APOLLO SCAFFOLDING SERVICES LTD SPIGOT CONNECTION TO EUROCODES DESIGN CHECK CALCULATIONS

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1 Alan White Design APOLLO SCAFFOLDING SERVICES LTD SPIGOT CONNECTION TO EUROCODES DESIGN CHECK CALCULATIONS Alan N White B.Sc., M.Eng., C.Eng., M.I.C.E., M.I.H.T. JUL 2013 Somerset House 11 Somerset Place GLASGOW G3 7JT Tel: Fax: S0140/001

2 Brief Project : Apollo beams - Spigot connection Element : Brief Document No : 001 Checked :anw Date: Jul 13 To check the capacity of the spigot for connecting booms of Apollo aluminium truss beams. Three beams will be examined as below: Alan white design 300mm ladder beam 450 lattice beam 750 X-beam Page 1of 11

3 Design Project : Element : Apollo beams - Spigot connection Brief Document No : 001 Checked :anw Date: Jul 13 Alan white design Design of Steel Structures EN Design of Aluminium Structures EN The following AWD documents are referenced: Apollo alloy lattice beam calc S Apollo alloy ladder beam calc R Apollo alloy X-beam calc R Design assumptions Steelwork yield strength for CHS members is 355N/mm 2 Analysis Aluminium yield strength for Solid bar is 255N/mm 2 All bolts M12 Grade 8.8 Note the steel design factor of safety is 1.5 for live loads From the calculations for the ladder beam R The capacities of the boom are: Moment Shear Tension Compression 0.92 knm knm kn kn From the calulations for the lattice beam S : Moment Shear Tension Compression 0.92 knm knm kn kn From the calculations for the X-beam R : Moment Shear Tension Compression 1.04 knm knm kn kn Page 2of 11

4 Project : Element : Apollo beams - Spigot connection Brief Document No : 001 Checked :anw Date: Jul 13 Alan white design Design capacities From above the spigots require to have the following capacities Moment Shear Tension Compression 1.04 knm knm kn kn Page 3of 11

5 Project : Apollo beams - Spigot connection Element : Steel Spigot Capacity Document No : 001 Checked :anw Date: Jul 13 Alan white design Steel Spigot Section 38.1 x 4.06 CHS S355 Steel Spigot Section A= 434 mm 2 I= mm 4 W el,x = 3348 mm 3 W pl,x = 4520 mm 3 r y = 12 mm Applied Loads Steel Spigot Bending moment Steel Spigot Shear Moment M Rd,x = 1.04 knm Shear V Rd = kn Tension N u,rd = kn Compression N b,rd = kn M cr,x = W p,l.f y /g m0 W pl,x = 4.52 cm 3 f y = 355 N/mm 2 g m0 = 1.00 = 4.52*355/1000 = 1.60 knm > 1.04 knm ok V cr = A v.f y /sqrt(3)/g m0 A v = 0.6A A v = 260 mm 2 f y = 355 N/mm 2 g m0 = 1.00 = 260*355/sqrt(3)/1000 = kn > kn ok Page 4of 11

6 λ - = Af y /N cr A= 434 mm 2 Calculation sheet Project : Element : Apollo beams - Spigot connection Steel Spigot Capacity Document No : 001 Checked :anw Date: Jul 13 Alan white design Steel Spigot Tension plastic resistance N plr = A.f y /g m0 A e = A-A (2 bolt holes) = *355/1000 = kn A e = 434-2*13*4.06 A e = mm 2 f y = 355 N/mm 2 g m0 = 1.00 ultimate resistance N ur = 0.9A.f u /g m2 0.9A= 296 mm 2 = 296*510/1250 = kn f u = 510 N/mm 2 g m2 = 1.25 Steel Spigot Compression Lesser Value= kn > kn ok. N b,rd = Χ A f y /g m2 Χ= 1/ϕ+ ϕ 2 -λ -2 ϕ= 0.5(1+α(λ )+λ -2 λ - = A.f y /N cr α= 0.21 Table 6.1 N cr = π 2 EI/L 2 E= N/mm 2 = pi()^2*210000*63781/(220^2) = 2,731, N I= mm 4 L= 220 mm = 0.24 ϕ= 0.5(1+α(λ )+λ -2 ) = 0.53 f y = 355 N/mm 2 α= 0.21 Table 6.1 Χ= 1/ϕ+ ϕ 2 -λ -2 = 0.99 N b,rd = Χ A f y /g m0 N b,rd = kn > kn ok Page 5of 11

7 F b,rd = k 1 α b f u d t / g M2 d o = 13 mm F b,rd = k 1 α b f u d t / g M2 d o = 13 mm Calculation sheet Bearing in spigot Project : Element : Apollo beams - Spigot connection Steel Spigot Capacity Document No : 001 Checked :anw Date: Jul 13 Alan white design Bolts are M12 grade 8.8 F b,rd = (2.5*1.00*510*12*4.06)/1250 = kn e 1 = e 2 = k 1 = 6.92 >2.5 therefore k 1 = 2.5 t= 4.06 mm d= 12 mm f u = 510 N/mm 2 f ub = 800 N/mm 2 g M2 = 1.25 α b = 1.03 >1 Therefore, α b = 1.00 Load transferred via 2No Bolts with 2No holes leading to 4No Bearing surfaces Total Bearing capacity= 4*49.69 F b,rd = kn > kn ok Bearing in boom Bolts are M12 grade 8.8 F b,rd = (2.5*1*295*12*4.4)/1250 = kn e 1 = e 2 = k 1 = 6.92 >2.5 therefore k 1 = 2.5 t= 4.4 mm d= 12 mm f u = 295 N/mm 2 f ub = 800 N/mm 2 g M2 = 1.25 α b = 1.03 >1 Therefore, α b = 1.00 Load transferred via 2No Bolts with 2No holes leading to 4No Bearing surfaces Total Bearing capacity= 4*31.15 F b,rd = kn > kn ok Page 6of 11

8 Project : Apollo beams - Spigot connection Element : Aluminium Spigot Capacity Document No : 001 Checked : anw Date: Jul 13 Alan white design Aluminium Spigot Section 38.1 mm CHS The section of the aluminium spigot is a solid bar with 2 holes through each end to match the holes in the end of the booms. Aluminium Spigot Section A= 11 2 I= mm 4 W el,x = 5430 mm 3 W pl,x = 9230 mm 3 r y = 10 mm Applied Loads Moment M Rd,x = 1.04 knm Shear V Rd = kn Tension N u,rd = kn Compression N b,rd = kn Aluminium Spigot Moment Capacity ( ) M c,rd = aw el f o / g M1 a = W pl/w el (Table 6.4) = 1.70 W el = 5.43 cm 3 f o = 255 N/mm 2 g M1 = 1.10 (6.1.3) = 1.70*5.43*255/1100 M c,rd = 2.14 knm > 1.0 knm ok Aluminium Spigot Shear Capacity (6.2.6) V Rd = A v f o / 3g M1 = 912*255/(SQRT(3)*1100) V Rd = kn > 48.7 kn A v = 0.8A e = 912 mm 2 g M1 = 1.10 f o = 255 N/mm 2 Page 7of 11

9 General yielding N o,rd = A g f o /g M1 f o = 255 N/mm 2 Calculation sheet Project : Element : Apollo beams - Spigot connection Aluminium Spigot Capacity Document No : 001 Checked : anw Date: Jul 13 Alan white design Aluminium Spigot Axial Tension Capacity (6.2.3) Local failure = 1140*255/1100 = kn A g = 11 2 g M1 = 1.1 N u,rd = 0.9 A net f u /g M2 f u = 295 N/mm 2 = 0.9*644.7*295/1250 = kn A net = A-A (1 Bolt Hole) = mm 2 g M1 = 1.25 Lesser Value= kn > 91.7 kn Aluminium Spigot Compression Capacity N b,rd = k X A eff f o /g M1 k= ω x ω x = r u,haz f u / g M2 f o / g M1 = (0.64*290/1.25)/(250/1.1) = 0.65 k= 0.65 N cr = π 2 EI / k 2 L 2 E = 70,000 N/mm 2 I = 103,435 mm 4 k= 0.50 L = 220 mm N cr = ((PI()^2)*70000*103435)/((0.5^2)*(220^2)) = 5,905, N λ = A eff f o / N cr ( ) A= 1,1 2 = 0.22 X = 1/ Φ+ Φ 2 -λ 2 Φ = 0.5(1+ά(λ-λ o )+λ 2 ) X = 0.94 ά = 0.20 Table 6.6 λ o = 0.10 Table 6.6 Φ = 0.54 N b,rd = 0.65*0.94*1140*255/1100 = kn > kn Page 8of 11

10 F b,rd = k 1 α b f u d t/g M2 d o = 13 mm F b,rd = k 1 α b f u d t/g M2 d o = 13 mm Calculation sheet Bearing in spigot Project : Element : Apollo beams - Spigot connection Aluminium Spigot Capacity Document No : 001 Checked : anw Date: Jul 13 Alan white design Bolts are M12 grade 8.8 e 1 = e 2 = k 1 = 6.92 >2.5 therefore k 1 = 2.5 t= 38.1 mm d= 12 mm f u = 295 N/mm 2 f ub = 800 N/mm 2 g M2 = 1.25 α b = 1.03 >1 Therefore, α b = 1.00 F b,rd = (2.5*1.00*295*12*38.1)/1250 = kn > kn ok Bearing in boom Bolts are M12 grade 8.8 F b,rd = (2.5*1.00*295*12*4.4)/1250 = kn e 1 = e 2 = k 1 = 6.92 >2.5 therefore k 1 = 2.5 t= 4.4 mm d= 12 mm f u = 295 N/mm 2 f ub = 800 N/mm 2 g M2 = 1.25 α b = 1.03 >1 Therefore, α b = 1.00 Load transferred via 2No Bolts with 2No holes leading to 4No Bearing surfaces Total Bearing capacity= 4*31.15 F b,rd = kn > kn ok Page 9of 11

11 Results Project : Apollo beams - Spigot connection Element : Summary Document No : 001 Checked : anw Date: Jul 13 Alan white design Action Formula Ultimate Calculated Factor Steel Spigot Capacity Moment M Rd,x Shear V Rd Tension N u,rd Compression N b,rd Bearing - Spigot F b,rd Bearing - Boom F b,rd Alu Spigot Capacity Moment M Rd,x Shear V Rd Tension N u,rd Compression N b,rd Bearing - Spigot F b,rd Bearing - Boom F b,rd Page 10of 11

12 Project : Apollo beams - Spigot connection Element : Summary Document No : 001 Checked : anw Date: Jul 13 Alan white design Summary The required capacities for the three different beams listed below were extracted from their design calculations and the capacities of spigots made from two different materials were compared. The beams were Apollo alloy ladder beam Apollo alloy lattice beam Apollo alloy X-beam The spigots that were checked were: Steel Aluminium 38.1mm diameter 4.06mm seamless tube to Grade S diameter solid bar made from 6082T6 aluminium alloy The calculations showed that both of these spigots have the required capacities and are suitable for use in these beams. Page 11of 11

APOLLO SALES LTD PUBLIC ACCESS SCAFFOLD STEP DESIGN CHECK CALCULATIONS

Alan White Design APOLLO SALES LTD PUBLIC ACCESS SCAFFOLD STEP DESIGN CHECK CALCULATIONS Alan N White B.Sc., M.Eng., C.Eng., M.I.C.E., M.I.H.T. Feb 2014 Somerset House 11 Somerset Place GLASGOW G3 7JT