Trolley Beam Design Example

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Page: 1 Made by: PB Date: 30.03.16 Ref No: ───────────────────────────────────────────────────────────────────────

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Steel runway beam design ──────────────────────── ─┬─ ─┬─ Beam is designed in │ │ accordance with ı═Ï══════════════════════════════════Ï═© BS 2853 : 1957 │ │ È══════════════════════════════════════¥ <────────────────L─────────────────> Runway beam is suspended Beam span Effective length of beam Loading ─────── Trolley capacity Number of wheels on trolley Self-weight of trolley

L=3 m Le=3.6 m

Wcap=2 Tonnes Nowheels=4 Tsw'= 200 kg Tsw=Tsw'*9.81*1E-3 =200*9.81*1E-3 =1.962 kN W=2 Tonnes Wk=W*9.81+Tsw=2*9.81+1.962=21.58 kN

Load to be carried by trolley Applied load in kilo Newtons Hoist is hand operated. Dynamic multiplier for hoist type Dyn=1.10 Section properties ────────────────── Section size Depth of steel section Width of steel section Thickness of web Thickness of flange Root radius Inertia about major axis Inertia about minor axis Elastic modulus Radius of gyration Area of section Depth to Flange thickness Self-weight

254 x 146 x 37 Universal Beam D=256 mm B=146.4 mm t=6.3 mm T=10.9 mm r=7.6 mm Ix=5537 cm4 Iy=571 cm4 Zx=432578 mm3 ryy=34.78 mm A=47.2 cm2 D'T=D/T=256/10.9=23.49 SW=A*7.701*1E-3 =47.2*7.701*1E-3 =0.3635 kN/m

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Strength of steel BS 449 Clause 3.a.(1) ───────────────── Steel design grade (43, or 50) Grade=43 Permissible stresses from BS 2853 Maxm long'l bending stress F1max=162 N/mm2 Maxm trans bending stress F2max=223 N/mm2 Maxm shear stress Fvmax=100 N/mm2 Young's Modulus E=205 kN/mm2 Design shear force ────────────────── At the support shear force

Fve=SW*L/2+Wk*Dyn =0.3635*3/2+21.58*1.1 =24.29 kN Allowable Shear stress Pv=100 N/mm2 Actual Shear stress Fv=Fve*1000/(D*t) =24.29*1000/(256*6.3) =15.06 N/mm2 Actual shear stress does not exceed the maximum permissible ( 15.06 <= 100 ) Design moment ───────────── Max moment occurs at centre

M=SW*L^2/8+Wk*Dyn*L/4 =0.3635*3^2/8+21.58*1.1*3/4 =18.21 kNm Slenderness ratio Leff=Le*1E3/ryy=3.6*1E3/34.78=103.5 From table 1 for l/r=103.5 and D/T=23.49 Allowable long'l bending stress Pbc=9.593 Tonf/in2 Convert Pbc=Pbc*15.44 =9.593*15.44 =148.1 N/mm2 Actual long'l bending stress Fbc=M*1E6/Zx =18.21*1E6/432578 =42.11 N/mm2 Actual long'l bending stress does not exceed permissible. ( 42.11 <= 148.1 ) Cross flange bending ──────────────────── Cross flange bending due to wheels on trolley Wheel spacing along beam WS=157 mm Convert to inches W1=WS/25.4 =157/25.4 =6.181 inches Flange width in inches B1=B/25.4=146.4/25.4=5.764 inches From table 3 Factor C C=0.5414 Wheel spacing in from edge of flange Wsi=30 mm Wheel set in B'=(B-2*Wsi)/B =(146.4-2*30)/146.4 =0.5902 From table 4 Factor K1=1.428 From table 5

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Factor Transverse bending stresses when trolley remote from end

K2=0.7051 Ftr1=1.4*C*Wk*1E3*Dyn/(K1*T*T) =1.4*0.5414*21.58*1E3*1.1/(1.428 *10.9*10.9) =106.1 N/mm2

Transverse bending stresses when trolley at end of beam

Ftr2=1.4*C*Wk*1E3*Dyn/(K2*T*T) =1.4*0.5414*21.58*1E3*1.1 /(0.7051*10.9*10.9) =214.8 N/mm2 The actual trans. bending stress does not exceed the max. permissible when load is remote from the end of the beam ( 106.1 <= 223 ) The actual trans. bending stress does not exceed the max. permissible when load is near end of beam ( 214.8 <= 223 ) Combined stress check ───────────────────── Actual long'l bending stress Change back to Tonf/in2

Fbc=42.11 N/mm2 F1=Fbc/15.44 =42.11/15.44 =2.727 Tonf/in2 From BS 2853 figure 5 for F1=2.727 Tonf/in2 Allowable cross flange bending PK2=14.46 Tonf/in2 Convert to N/mm2 PK2=PK2*15.44 =14.46*15.44 =223.3 N/mm2 The interaction of the longitudinal and transverse stresses at the centre of the span is satisfactory. ( 106.1 <= 223.3 ) Check for deflection ──────────────────── Beam self-wt deflection

D1=(5*SW*L^4/384)*10^5/(E*Ix) =(5*0.3635*3^4/384)*10^5/(205*5537) =0.03377 Defln due to central point load D2=Wk*Dyn*10^5*(L^3)/(48*E*Ix) =21.58*1.1*10^5*(3^3)/(48*205*5537) =1.176 Total deflection DEL=D1+D2=0.03377+1.176=1.21 mm Limiting deflection DELlim=L*1E3/500 =3*1E3/500 =6 mm Since DEL <= DELlim ( 1.21 <= 6 ) deflection within limiting value.

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Page: 4 Made by: PB Date: 30.03.16 Ref No: ─────────────────────────────────────────────────────────────────────── DESIGN SUMMARY ─────────────Beam is suspended. Beam span is 3 m Beam effective length 3.6 m Trolley capacity 2 Te Beam S.W.L. 2 Te Hoist is hand operated Dynamic factor 1.1 Section size 254 x 146 x 37 Universal Beam Section OK for long'l and transverse bending, shear and deflection. Runway beam to be clearly marked for S.W.L. of 2 Tonnes. No355

Trolley Beam Design Example

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