in low shear at position of max moment Loadcase 2 - Vv2 <= 0.6Pvv - Beam is in low shear at position of max moment Horizontal shear capacity (cl. 4.2.3) Pvh = 0.6  py  0.9  Tbm  Bbm = 1399.2 kN

Horizontal shear capacity of beam flange;

PASS - Vh <= Pvh - Horizontal shear capacity adequate (UF2 = 0.019 - low shear) Vertical bending capacity (cl. 4.2.5) Mcxz = 1.2  py  Zxxbm = 2095.4 kNm

Vertical bending capacity of beam;

Mcxs = py  Sxxbm = 1983.8 kNm Mcx = min(Mcxz,Mcxs) = 1983.8 kNm PASS - Mv1 <= Mcx - Vertical moment capacity adequate (UF3 = 0.170) Effective length for buckling moment (Table 13) Length factor for end 1;

KL1 = 1.00

Length factor for end 2;

KL2 = 1.00

Depth factor for end 1;

KD1 = 0.00

Depth factor for end 2;

KD2 = 0.00

Effective length;

Le = L  (KL1 + KL2)/2 + Dbm  (KD1 + KD2)/2 = 4400 mm

Lateral torsional buckling capacity (Annex B.2.1, 2.2 & 2.3) Slenderness ratio;

 = Le/ryybm = 60.9;

Slenderness factor;

v = 1/[1 + 0.05  (/xbm)2]0.25 = 0.918;

Section is class 1 plastic therefore;

w = 1.0

Equivalent slenderness;

LT = ubm  v    (w) = 49.5;

Robertson constant;

LT = 7.0

Limiting equivalent slenderness;

L0 = 0.4  (2  ES5950/py)0.5 = 35.0;

Perry factor;

LT = max(LT  (LT - L0)/1000,0) = 0.102;

Euler buckling stress;

pE = 2  ES5950/LT2 = 825.2 N/mm2

Factor phi;

LT = [py + (LT + 1)  pE]/2 = 587.2 N/mm2

Bending strength;

pb = pE  py/[LT + (LT2 - pE  py)0.5] = 232.1 N/mm2

Buckling resistance moment;

Mb = pb  Sxxbm = 1737.4 kNm

Equivalent uniform moment factor;

mLT = 1.0

Allowable buckling moment;

Mballow = Mb/mLT = 1737.4 kNm PASS - Mv1 <= Mballow - Buckling moment capacity adequate (UF4 = 0.194)

Horizontal bending capacity (loadcase 2 only) cl. 4.2.5 Horizontal moment capacity of top flange;

Mctf = min(py  Stf,1.2  py  Ztf) = 161.4 kNm PASS - Mh <= Mctf - Horizontal moment capacity adequate (UF5 = 0.167)

Combined vertical and horizontal bending (loadcase 2 only) Cross section capacity (cl. 4.8.3.2) Section utilisation;

UF6 = Mv2/Mcx + Mh/Mctf = 0.316; PASS - Section capacity adequate (UF6 = 0.316) 4

Project- Nymagasani 2

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Section-Nymagasani 2-Power house-Crane beam design

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Member buckling resistance (cl. 4.8.3.3.1) Uniform moment factors;

mx = 1.0 my = 1.0

Case 1;

UF7 = mx  Mv2/(py  Zxxbm) + my  Mh/(py  Ztf) = 0.370;

Case 2;

UF8 = mLT  Mv2/Mb + my  Mh/(py  Ztf) = 0.371; PASS - Buckling capacity adequate (UF7&8 = 0.371)

Check beam web bearing under concentrated wheel loads (cl. 4.5.2.1) End location Maximum ultimate wheel load;

Wvult1 = 298.3 kN

Stiff bearing length (dispersal through rail);

b1 = hr = 100 mm

Bearing capacity of unstiffened web;

Pbw = [b1 + 2  (Tbm + rbm)]  tbm  py = 954.7 kN PASS - Wvult1 <= Pbw - Web bearing capacity adequate (UF9 = 0.312);

Check beam web buckling under concentrated wheel loads (cl. 4.5.3.1) End location - top flange not effectively restrained rotationally or laterally Maximum ultimate wheel load; Wvult1 = 298.3 kN Stiff bearing length (dispersal through rail);

b1 = hr = 100 mm

Effective length of web;

LEweb = 1.2  dbm = 648 mm

Buckling capacity of unstiffened web;

Pxr = 1/225tbm/[(b1+2(Tbm+rbm))dbm]1/20.7dbm/LEwebPbw Pxr = 401.3 kN PASS - Wvult1 <= Pxr - Web buckling capacity adequate (UF10 = 0.743)

Allowable deflections Allowable vertical deflection = span/600;

vallow = L/limitv = 7.3 mm

Allowable horizontal deflection = span/500;

hallow = L/limith = 8.8 mm

Calculated vertical deflections Modulus of elasticity;

E = ES5950 = 205 kN/mm2

Due to self weight;

sw = 5  wsw  L4/(384  E  Ixxbm) = 0.0 mm

Due to wheels at position of maximum moment;

v1 = W stat  L3/(48  E  Ixxbm) = 0.6 mm

Total vertical deflection;

v = sw + v1 = 0.6 mm PASS - v <= vallow - Vertical deflection acceptable (Actual deflection = span/6783)

Calculated horizontal deflection Due to surge (wheels at position of max moment);

hs = W sur L3/(48  E  Iyybm/2) = 1.6 mm

Horizontal crabbing deflection;

hc = W cra  L3/(48  E  Iyybm/2) = 1.9 mm

Maximum horizontal deflection;

h = max(hs,hc) = 1.9 mm PASS - h <= hallow - Horizontal deflection acceptable (Actual deflection = span/2303)

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