Apollo-1.5m X-Beam-to Eurocode.pdf

Alan White Design

R0142/001

APOLLO CRADLES LTD 1.5m X-BEAM CALCULATION TO BS EN 1999-1-1 DESIGN CHECK CALCULATIONS Alan N White B.Sc., M.Eng., C.Eng., M.I.C.E., M.I.H.T. Nov 2012 Somerset House 11 Somerset Place GLASGOW G3 7JT Tel:0141 354 6579 Fax:0141 354 6549

Project : Apollo 1.5m X-Beam to EurocodeElement : BriefJob Number : R0142 By : eas Date:Nov-12Document No : 001 Checked :anw Date:Nov-12

Brief The brief is to prepare calculated values for the capacity of the Apollo 1.5m X-Beam to BS EN 1999-1-1.

The beams are manufactured from tube extrusions in aluminium alloy6082 T6.

Alloy The alloy used is 6082 T6:

fo= 255 N/mm2

fu= 295 N/mm2

Layout All beam lengths define the overall length of beam and not the span. As the

beam is supported at the verticals, all spans are 1m less than the beam length.

The geometry of the beam is shown in the drawing below:

DesignEurocode 9: Design of Aluminium structures EN 1999-1-1Alloy used is 6082 T6 throughout

STRAP ModelThe structure was analysed in STRAP structural analysis program.(3m length 1.5m X-Beam shown below, larger beams are scaled versions of below)

Main Boom Vertical

Diagonal

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Load Cases Images are shown for a 3m beam, loading for larger beams is applied using the same methodology.

Load Case 1 Self WeightSelf weight of all members factored by 1.15 to account for connections

Load Case 2 UDL10kN/m Load Applied to top boom over full length of the Ladder Beam at node points

Load Case 3 Central Point Load10kN Point Load Applied to Centre of Top Boom of the Ladder Beam

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Load Case 4 Two Point Loads 2No 10kN point loads applied at third points along the top boom of the Ladder Beam.

Load Case 5 Three Point Loads3No 10kN Point Loads applied at quarter points along the Ladder Beam

Load Case 6 End Shear10kN Point Load applied 1.0m from support

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Load Combinations

Combination Number Load Cases

1 1+22 1+33 1+44 1+55 1+6

Above Combinations were checked for the following design factors:

gD= 1.25

gL= 1.50

Combination DescriptionUDL

Central Point LoadTwo Point Loads

Three Point LoadsEnd Shear

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Project : Apollo 1.5m X-Beam to EurocodeElement : Main Boom CapacityJob Number : R0142 By : eas Date:Nov-12Document No : 001 Checked :anw Date:Nov-12

SHS boom Layout101.6x101.6x6.35 SHS

101.6mm

6.35mm 88.9mm

Section Properties A= 2419 mm2

I= 3674543 mm4

Wel= 72334 mm3

Wpl= 86800 mm3

ry= 38.9 mm

for slenderness b= b/t b= 101.6 = 16.00 t = 6.35

e= sqrt(250/fo) fo= 255N/mm2

= 0.99

for welded internal b1= 11e

= 11*0.99 = 10.89< 16.00

for welded internal b2= 16e

= 16*0.99 = 15.84< 16.00

Section is class A

Alan white design

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Project : Apollo 1.5m X-Beam to EurocodeElement : Main Boom CapacityJob Number : R0142 By : eas Date:Nov-12Document No : 001 Checked :anw Date:Nov-12 Alan white design

Boom 101.6x101.6x6.35 SHS HAZ

There are HAZ's at welded joints to the diagonal and vertical.HAZ Section at diagonal not considered as Vertical HAZ is more detrimental

Two HAZ sections considered at the vertical, one at the edge of the vertical (A-A)and one through the mid-section of the vertical (B-B).

A B Vertical Member

Main Boom

Extent of HAZ

A BPLAN VIEW OF VERTICAL TO MAIN BOOM CONNECTION

Take sections shown below as heat affected

Section A-A Section B-B

HAZ Section Properties

A-A B-BA= 1774.2 2305.0 mm2

I= 3119567.0 3465141.0 mm4

Wel= 65502.7 72758.9 mm3

Wpl= 78603.3 87310.6 mm3

ry= 41.9 38.8 mm

Use section A-A as HAZ section properties are lower.

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Boom SHS Moment Capacity (6.2.5.1)

Non-HAZ Mc,Rd = aWel fo / gM1

a = Wpl/Wel (Table 6.4)

= 1.20Wel = 72.33 cm3

fo = 255 N/mm2

gM1 = 1.1 (6.1.3)

= 1.20*72.33*255/1100Mc,Rd = 20.12 kNm

HAZ Mu,Rd = Wnet fu / gM2

Wnet = Wel haz

= 65.50 cm3

fu = 295 N/mm2

gM2 = 1.25 (6.1.3) = 65.50*295/1250

Mu,Rd = 15.46 kNm

MRd,x = 15.46 kNm lesser value of Mc,Rd / Mu,Rd

Boom SHS Shear Capacity (6.2.6)

VRd = Av fo/ √3gM1 Conservatively

Av= 2No*3.18*101.6

Av= 2*3.18*101.6

Av= 646.18 mm2

gM1= 1.1fo = 255 N/mm2

= 646.18*255/(SQRT(3)*1100)VRd = 86.48 kN

Boom SHS Axial Comp Capacity @ 1000mm (effective length of beam between restraints)

Nb,Rd = k X Aeff fo /gM1 (6.3.1.1)

Ncr = π2 EI / k2 L2 (Appendix I.3)

E = 70,000 N/mm2

I = 3,674,543 mm4

k = 0.50L = 1,000 mm

Ncr = ((PI()^2)*70000*3674543)/((0.5^2)*(1000^2))= 10,154,560.01 N

λ = √Aeff fo / Ncr (6.3.1.2)

= 0.25 Aeff = 2419 mm2

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X = 1/ Φ+√Φ2-λ2

Φ = 0.5(1+ά(λ-λo)+λ2)

ά = 0.20 Table 6.6λo= 0.10 Table 6.6Φ = 0.55

X = 0.93

k= 1-(1-(A1/A)10-l-(0.005+0.1(A1/A))l1.3(1-l)

A1= A-AHAZ(1-po,HAZ)

= 2419-645*(1-0.5)= 2,096.50 mm2

k= 0.96

Nb,Rd = 0.93*0.96*2419*255/1100= 500.65 kN

Boom SHS Axial Tension Capacity (6.2.3)

1. General yieldingNo,Rd = Ag fo /gM1

fo = 255N/mm2

Ag = 2419mm2

gM1 = 1.1 = 2419*255/1100 = 560.77 kN

2. Local failureNu,Rd = Anetfu /gM2

fu = 295N/mm2

Anet = Ahaz

= 1774.2mm2

gM1 = 1.25

= 1774.2*295/1250 = 418.71 kN

Lesser Value= 418.71 kN

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Project : Apollo 1.5m X-Beam to EurocodeElement : Vertical capacityJob Number : R0142 By : eas Date:Nov-12Document No : 001 Checked :anw Date:Nov-12

Vertical 48.3 x 4.4mm CHS

Vertical CHS Layout

Section Properties A= 607 mm2

I= 147654 mm4

Wel= 6114 mm3

Wpl= 8254 mm3

ry= 15.6 mm

for slenderness b= b/t b= 48.3 = 10.98 t = 4.4

e= sqrt(250/fo) fo= 255N/mm2

= 0.99

Class A, without welds, Internal parts b1= 11e

= 11*0.99 = 10.89< 10.98

Section is class 1

Alan white design

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Project : Apollo 1.5m X-Beam to EurocodeElement : Vertical capacityJob Number : R0142 By : eas Date:Nov-12Document No : 001 Checked :anw Date:Nov-12 Alan white design

Vertical CHS Moment Capacity (6.2.5.1)

Mc,Rd = aWel fo / gM1

a = Wpl/Wel (Table 6.4)= 1.35

Wel = 6.11 cm3

fo = 255 N/mm2

gM1 = 1.1 (6.1.3) = 1.35*6.11*255/1100

Mc,Rd = 1.91 kNm

Mu,Rd = Wnet fu / gM2

Wnet = Wel * ρu, haz

= 6.11*0.64= 3.91 cm3

fu = 295 N/mm2

gM2 = 1.25 (6.1.3) = 3.91*295/1250

Mu,Rd = 0.92 kNm

MRd,x = 0.92 kNm lesser value of Mc,Rd / Mu,Rd

Vertical CHS Shear Capacity (6.2.6)

VRd = Av fo/ √3gM1

Av= 0.6A

Av= 0.6*607

Av= 364.20 mm2

gM1= 1.1fo = 255 N/mm2

= 364.20*255/(SQRT(3)*1100)VRd = 48.74 kN

Vertical CHS Axial Comp Capacity @ 1297mm (effective length of beam)


k = ωx

ωx = ru,haz fu / gM2

fo / gM1

= (0.64*290/1.25)/(250/1.1)= 0.65

k= 0.65Ncr = π

2 EI / k2 L2 (Appendix I.3)

E = 70,000 N/mm2

I = 147,654 mm4

k = 0.50L = 1,297 mm

Ncr = ((PI()^2)*70000*147654)/((0.5^2)*(1297^2))

= 242,562.15 N

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Project : Apollo 1.5m X-Beam to EurocodeElement : Vertical capacityJob Number : R0142 By : eas Date:Nov-12Document No : 001 Checked :anw Date:Nov-12 Alan white design

λ = √Aeff fo / Ncr (6.3.1.2)

= 0.80 Aeff = 607 mm2

X = 1/ Φ+√Φ2-λ2

Φ = 0.5(1+ά(λ-λo)+λ2)

ά = 0.20 Table 6.6λo= 0.10 Table 6.6Φ = 0.89

X = 0.56

Nb,Rd = 0.65*0.56*607*255/1100= 51.22 kN

Vertical CHS Axial Tension Capacity (6.2.3)


fo = 255N/mm2

Ag = 607mm2

gM1 = 1.1 = 607*255/1100 = 140.71 kN


fu = 295N/mm2

Anet = A* ru,haz

= 607*0.64= 388.5mm2

gM1 = 1.25 = 388.5*295/1250 = 91.69 kN


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Project : Apollo 1.5m X-Beam to EurocodeElement : Diagonal capacityJob Number : R0142 By : eas Date:Nov-12Document No : 001 Checked :anw Date:Nov-12

Diagonal 50.8x50.8x4.76 SHS

50.8mm

50.8mm 41.28mm

4.76mm

A= 877 mm2

I= 289000 mm4

Wel= 11600 mm3

Wpl= 14500 mm3

ry= 18.20 mm

The diagonal has a full perimeter weld at the joint to the main boom. Therefore the entire section is affected by HAZ.

As per BS EN 1999-1-1, for HAZ wall thickness reduced by 50%

Alan white design

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Project : Apollo 1.5m X-Beam to EurocodeElement : Diagonal capacityJob Number : R0142 By : eas Date:Nov-12Document No : 001 Checked :anw Date:Nov-12 Alan white design

HAZ Section Layout46.04mm

46.04mm 2.38mm

HAZ Section Properties A= 461 mm2

I= 180555 mm4

Wel= 7108 mm3

Wpl= 8530 mm3

ry= 19.80 mm

Diagonal Axial Comp Capacity @ 732mm (effective length of beam)


k = ωx

ωx = ru,haz fu / gM2

fo / gM1

= (0.64*290/1.25)/(250/1.1)= 0.65

k= 0.65Ncr = π

2 EI / k2 L2 (Appendix I.3)

E = 70,000 N/mm2

I = 180,555 mm4

k = 0.50L = 732 mm

Ncr = ((PI()^2)*70000*180555)/((0.5^2)*(732^2))= 931,204.65 N

λ = √Aeff fo / Ncr (6.3.1.2)

= 0.49 A= 877 mm2

X = 1/ Φ+√Φ2-λ2

Φ = 0.5(1+ά(λ-λo)+λ2)

ά = 0.20 Table 6.6λo= 0.10 Table 6.6Φ = 0.66

X = 0.76

Nb,Rd = 0.65*0.76*877*255/1100= 100.43 kN

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Project : Apollo 1.5m X-Beam to EurocodeElement : Diagonal capacityJob Number : R0142 By : eas Date:Nov-12Document No : 001 Checked :anw Date:Nov-12 Alan white design

Diagonal Axial Tension Capacity (6.2.3)


fo = 255N/mm2

Ag = 877mm2

gM1 = 1.1 = 877*255/1100 = 203.30 kN


fu = 295N/mm2

Anet = Ahaz

= 461mm2

gM1 = 1.25

= 461*295/1250 = 108.80 kN


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Project : Apollo 1.5m X-Beam to EurocodeElement : 12m ResultsJob Number : R0142 By : eas Date:Nov-12Document No : 001 Checked :anw Date:Nov-12

12m 1.5m X-Beam Results

Alan white design

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Project : Apollo 1.5m X-Beam to EurocodeElement : 12m ResultsJob Number : R0142 By : eas Date:Nov-12Document No : 001 Checked :anw Date:Nov-12 Alan white design


Load Comb.1 UDL load 10kN/m applied along beam

Element Action Formula Ultimate Calculated Factor

Boom Moment Mc,Rd 15.46 2.80 5.52

Shear VRd 86.48 8.97 9.64

Tension No,Rd 418.71 54.48 7.69

Compression Nb,Rd 500.65 164.80 3.04Deflection d 120 10.34 11.61Combined (Ned/NRd)

1.3 + [(Med,x/Mrd,x)

1.7]0.6 < 1.0 1.00 2.11

Vertical Moment Mc,Rd 0.92 0.09 10.25

Shear VRd 48.74 0.13 389.96

Tension No,Rd 91.69 0.61 150.30

Compression Nb,Rd 51.22 23.15 2.21Combined (Ned/NRd)


1.7]0.6 < 1.0 1.00 1.90

Diagonal Tension No,Rd 108.80 39.61 2.75

Compression Nb,Rd 100.43 52.64 1.91

Factor 1.90

11.0m Ra Rb

Max Moment= ML2/8

so for ultimate condition W= 1.5*10

15.00 kN

apply factor from aboveWf= 15*1.90

= 28.50 kN

so maximum moment is as above Ultimate Mu= Wf*L2/8

= (28.50*11^2)/8= 431.06 kNm

and for allowable valueallowable Ma= 431.06/1.50

= 287.37 kNm

Moment values Ultimate 431.06 kNmAllowable 287.37 kNm

w w

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Load Comb. 2 Point load 10kN load applied at midspan of beam



Shear VRd 86.48 1.69 51.08

Tension No,Rd 418.71 15.50 27.01

Compression Nb,Rd 500.65 31.32 15.99Deflection d 120.00 2.90 41.38Combined (Ned/NRd)


1.7]0.6 < 1.0 1.00 10.85


Shear VRd 48.74 0.02 2867.33

Tension No,Rd 91.69 0.73 125.60



1.7]0.6 < 1.0 1.00 17.53



Factor 10.85

W 5.5m

11.00m Ra Rb

Max Moment= ML/4


= 15.00 kN


= 162.75 kN

so maximum moment is as above Ultimate Mu= Wf*L/4

= 162.75*11/4= 447.56 kNm


= 300.30 kNm


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Load Comb. 3 PL at third points 10kN load applied at each of the two third points



Shear VRd 86.48 1.79 48.40

Tension No,Rd 418.71 13.52 30.97



1.7]0.6 < 1.0 1.00 8.91


Shear VRd 48.74 0.03 1624.82

Tension No,Rd 91.69 0.83 110.47



1.7]0.6 < 1.0 1.00 9.84



Factor 8.91

3.66 W W 3.66

11.00m Ra Rb

Max Moment= ML/3


15.00 kN


= 133.65 kN


= (133.65*11)/3= 490.05 kNm


= 326.70 kNm


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Load Comb. 4 PL at quarter points10kN load applied at each of the three quarter points



Shear VRd 86.48 2.56 33.85

Tension No,Rd 418.71 21.42 19.55



1.7]0.6 < 1.0 1.00 6.36


Shear VRd 48.74 0.04 1107.83

Tension No,Rd 91.69 0.96 95.51



1.7]0.6 < 1.0 1.00 6.87



Factor 6.36

2.75 W 2.75 W 2.75 W 2.75

11.00m Ra Rb

Max Moment= ML/2


15.00 kN


= 95.40 kN


= (95.40*11/2)= 524.70 kNm


= 349.80 kNm


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Load Comb. 5 End Shear 10kN load applied at a 0.6m distance from the support



Shear VRd 86.48 1.93 44.76

Tension No,Rd 418.71 3.74 111.95

Compression Nb,Rd 500.65 11.43 43.80Deflection d 120.00 0.98 122.45Combined Axial (Ned/NRd)


1.7]0.6 < 1.0 1.00 17.51


Shear VRd 48.74 0.01 3481.76

Tension No,Rd 91.69 0.15 611.24

Compression Nb,Rd 51.22 3.91 13.10Combined Axial (Ned/NRd)


1.7]0.6 < 1.0 1.00 11.72



Factor 10.72

W 1.0m

11.00m Ra Rb

Max Shear Rb= W*10/11


15.00 kNapply factor from above

Wf= 15*10.72= 160.80 kN

so maximum shear is as above Ultimate Qu= Wf*10/11

= (160.80*10)/11= 146.18 kN

and for allowable valueallowable Qu= 146.18/1.50

= 97.45 kN

Shear values Ultimate 146.18 kNAllowable 97.45 kN

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Loadcase Ultimate AllowableNo. Moment Moment1 UDL 431.06 287.372 Point 447.56 300.303 Third 490.05 326.704 Quarter 524.70 349.80

Loadcase Ultimate AllowableNo. Shear Shear5 End Shear 146.18 97.45

Max Allowable Moment = 287.3 kNm

Max Allowable Shear = 97.4 kN

1.5m X-Beam

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From 12m 1.5m X-Beam Analysis with restraints to compression chord at 1.0m c/c

For simply supported Apollo single 1.5m X-Beam TO EUROCODE EN 1999-1

Allowable Bending Moment 287.3 kNmAllowable Shear 97.4 kN

Type of Load11 12 13 14 15 16 17 18 19 20 21 22 23

Uniformly Distributed load kN/m 17.7 16.0 13.6 11.7 10.2 9.0 8.0 7.1 6.4 5.7 5.2 4.7 4.3Total UDL kN 194.8 191.5 176.8 164.2 153.2 143.7 135.2 127.7 121.0 114.9 109.4 104.5 99.9Single point load (mid Point) kN 104.5 95.8 88.4 82.1 76.6 71.8 67.6 63.8 60.5 57.5 54.7 52.2 50.0Two point loads (third points) Each kN 78.4 71.8 66.3 61.6 57.5 53.9 50.7 47.9 45.4 43.1 41.0 39.2 37.5Three point loads ( quarter points) Each kN 52.2 47.9 44.2 41.0 38.3 35.9 33.8 31.9 30.2 28.7 27.4 26.1 25.0

24 25 26 27 28 29 30 31 32 33 34 35 36Uniformly Distributed load kN/m 4.0 3.7 3.4 3.2 2.9 2.7 2.6 2.4 2.2 2.1 2.0 1.9 1.8Total UDL kN 95.8 91.9 88.4 85.1 82.1 79.3 76.6 74.1 71.8 69.6 67.6 65.7 63.8Single point load (mid Point) kN 47.9 46.0 44.2 42.6 41.0 39.6 38.3 37.1 35.9 34.8 33.8 32.8 31.9Two point loads (third points) Each kN 35.9 34.5 33.2 31.9 30.8 29.7 28.7 27.8 26.9 26.1 25.4 24.6 23.9Three point loads ( quarter points) Each kN 23.9 23.0 22.1 21.3 20.5 19.8 19.2 18.5 18.0 17.4 16.9 16.4 16.0

Notes: 1. Above allowable loads may be increased by 1.11 for wind loading only2. This table is provided as a guide only and assume all loads are applied at nodes. All scaffolds and structures should

be checked by a qualified structural engineer. Loads indicated in italics and shaded are limited by shear.3. Maximum capacity of a point load mid way between nodes is 35kN but overall buckling of the top chord should be

checked if loads are placed other than at restrained loads. Compression chord restraint required at 1m c/c

Clear span (m)

Clear span (m)

Alan white design

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Alan white design

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Shear VRd 86.48 13.70 6.31

Tension No,Rd 418.71 131.51 3.18



1.7]0.6 < 1.0 1.00 0.99


Shear VRd 48.74 0.21 234.35

Tension No,Rd 91.69 2.34 39.18



1.7]0.6 < 1.0 1.00 1.27



Factor 0.99

17.0m Ra Rb

Max Moment= ML2/8



Wf= 15*1.00= 15.00 kN


= (15.00*17^2)/8= 541.88 kNm


= 361.25 kNm


w w

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Shear VRd 86.48 1.66 51.97

Tension No,Rd 418.71 25.59 16.36



1.7]0.6 < 1.0 1.00 7.29


Shear VRd 48.74 0.02 2565.51

Tension No,Rd 91.69 0.84 109.15



1.7]0.6 < 1.0 1.00 15.82



Factor 7.29

W 8.5m

17.00m Ra Rb

Max Moment= ML/4


= 15.00 kN


= 109.35 kN


= 109.35*17/4= 464.74 kNm


= 311.95 kNm


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Shear VRd 86.48 1.92 45.00

Tension No,Rd 418.71 22.41 18.68



1.7]0.6 < 1.0 1.00 5.91


Shear VRd 48.74 0.03 1523.27

Tension No,Rd 91.69 1.01 90.78



1.7]0.6 < 1.0 1.00 9.48



Factor 5.91

5.66m W W 5.66m

17.00m Ra Rb

Max Moment= ML/3



Wf= 15*5.91= 88.65 kN


= (88.65*17)/3= 502.35 kNm


= 334.90 kNm


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Shear VRd 86.48 2.68 32.23

Tension No,Rd 418.71 35.59 11.76



1.7]0.6 < 1.0 1.00 4.25


Shear VRd 48.74 0.05 1059.67

Tension No,Rd 91.69 1.16 79.04



1.7]0.6 < 1.0 1.00 6.72



Factor 4.25

4.25m W 4.25m W 4.25m W 4.25m

17.00m Ra Rb

Max Moment= ML/2


15.00 kN


= 63.75 kN


= (63.75*17/2)= 541.88 kNm


= 361.25 kNm


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Shear VRd 86.48 2.106 41.07

Tension No,Rd 418.71 4.45 94.09



1.7]0.6 < 1.0 1.00 14.25


Shear VRd 48.74 0.02 2867.33

Tension No,Rd 91.69 0.19 482.56



1.7]0.6 < 1.0 1.00 10.55



Factor 9.63

W 1.0m

17.00m Ra Rb




Wf= 15*9.63= 144.45 kN


= (144.45*16)/17= 135.95 kN

and for allowable valueallowable Qa= 135.95/1.50

= 90.63 kN


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1.5m X-Beam

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Allowable loads for load distributionsType of Load






Clear span (m)

Clear span (m)

Alan white design

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Alan white design

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Shear VRd 86.48 18.48 4.68

Tension No,Rd 418.71 241.38 1.73



1.7]0.6 < 1.0 1.00 0.57


Shear VRd 48.74 0.29 167.51

Tension No,Rd 91.69 4.69 19.55



1.7]0.6 < 1.0 1.00 0.97



Factor 0.57

23.0m Ra Rb

Max Moment= ML2/8



Wf= 15*0.57= 8.55 kN


= (8.55*23^2)/8= 565.37 kNm


= 376.91 kNm


w w

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Shear VRd 86.48 1.63 53.06

Tension No,Rd 418.71 36.54 11.46



1.7]0.6 < 1.0 1.00 5.32


Shear VRd 48.74 0.02 2321.17

Tension No,Rd 91.69 0.98 93.56



1.7]0.6 < 1.0 1.00 14.59



Factor 5.32

W 11.5m

23.00m Ra Rb

Max Moment= ML/4


= 15.00 kN


= 79.80 kN


= 79.80*23/4= 458.85 kNm


= 305.90 kNm


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Shear VRd 86.48 2.06 42.02

Tension No,Rd 418.71 32.47 12.90



1.7]0.6 < 1.0 1.00 4.32


Shear VRd 48.74 0.04 1392.70

Tension No,Rd 91.69 1.20 76.41



1.7]0.6 < 1.0 1.00 9.15



Factor 4.32

7.66m W W 7.66m

23.00m Ra Rb

Max Moment= ML/3



Wf= 15*4.32= 64.80 kN


= (64.80*23)/3= 496.80 kNm


= 331.20 kNm


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Shear VRd 86.48 2.83 30.61

Tension No,Rd 418.71 53.23 7.87



1.7]0.6 < 1.0 1.00 3.03


Shear VRd 48.74 0.05 1015.51

Tension No,Rd 91.69 1.43 64.12



1.7]0.6 < 1.0 1.00 6.53



Factor 3.03

5.75m W 5.75m W 5.75m W 5.75m

23.00m Ra Rb

Max Moment= ML/2



Wf= 15*3.03= 45.45 kN


= (45.45*23/2)= 522.68 kNm


= 348.45 kNm


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Shear VRd 86.48 2.255 38.35

Tension No,Rd 418.71 6.98 59.99



1.7]0.6 < 1.0 1.00 11.21


Shear VRd 48.74 0.02 2437.23

Tension No,Rd 91.69 0.25 366.74



1.7]0.6 < 1.0 1.00 9.72



Factor 8.85

W 1.0m

23.00m Ra Rb




Wf= 15*8.85= 132.75 kN


= (132.75*22)/23= 126.98 kN


= 84.65 kN


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1.5m X-Beam

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Type of Load11 12 13 14 15 16 17 18 19 20 21 22 23






Clear span (m)

Alan white design

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Alan white design

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Shear VRd 86.48 28.16 3.07

Tension No,Rd 418.71 560.02 0.75



1.7]0.6 < 1.0 1.00 0.26


Shear VRd 48.74 0.46 106.66

Tension No,Rd 91.69 11.25 8.15



1.7]0.6 < 1.0 1.00 0.66



Factor 0.26

35.0m Ra Rb

Max Moment= ML2/8



Wf= 15*0.26= 3.90 kN


= (3.90*35^2)/8= 597.19 kNm


= 398.13 kNm


w w

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Shear VRd 86.48 1.56 55.47

Tension No,Rd 418.71 61.03 6.86



1.7]0.6 < 1.0 1.00 3.27


Shear VRd 48.74 0.03 1874.79

Tension No,Rd 91.69 1.29 71.07



1.7]0.6 < 1.0 1.00 12.61



Factor 3.27

W 17.5m

35.00m Ra Rb

Max Moment= ML/4


= 15.00 kN


= 49.05 kN


= 49.05*35/4= 429.19 kNm


= 286.13 kNm


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Shear VRd 86.48 2.33 37.12

Tension No,Rd 418.71 55.19 7.59



1.7]0.6 < 1.0 1.00 2.68


Shear VRd 48.74 0.04 1249.86

Tension No,Rd 91.69 1.64 55.91



1.7]0.6 < 1.0 1.00 8.32



Factor 2.68

11.66m W W 11.66m

35.00m Ra Rb

Max Moment= ML/3



Wf= 15*2.68= 40.20 kN


= (40.20*35)/3= 469.00 kNm


= 312.67 kNm


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Shear VRd 86.48 3.11 27.83

Tension No,Rd 418.71 85.76 4.88



1.7]0.6 < 1.0 1.00 1.95


Shear VRd 48.74 0.05 919.71

Tension No,Rd 91.69 1.98 46.31



1.7]0.6 < 1.0 1.00 6.20



Factor 1.95

8.75m W 8.75m W 8.75m W 8.75m

35.00m Ra Rb

Max Moment= ML/2



Wf= 15*1.95= 29.25 kN


= (29.25*35/2)= 511.88 kNm


= 341.25 kNm


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Shear VRd 86.48 2.534 34.13

Tension No,Rd 418.71 15.13 27.67



1.7]0.6 < 1.0 1.00 7.30


Shear VRd 48.74 0.03 1949.79

Tension No,Rd 91.69 0.42 218.30



1.7]0.6 < 1.0 1.00 8.58



Factor 7.30

W 1.0m

35.00m Ra Rb




Wf= 15*7.30= 109.50 kN


= (109.50*34)/35= 106.37 kN


= 70.91 kN


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1.5m X-Beam

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Type of Load11 12 13 14 15 16 17 18 19 20 21 22 23






Clear span (m)

Alan white design

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Project : Apollo 1.5m X-Beam to EurocodeElement : Overall 1.5m X-Beam ResultsJob Number : R0142 By : eas Date:Nov-12Document No : 001 Checked :anw Date:Nov-12

Overall 1.5m X-Beam Results

Alan white design

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Overall Graded Results for Allowable Working Loads on a 1.5m X-beam

For simply supported Apollo 1.5m X-Beam with a compression chord restraint at 1m intervals

Calculation Results

12 18 24 36Allowable Moment 287.3 311.9 305.9 286.1Allowable Shear 97.4 90.6 84.6 70.9

Extrapolated Allowable loads for load distributions



Span(m)

Clear span (m)

Clear span (m)

Alan white design

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Graph Summary of Allowable Working Loads for a Ladder Beam to BS EN 1999-1-1

Alan white design

0.0

50.0

100.0

150.0

200.0

250.0

7 12 17 22 27 32 37

Load

ing

(kN

)

Length of 1.5m X- Beam (m)

1.5m X-Beam Loading Capacity to BS EN 1999-1

Total UDL

Single point load (midPoint)

Two point loads (thirdpoints)

Three point loads (quarter points)

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Apollo-1.5m X-Beam-to Eurocode.pdf

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Transcript of Apollo-1.5m X-Beam-to Eurocode.pdf