v0095-001c apollo scaffold services ltd 1.3m x-beam …
TRANSCRIPT
AWD016-01 Rev 1 By EMcG 16-01-2016
V0095-001C APOLLO SCAFFOLD SERVICES LTD 1.3M X-BEAM DESIGN CHECK CALCULATIONS
Alan N White B.Sc., M.Eng., C.Eng., M.I.C.E., M.I.H.T.
Malachy Ryan B.Eng, M.Sc., C.Eng., M.I.C.E.
NOV 2017
17-19 Hill Street Kilmarnock KA3 1HA Tel:01563 594 621 Fax:01563 593 056
AWD016-01 Rev 1 By EMcG 16-01-2016
Document Revision History
Revision Description Author Revision Date Checked A Initial Issue MRB 11/02/16 MMR
B Revised Issue MRB 08/09/16 MMR
C Checker Comments corrections. MO 14/11/17 MMR
DESIGN REPORT
TABLE OF CONTENTS
TABLE OF CONTENTS ................................................................................................ 1
INTRODUCTION ........................................................................................................... 2
EXECUTIVE SUMMARY ............................................................................................... 2
DESIGN PHILOSOPHY ................................................................................................ 2
ANALYSIS ..................................................................................................................... 3
CONCLUSIONS ............................................................................................................ 3
CALCULATIONS������������������������������4
V0095-001C - Apollo 1.30m X- Beam Page 2
INTRODUCTION
Alan White Design Ltd has been commissioned by APOLLO SCAFFOLD SERVICES Ltd as consultants to provide design and detailed calculations to allow the safe use and manufacture of the Aluminium X-beam as per BS EN 1999-1-1. The report investigates various lengths of X-Beams under various loading conditions from which the minimum values are then used to extrapolate an easy to read graph and table for allowable working loads for the various loading methods. This report is intended to provide the information necessary for scrutinising verification authorities to discern the relevant structural engineering aspects for this aluminium structure. This report provides the details of the loading methods and structural capacity of all members and their performance in the structure. The results for each loading method for a 9m, 12m, 15m, 18m and 24m X-beams are given and summarised. The overall recommended allowable values are then tabulated.
EXECUTIVE SUMMARY
The X-Beams can be used in a variety of methods and a variety of locations and it is the responsibility of the contractor to ensure that the recommended results from this report are a suitable assumption for their usage of the system, all based upon restraint to top & bottom booms at 1.0m c/c.
DESIGN PHILOSOPHY
The X-Beam is made up a top and bottom boom both using Alu scaffold tubes, with Alu scaffold tubes verticals at 1m spacing�s. These vertical are then braced using Alu rectangular hollow sections in a 500mm wide X shape, with two of these brace systems between each vertical.
V0095-001C - Apollo 1.30m X- Beam Page 3
ANALYSIS
Detailed structural analysis has been completed using STRAP structural analysis software. This model was subjected to the worst possible loading conditions to determine the structures expected maximum stresses. This model has been used to identify the member forces and deflections in the structure. Hand calculations have been incorporated to check element capacities and the maximum stresses were compared to the allowable stresses to verify the safety of the structure.
CONCLUSIONS
The recommended allowable loadings for the X-Beam according to BS EN 1999-1 are contained at the end of the report.
V0095-001C - Apollo 1.30m X- Beam Page 4
CALCULATIONS
Project : Apollo 1.3m X-beamElement : BriefJob Number : V0095 By : mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Brief The brief is to prepare calculated values for the capacity of the Apollo 1300mm deep X-Beam with horizontal restraints every 1.0m 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= 250 N/mm2
fu= 290 N/mm2
Layout 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
Design Assumptions
6082 T6 Aluminium is to be utilised throughout.
X-beam top and bottom booms are to be restrained at 1.00m c/c's/
All loads are to be applied at node locations.
48.3
Page 5
Project : Apollo 1.3m X-beamElement : BriefJob Number : V0095 By : mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
STRAP ModelThe structure was analysed in STRAP structural analysis program.(9m X-Beam shown below, larger spans are modules of below)
Top Boom Alu Scaffold Tube Diagonal RHS Vertical CHSø48.3mm x 4.4mm 50 x 19 x 3.5mm oval ø48.3mm x 4.4mm
Bottom Boom Alu Scaffold Tubeø48.3mm x 4.4mm
Load Cases Images are shown of the 3m beam, loading for larger spans is applied using the same methodology.
Load Case 1 Self WeightSelf weight of all members factored by 1.15 to account for all connections
Load Case 2 UDL10kN/m Load Applied to top boom over full length of the X-Beam at node points
Page 6
Project : Apollo 1.3m X-beamElement : BriefJob Number : V0095 By : mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Case 3 Central Point Load10kN Point Load Applied to Centre of Top Boom of the X-Beam
Load Case 4 Two Point Loads 2No 10kN point loads applied at third points along the top boom of the X-Beam.
Load Case 5 Three Point Loads3No 10kN Point Loads applied at quarter points along the X-Beam
Load Case 6 End Shear10kN Point Load applied 1m from support
Page 7
Project : Apollo 1.3m X-beamElement : BriefJob Number : V0095 By : mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
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= 1.35
gL= 1.50
Combination Description
UDLCentral Point LoadTwo Point Loads
Three Point LoadsEnd Shear
Page 8
Project : Apollo 1.3m X-beamElement : Main Boom CapacityJob Number : V0095 By : mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Main Boom Capacityø48.3mm x 4.4mm CHS 6082-T6
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 mm = 10.98 t = 4.4 mm
e= sqrt(250/fo) fo= 250 N/mm2
= 1.00
Class A, without welds, Internal parts b1= 11e
= 11*1.0 = 11.00> 10.98
Section is class 1
Alan white design
Page 9
Project : Apollo 1.3m X-beamElement : Main Boom CapacityJob Number : V0095 By : mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17 Alan white design
Main Boom HAZThere is a HAZ at welded joint to the diagonal brace
tboom= 4.40mm
tdiagonal= 3.5mm
taverage= 3.95mm
All welds are TIG. As per EN 1999-1-1 6.1.6.3
bhaz = 30mm
Therefore HAZ extends 30mm from intersection of welded materials
Page 10
Project : Apollo 1.3m X-beamElement : Main Boom CapacityJob Number : V0095 By : mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17 Alan white design
HAZ Section Layout
Take section shown as non-HAZ.
HAZ Section Properties A= 418 mm2
I= 92785 mm4
Wel= 3398 mm3
Wpl= 4587 mm3
ry= 14.7 mm
Main Boom Moment Capacity (6.2.5.1)
Mc,Rd = aWel fo / gM1
a = Wpl/Wel (Table 6.4)= 1.35
Wel = 3.40 cm3
fo = 250 N/mm2
gM1 = 1.1 (6.1.3)
= 1.35*3.40*250/1100Mc,Rd = 1.04 kNm
Main Boom Shear Capacity (6.2.6)
VRd = Av fo/ √3gM1
Av= 0.6A
Av= 0.6*418
Av= 250.80 mm2
gM1= 1.1fo = 250 N/mm2
= 250.80*250/(SQRT(3)*1100)VRd = 32.91 kN
Page 11
Project : Apollo 1.3m X-beamElement : Main Boom CapacityJob Number : V0095 By : mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17 Alan white design
Main Boom 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 = 147,654 mm4
k = 0.50 (Table I.2)L = 1,000 mm
Ncr = ((PI()^2)*70000*147654)/((0.5^2)*(1000^2))= 408,040.24 N
λ = √Aeff fo / Ncr (6.3.1.2)= 0.61 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 = 0.74
X = 0.87
k= 1-(1-(A1/A)10-l-(0.05+0.1(A1/A))l1.3(1-l)
A1= A-AHAZ(1-po,HAZ)
= 607-(189*(1-0.5))= 512.50 mm2
k= 0.86
Nb,Rd = k x Aeff fo /gM1
= 0.86*0.87*607*250/1100= 103.22 kN
Page 12
Project : Apollo 1.3m X-beamElement : Main Boom CapacityJob Number : V0095 By : mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17 Alan white design
Main Boom Axial Tension Capacity (6.2.3)
General yieldingNo,Rd = Ag fo /gM1
fo = 250 N/mm2
Ag = 607 mm2
gM1 = 1.1 = 607*250/1100 = 137.95 kN
Local failureNu,Rd = Anet fu /gM2
fu = 290 N/mm2
Anet = ru,haz * A
= 0.64*607= 388.50 mm2
gM1 = 1.25 = 388.5*290/1250 = 90.13 kN
Page 13
Project : Apollo 1.3m X-beamElement : Diagonal CapacityJob Number : V0095 By : mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
RHS diagonal LayoutDiagonal 50 x 19 x 3.5mm oval 6082-T6
Section Properties A= 406 mm2
I= 112174 mm4
Wel= 3974 mm3
Wpl= 4968 mm3
ry= 7.3 mm
for slenderness b= b/t b= 50-2*3.25 = 43.50
= 13.38 t = 3.25
e= sqrt(250/fo) fo= 250N/mm2
= 1.00
Class A, without welds, Internal parts b1= 11e
= 11*1.0 = 11.00< 13.38
Class A, without welds, Internal parts b2 = 16e
= 16*1.00 = 16.00> 13.38
Section is class 2
Alan white design
19.00
38.003.25 50.00
Page 14
Project : Apollo 1.3m X-beamElement : Diagonal CapacityJob Number : V0095 By : mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17 Alan white design
Diagonal Axial Comp Capacity @ 700mm (effective length of beam)
Nb,Rd = k x Aeff fo /gM1 (6.3.1.1)
k = ωx
ωx = ru,haz fu / gM2
fo / gM1
= (0.64*290/1.25)/(250/1.1)= 0.65
k= 0.65
Ncr = π2 EI / k2 L2 (Appendix I.3)
E = 70,000 N/mm2
I = 112,174 mm4
k = 0.50L = 700 mm
Ncr = ((PI()^2)*70000*112174)/((0.5^2)*(700^2))= 632,636.00 N
λ = √Aeff fo / Ncr (6.3.1.2)
= 0.40 Aeff = 406 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 = 0.61
X = 0.82
Nb,Rd = 0.65*0.82*406*250/1100= 49.18 kN
Page 15
Project : Apollo 1.3m X-beamElement : Diagonal CapacityJob Number : V0095 By : mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17 Alan white design
Diagonal Axial Tension Capacity (6.2.3)
General yieldingNo,Rd = Ag fo /gM1
fo = 250 N/mm2
Ag = 406 mm2
gM1 = 1.1 = 406*250/1100 = 92.27 kN
Local failureNu,Rd = Aeff fu /gM2
fu = 290 N/mm2
Anet = ru,haz * A
= 0.64*406= 259.84 mm2
gM1 = 1.25
= 259.84*290/1250 = 60.28 kN
Page 16
Project : Apollo 1.3m X-beamElement : Vertical CHS Member CapacityJob Number : V0095 By : mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Vertical CHS Member Capacityø48.3mm x 4.4mm CHS 6082-T6
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 mm = 10.98 t = 4.4 mm
e= sqrt(250/fo) fo= 250 N/mm2
= 1.00
Class A, without welds, Internal parts b1= 11e
= 11*1.0 = 11.00> 10.98
Section is class 1
Alan white design
Page 17
Project : Apollo 1.3m X-beamElement : Vertical CHS Member CapacityJob Number : V0095 By : mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17 Alan white design
Vertical CHS Member Moment Capacity (6.2.5.1)
Mc,Rd = aWel fo / gM1
a = Wpl/Wel (Table 6.4)= 1.35
Wel = 6.11 cm3
fo = 250 N/mm2
gM1 = 1.1 (6.1.3) = 1.35*6.11*250/1100
Mc,Rd = 1.87 kNm
Mu,Rd = Wnet fu / gM2
Wnet = Wel * ρu, haz
= 6.11*0.64= 3.91 cm3
fu = 290 N/mm2
gM2 = 1.25 (6.1.3) = 3.91*290/1250
Mu,Rd = 0.91 kNm
MRd,x = 0.91 kNm lesser value of Mc,Rd / Mu,Rd
Vertical CHS Member Shear Capacity (6.2.6)
VRd = Av fo/ √3gM1 Av= 0.6AAv= 0.6*607Av= 364.20 mm2
gM1= 1.1fo = 250 N/mm2
= 364.20*250/(SQRT(3)*1100)VRd = 47.79 kN
Vertical CHS Member Axial Comp Capacity @ 1200mm (effective length of beam)
Nb,Rd = k x Aeff fo /gM1 (6.3.1.1)
k = ωx
ωx = ru,haz fu / gM2
fo / gM1
= (0.64*290/1.25)/(250/1.1)= 0.65
k= 0.65
Ncr = π2 EI / k2 L2 (Appendix I.3)
E = 70,000 N/mm2
I = 147,654 mm4
k = 0.50L = 1,200 mm
Ncr = ((PI()^2)*70000*147654)/((0.5^2)*(1200^2))
= 283,361.28 N
Page 18
Project : Apollo 1.3m X-beamElement : Vertical CHS Member CapacityJob Number : V0095 By : mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17 Alan white design
λ = √Aeff fo / Ncr (6.3.1.2)
= 0.73 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 = 0.83
X = 0.60
Nb,Rd = k x Aeff fo /gM1
= 0.65*0.60*607*250/1100= 53.80 kN
Vertical CHS Member Axial Tension Capacity (6.2.3)
General yieldingNo,Rd = Ag fo /gM1
fo = 250 N/mm2
Ag = 607 mm2
gM1 = 1.1 = 607*250/1100 = 137.95 kN
Local failureNu,Rd = Anetfu /gM2
fu = 290 N/mm2
Anet = A* ru,haz
= 607*0.64= 388.50 mm2
gM1 = 1.25
= 388.5*290/1250 = 90.13 kN
Page 19
Project : Apollo 1.3m X-beamElement : Overall X-Beam ResultsJob Number : V0095 By : mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Overall X-Beam Results
Alan white design
Page 20
Project : Apollo 1.3m X-beamElement : X-Beam ResultsJob Number : V0095 By : mo Date: Nov 17Document No : 001C Checked :mmr Date: Nov 17
Load case 1 : UDL
Loadcase 1Length (m)
912151824
Average kNmMinimum kNm
Load case 2 : Central Point Load
Loadcase 1Length (m)
912151824
Average kNmMinimum kNm
Load case 3 : Two Point Loads at Third Points
Loadcase 3Length (m)
912151824
Average kNmMinimum kNm
Moment108.34110.70110.25108.68
106.65108.60109.50108.90
UltimateMoment110.87
110.87
Ultimate
116.10118.13121.50118.80
106.20
108.33106.65
117.08
108.83106.20
UltimateMoment
108.00
1.3m X-BEAM
1.3m X-BEAM
1.3m X-BEAM
Alan white design
Page 21
Project : Apollo 1.3m X-beamElement : X-Beam ResultsJob Number : V0095 By : mo Date: Nov 17Document No : 001C Checked :mmr Date: Nov 17 Alan white design
Load case 4 : Three Point Loads at Quarter Points
Loadcase 4Length (m)
912151824
Average kNmMinimum kNm
Load case 5 : Shear
Loadcase 5Length (m)
912151824
Average kNMinimum kN
Ultimate
113.63116.10
Moment
83.4780.5878.5475.79
102.60
113.81102.60
121.50115.20
66.56
76.9966.56
1.3m X-BEAM
1.3m X-BEAMUltimate
Shear
Page 22
Overall Graded Results for Allowable Working Loads on a 1.3m X-Beam
By : moDate: Nov 17
For simply supported Apollo1.3m X-BEAM with a compression chord restraint at 1.0m intervals001C Date: Nov 17
Test Results
9 12 15 18 2471.10 72.25 73.00 72.50 68.2555.50 53.00 52.25 50.50 44.25
Allowable loads for load distributions from resultsType of Load
9 12 15 18 24Uniformly Distributed load 7.0 4.0 2.6 1.8 0.9Total UDL 63.2 48.2 38.9 32.2 22.8Single point load (mid Point) 31.6 24.1 19.5 16.1 11.4Two point loads (third points) 23.7 18.1 14.6 12.1 8.5Three point loads ( quarter points) 15.8 12.0 9.7 8.1 5.7
Extrapolated Allowable loads for load distributions
Type of Load6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Uniformly Distributed load kN/m 15.8 11.6 8.9 7.0 5.7 4.7 4.0 3.4 2.9 2.6 2.3 2.0 1.8 1.5 1.4 1.2 1.1Total UDL kN 94.8 81.3 71.1 63.2 56.9 51.7 48.2 44.5 41.3 38.9 36.5 34.1 32.2 28.7 27.3 26.0 24.8Single point load (mid Point) kN 47.4 40.6 35.6 31.6 28.4 25.9 24.1 22.2 20.6 19.5 18.3 17.1 16.1 14.4 13.7 13.0 12.4Two point loads (third points) Each kN 35.6 30.5 26.7 23.7 21.3 19.4 18.1 16.7 15.5 14.6 13.7 12.8 12.1 10.8 10.2 9.8 9.3Three point loads ( quarter points) Each kN 23.7 20.3 17.8 15.8 14.2 12.9 12.0 11.1 10.3 9.7 9.1 8.5 8.1 7.2 6.8 6.5 6.2Type of Load
23 24Uniformly Distributed load kN/m 1 0.9Total UDL kN 23.7 22.8Single point load (mid Point) kN 11.9 11.4Two point loads (third points) Each kN 8.9 8.5Three point loads ( quarter points) Each kN 5.9 5.7
Span (m)
Allowable MomentAllowable Shear (Load on Vertical)
kN/m
Each kNEach kN
Clear span (m)
kNkN
Clear span (m)
Clear span (m)
Alan white design
Page 23
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.3. Maximum capacity of a point load mid way between nodes is 15kN but overall buckling of the top chord should be
checked if loads are placed other than at restrained loads. Compression chord restraint required at 1.0m c/c4. Factor of Safety = 1.655. Calculations as per BS EN 1999-1-16. For design purposes the allowable bending moment is 71.10kNm and the allowable shear is 44.25kN.
Graph Summary of Allowable Working Loads for a 1.3m X-Beam to BS EN 1999-1-1
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
90.0
100.0
0 5 10 15 20 25
Load
ing
(kN
)
Length of X-Beam
1.3m X-Beam Loading Capacity to BS EN 1999-1 (1.0m Restraint)
Total UDL
Single point load (mid Point)
Two point loads (thirdpoints)
Three point loads ( quarterpoints)
Alan white design
Page 24
Overall Graded Results for Allowable Working Loads on a 1.3m X-Beam
By : moDate: Nov 17
For simply supported Apollo X-BEAM with a compression chord restraint at 1.0m intervals001C Date: Nov 17
Extrapolated Allowable loads for load distributions
Type of Load6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Uniformly Distributed load kN/m 15.8 11.6 8.9 7.0 5.7 4.7 4.0 3.4 2.9 2.6 2.3 2.0 1.8 1.5 1.4 1.2 1.1Total UDL kN 94.8 81.3 71.1 63.2 56.9 51.7 48.2 44.5 41.3 38.9 36.5 34.1 32.2 28.7 27.3 26.0 24.8Single point load (mid Point) kN 47.4 40.6 35.6 31.6 28.4 25.9 24.1 22.2 20.6 19.5 18.3 17.1 16.1 14.4 13.7 13.0 12.4Two point loads (third points) Each kN 35.6 30.5 26.7 23.7 21.3 19.4 18.1 16.7 15.5 14.6 13.7 12.8 12.1 10.8 10.2 9.8 9.3Three point loads ( quarter points) Each kN 23.7 20.3 17.8 15.8 14.2 12.9 12.0 11.1 10.3 9.7 9.1 8.5 8.1 7.2 6.8 6.5 6.2Type of Load
23 24Uniformly Distributed load kN/m 1 0.95Total UDL kN 23.7 22.8Single point load (mid Point) kN 11.9 11.4Two point loads (third points) Each kN 8.9 8.53Three point loads ( quarter points) Each kN 5.9 5.69
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.3. Maximum capacity of a point load mid way between nodes is 15kN but overall buckling of the top chord should be
checked if loads are placed other than at restrained loads. Compression chord restraint required at 1.0m c/c4. Factor of Safety = 1.655. Calculations as per BS EN 1999-1-16. For design purposes the allowable bending moment is 71.10kNm and the allowable shear is 44.25kN.
Clear span (m)
Clear span (m)
Alan white design
Page 25
Graph Summary of Allowable Working Loads for a 1.3m X-Beam to BS EN 1999-1-1
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
90.0
100.0
0 5 10 15 20 25
Load
ing
(kN
)
Length of X-Beam
1.3m X-Beam Loading Capacity to BS EN 1999-1 (1.0m Restraint)
Total UDL
Single point load (mid Point)
Two point loads (thirdpoints)
Three point loads ( quarterpoints)
Page 26
Project : Apollo 1.3m X-beamElement : 9m X-Beam ResultsJob Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
9m X-Beam Results
Alan white design
Page 27
Project : Apollo 1.3m X-beamElement : 9m X-Beam Load Combination 1Job Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 1 UDL load 10kN/m applied along beam
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.29 3.60
Shear VRd 32.91 0.87 37.65
Tension No,Rd 90.13 39.52 2.28
Compression Nb,Rd 103.22 118.76 0.87Deflection d 90.00 21.94 4.10Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 0.73
Vertical Moment Mc,Rd 0.91 0.11 8.17
Shear VRd 47.79 0.17 289.63
Tension No,Rd 90.13 0.17 530.19
Compression Nb,Rd 53.80 31.65 1.70Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 1.47
Diagonal Tension No,Rd 60.28 31.62 1.91
Compression Nb,Rd 49.18 40.22 1.22Factor 0.73
Ra Rb
Max Moment= WL2/8
so for ultimate condition W= 1.5*10
15.00 kNapply factor from above
Wf= 15*0.73= 10.95 kN
so maximum moment is as above Ultimate Mu= Wf*9^2/8
= (10.95*9^2)/8= 110.87 kNm
and for allowable valueallowable max moment= 110.87/1.50
= 73.91 kNm
Moment values Ultimate 110.87 kNmAllowable 73.91 kNm
9.00m
Alan white design
w w
Page 28
Project : Apollo 1.3m X-beamElement : 9m X-Beam Load Combination 2Job Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 2 Point load 10kN load applied at midspan of beam
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.09 11.85
Shear VRd 32.91 0.27 121.44
Tension No,Rd 90.13 13.69 6.58
Compression Nb,Rd 103.22 25.45 4.06Deflection d 90.00 4.78 18.83Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 3.21
Vertical Moment Mc,Rd 0.91 0.03 36.28
Shear VRd 47.79 0.03 1,493.40
Tension No,Rd 90.13 2.83 31.85
Compression Nb,Rd 53.80 3.54 15.20Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 11.45
Diagonal Tension No,Rd 60.28 4.79 12.59
Compression Nb,Rd 49.18 7.75 6.35Factor 3.21
W 4.5m
Ra RbMax Moment= WL/4
so for ultimate condition W= 1.50*10
= 15.00 kNapply factor from above
Wf= 15*3.21= 48.15 kN
so maximum moment is as above Ultimate Mu= Wf*9/4
= 48.15*9/4= 108.34 kNm
and for allowable valueallowable max moment= 108.34/1.50
= 72.23 kNm
Moment values Ultimate 108.34 kNmAllowable 72.23 kNm
9.00m
Alan white design
Page 29
Project : Apollo 1.3m X-beamElement : 9m X-Beam Load Combination 3Job Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 3 PL at third points 10kN load applied at each of the two third points
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.08 13.04
Shear VRd 32.91 0.23 146.26
Tension No,Rd 90.13 12.62 7.14
Compression Nb,Rd 103.22 37.41 2.76Deflection d 90.00 7.00 12.86Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 2.37
Vertical Moment Mc,Rd 0.91 0.03 27.49
Shear VRd 47.79 0.05 955.78
Tension No,Rd 90.13 0.01 9,013.20
Compression Nb,Rd 53.80 6.70 8.03Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 6.56
Diagonal Tension No,Rd 60.28 9.17 6.57
Compression Nb,Rd 49.18 9.42 5.22Factor 2.37
3.0m W W 3.0m
Ra Rb
Max Moment= WL/3
so for ultimate condition W= 1.50*10
15.00 kNapply factor from above
Wf= 15.00*2.37= 35.55 kN
so maximum moment is as above Ultimate Mu= Wf*9/3
= (35.55*9)/3= 106.65 kNm
and for allowable valueallowable max moment= 106.65/1.50
= 71.10 kNm
Moment values Ultimate 106.65 kNmAllowable 71.10 kNm
9.00m
Alan white design
Page 30
Project : Apollo 1.3m X-beamElement : 9m X-Beam load Combination 4Job Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 4 PL at quarter points10kN load applied at each of the three quarter points
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.11 9.94
Shear VRd 32.91 0.32 102.52
Tension No,Rd 90.13 18.98 4.75
Compression Nb,Rd 103.22 49.38 2.09Deflection d 90.00 9.40 9.57Combined Axial (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 1.80
Vertical Moment Mc,Rd 0.91 0.05 19.30
Shear VRd 47.79 0.07 654.64
Tension No,Rd 90.13 2.95 30.55
Compression Nb,Rd 53.80 9.89 5.44Combined Axial (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 4.47
Diagonal Tension No,Rd 60.28 13.47 4.48
Compression Nb,Rd 49.18 13.85 3.55Factor 1.80
2.25m W 2.25m W 2.25m W 2.25m
Ra Rb
Max Moment= WL/2
so for ultimate condition W= 1.50*10
15.00 kNapply factor from above
Wf= 15.00*1.80= 27.00 kN
so maximum moment is as above Ultimate Mu= Wf*9/2
= (27*9)/2= 121.50 kNm
and for allowable valueallowable max moment= 121.50/1.50
= 81.00 kNm
Moment values Ultimate 121.50 kNmAllowable 81.00 kNm
9.00m
Alan white design
Page 31
Project : Apollo 1.3m X-beamElement : 9m X-Beam Load Combination 5Job Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 5 End Shear 10kN load applied at a 1m distance from the support
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.07 14.49
Shear VRd 32.91 0.23 141.24
Tension No,Rd 90.13 5.03 17.92
Compression Nb,Rd 103.22 10.79 9.57Deflection d 90.00 1.58 56.96Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 6.26
Vertical Moment Mc,Rd 0.91 0.02 53.36
Shear VRd 47.79 0.02 2,077.78
Tension No,Rd 90.13 0.03 3,004.40
Compression Nb,Rd 53.80 6.54 8.23Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 7.85
Diagonal Tension No,Rd 60.28 7.29 8.27
Compression Nb,Rd 49.18 7.77 6.33Factor 6.26
W 1.0m
Ra Rb
Max Shear Rb= W*8/9
so for ultimate condition W= 1.50*10
15.00 kNapply factor from above
Wf= 15.00*6.26= 93.90 kN
so maximum shear is as above Ultimate Qu= Wf*8/9
= (93.90*8)/9= 83.47 kN
and for allowable valueallowable max shear= 83.47/1.50
= 55.65 kN
Shear values Ultimate 83.47 kNAllowable 55.65 kN
9.00m
Alan white design
Page 32
Project : Apollo 1.3m X-beamElement : 9m X-Beam ResultsJob Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Loadcase Ultimate AllowableNo. Moment Moment1 UDL 110.87 73.912 Point 108.34 72.233 Third 106.65 71.104 Quarter 121.50 81.00
Loadcase Ultimate AllowableNo. Shear Shear5 End Shear 83.47 55.65
Max Allowable Moment = 71.10 kNm
Max Allowable Shear = 55.50 kN
9.0m X-BEAM
Alan white design
Page 33
From 9m 1.3m X-Beam Results with restraint to compression chord at 1.0m c/c:
For simply supported Apollo single 1.3m X-BEAM TO EUROCODE EN 1999-1-1
Allowable Bending Moment 71.10 kNmAllowable Shear 55.50 kN
Allowable loads for load distributions
Type of Load2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Uniformly Distributed load kN/m 55.5 37.0 27.8 22.2 15.8 11.6 8.9 7.0 5.7 4.7 4.0 3.4 2.9 2.5 2.2 2.0 1.8Total UDL kN 111.0 111.0 111.0 111.0 94.8 81.3 71.1 63.2 56.9 51.7 47.4 43.8 40.6 37.9 35.6 33.5 31.6Single point load (mid Point) kN 111.0 94.8 71.1 56.9 47.4 40.6 35.6 31.6 28.4 25.9 23.7 21.9 20.3 19.0 17.8 16.7 15.8Two point loads (third points) Each kN 55.5 55.5 53.3 42.7 35.6 30.5 26.7 23.7 21.3 19.4 17.8 16.4 15.2 14.2 13.3 12.5 11.9Three point loads ( quarter points) Each kN 37.0 37.0 35.6 28.4 23.7 20.3 17.8 15.8 14.2 12.9 11.9 10.9 10.2 9.5 8.9 8.4 7.9Type of Load
19 20 21 22 23 24 25 26 27 28 29 30Uniformly Distributed load kN/m 1.6 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.8 0.7 0.7 0.6Total UDL kN 29.9 28.4 27.1 25.9 24.7 23.7 22.8 21.9 21.1 20.3 19.6 19.0Single point load (mid Point) kN 15.0 14.2 13.5 12.9 12.4 11.9 11.4 10.9 10.5 10.2 9.8 9.5Two point loads (third points) Each kN 11.2 10.7 10.2 9.7 9.3 8.9 8.5 8.2 7.9 7.6 7.4 7.1Three point loads ( quarter points) Each kN 7.5 7.1 6.8 6.5 6.2 5.9 5.7 5.5 5.3 5.1 4.9 4.7
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.3. Maximum capacity of a point load mid way between nodes is 15kN but overall buckling of the top chord should be
checked if loads are placed other than at restrained loads. Compression chord restraint required at 1.0m c/c4. Factor of Safety = 1.655. Calculations as per BS EN 1999-1-1
Clear span (m)
Clear span (m)
Alan white design
Page 34
Project : Apollo 1.3m X-beamElement : 12m X-Beam ResultsJob Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
12m X-Beam Results
Alan white design
Page 35
Project : Apollo 1.3m X-beamElement : 12m X-Beam Load Combination 1Job Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 1 UDL load 10kN/m applied along beam
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.40 2.61
Shear VRd 32.91 1.21 27.31
Tension No,Rd 90.13 70.69 1.28
Compression Nb,Rd 103.22 211.99 0.49Deflection d 120.00 58.80 2.04Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 0.43
Vertical Moment Mc,Rd 0.91 0.16 5.74
Shear VRd 47.79 0.24 202.50
Tension No,Rd 90.13 0.62 145.37
Compression Nb,Rd 53.80 40.93 1.31Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 1.12
Diagonal Tension No,Rd 60.28 44.61 1.35
Compression Nb,Rd 49.18 53.60 0.92Factor 0.43
Ra Rb
Max Moment= WL2/8
so for ultimate condition W= 1.5*10
15.00 kNapply factor from above
Wf= 15*0.43= 6.45 kN
so maximum moment is as above Ultimate Mu= Wf*12^2/8
= (6.45*12^2)/8= 116.10 kNm
and for allowable valueallowable max moment= 116.10/1.50
= 77.40 kNm
Moment values Ultimate 116.10 kNmAllowable 77.40 kNm
12.00m
Alan white design
w w
Page 36
Project : Apollo 1.3m X-beamElement : 12m X-Beam Load Combination 2Job Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 2 Point load 10kN load applied at midspan of beam
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.07 14.49
Shear VRd 32.91 0.20 167.05
Tension No,Rd 90.13 17.59 5.12
Compression Nb,Rd 103.22 36.64 2.82Deflection d 120.00 9.36 12.82Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 2.46
Vertical Moment Mc,Rd 0.91 0.02 50.40
Shear VRd 47.79 0.03 1769.96
Tension No,Rd 90.13 0.12 751.10
Compression Nb,Rd 53.80 5.60 9.61Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 8.40
Diagonal Tension No,Rd 60.28 4.95 12.18
Compression Nb,Rd 49.18 5.12 9.61Factor 2.46
W 6.0m
Ra RbMax Moment= WL/4
so for ultimate condition W= 1.50*10
= 15.00 kNapply factor from above
Wf= 15*2.46= 36.90 kN
so maximum moment is as above Ultimate Mu= Wf*L/4
= 36.90*12/4= 110.70 kNm
and for allowable valueallowable max moment= 110.70/1.50
= 73.80 kNm
Moment values Ultimate 110.70 kNmAllowable 73.80 kNm
12.00m
Alan white design
Page 37
Project : Apollo 1.3m X-beamElement : 12m X-Beam Load Combination 3Job Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 3 PL at third points 10kN load applied at each of the two third points
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.09 11.85
Shear VRd 32.91 0.24 136.55
Tension No,Rd 90.13 16.87 5.34
Compression Nb,Rd 103.22 50.57 2.04Deflection d 120.00 14.27 8.41Combined Axial (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 1.81
Vertical Moment Mc,Rd 0.91 0.03 27.49
Shear VRd 47.79 0.05 937.04
Tension No,Rd 90.13 0.18 500.73
Compression Nb,Rd 53.80 6.78 7.94Combined Axial (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 6.49
Diagonal Tension No,Rd 60.28 9.32 6.47
Compression Nb,Rd 49.18 9.60 5.12Factor 1.81
4.0m W W 4.0m
Ra Rb
Max Moment= WL/3
so for ultimate condition W= 1.50*10
15.00 kNapply factor from above
Wf= 15.00*1.81= 27.15 kN
so maximum moment is as above Ultimate Mu= Wf*L/3
= (27.15*12)/3= 108.60 kNm
and for allowable valueallowable max moment= 108.60/1.50
= 72.40 kNm
Moment values Ultimate 108.60 kNmAllowable 72.40 kNm
12.00m
Alan white design
Page 38
Project : Apollo 1.3m X-beamElement : 12m X-Beam Load Combination 4Job Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 4 Load at quarter points10kN load applied at each of the three quarter points
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.11 9.48
Shear VRd 32.91 0.33 98.83
Tension No,Rd 90.13 26.55 3.39
Compression Nb,Rd 103.22 72.55 1.42Deflection d 120.00 19.90 6.03Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 1.28
Vertical Moment Mc,Rd 0.91 0.05 18.51
Shear VRd 47.79 0.08 637.18
Tension No,Rd 90.13 0.01 9,013.20
Compression Nb,Rd 53.80 9.93 5.42Combined Axial (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 4.42
Diagonal Tension No,Rd 60.28 13.69 4.40
Compression Nb,Rd 49.18 14.08 3.49Factor 1.28
3.0m W 3.0m W 3.0m W 3.0m
12.00m Ra Rb
Max Moment= WL/2
so for ultimate condition W= 1.50*10
15.00 kNapply factor from above
Wf= 15.00*1.28= 19.20 kN
so maximum moment is as above Ultimate Mu= Wf*12/2
= (19.20*12)/2= 115.20 kNm
and for allowable valueallowable max moment= 115.20/1.50
= 76.80 kNm
Moment values Ultimate 115.20 kNmAllowable 76.80 kNm
Alan white design
Page 39
Project : Apollo 1.3m X-beamElement : 12m X-Beam Load Combination 5Job Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 5 End Shear 10kN load applied at a 1.0m distance from the support
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.07 14.10
Shear VRd 32.91 0.24 138.27
Tension No,Rd 90.13 4.80 18.78
Compression Nb,Rd 103.22 11.75 8.78Deflection d 120.00 2.63 45.63Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 5.86
Vertical Moment Mc,Rd 0.91 0.02 50.40
Shear VRd 47.79 0.02 1991.20
Tension No,Rd 90.13 0.04 2253.30
Compression Nb,Rd 53.80 6.83 7.88Combined Axial (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 7.05
Diagonal Tension No,Rd 60.28 7.69 7.84
Compression Nb,Rd 49.18 8.18 6.01Factor 5.86
W 1.0m
12.00m Ra Rb
Max Shear Rb= W*11/12
so for ultimate condition W= 1.50*10
15.00 kNapply factor from above
Wf= 15.0*5.86= 87.90 kN
so maximum shear is as above Ultimate Qu= Wf*11/12
= (87.90*11)/12= 80.58 kN
and for allowable valueallowable max shear= 80.58/1.50
= 53.72 kN
Shear values Ultimate 80.58 kNAllowable 53.72 kN
Alan white design
Page 40
Project : Apollo 1.3m X-beamElement : 12m X-Beam ResultsJob Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Loadcase Ultimate AllowableNo. Moment Moment1 UDL 116.10 77.402 Point 110.70 73.803 Third 108.60 72.404 Quarter 115.20 76.80
Loadcase Ultimate AllowableNo. Shear Shear5 End Shear 80.58 53.72
Max Allowable Moment = 72.25 kNm
Max Allowable Shear = 53.00 kN
12.0m X-BEAM
Alan white design
Page 41
From 12m 1.3m X-Beam Results with restraint to compression chord at 1.0m c/c:
For simply supported Apollo single 1.3m X-BEAM TO EUROCODE EN 1999-1-1
Allowable Bending Moment 72.25 kNmAllowable Shear 53.00 kN
Allowable loads for load distributionsType of Load
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Uniformly Distributed load kN/m 53.0 35.3 26.5 21.2 16.1 11.8 9.0 7.1 5.8 4.8 4.0 3.4 2.9 2.6 2.3 2.0 1.8Total UDL kN 106.0 106.0 106.0 106.0 96.3 82.6 72.3 64.2 57.8 52.5 48.2 44.5 41.3 38.5 36.1 34.0 32.1Single point load (mid Point) kN 106.0 96.3 72.3 57.8 48.2 41.3 36.1 32.1 28.9 26.3 24.1 22.2 20.6 19.3 18.1 17.0 16.1Two point loads (third points) Each kN 53.0 53.0 53.0 43.4 36.1 31.0 27.1 24.1 21.7 19.7 18.1 16.7 15.5 14.5 13.5 12.8 12.0Three point loads ( quarter points) Each kN 35.3 35.3 35.3 28.9 24.1 20.6 18.1 16.1 14.5 13.1 12.0 11.1 10.3 9.6 9.0 8.5 8.0Type of Load
19 20 21 22 23 24 25 26 27 28 29 30Uniformly Distributed load kN/m 1.6 1.4 1.3 1.2 1.1 1.0 0.9 0.9 0.8 0.7 0.7 0.6Total UDL kN 30.4 28.9 27.5 26.3 25.1 24.1 23.1 22.2 21.4 20.6 19.9 19.3Single point load (mid Point) kN 15.2 14.5 13.8 13.1 12.6 12.0 11.6 11.1 10.7 10.3 10.0 9.6Two point loads (third points) Each kN 11.4 10.8 10.3 9.9 9.4 9.0 8.7 8.3 8.0 7.7 7.5 7.2Three point loads ( quarter points) Each kN 7.6 7.2 6.9 6.6 6.3 6.0 5.8 5.6 5.4 5.2 5.0 4.8
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.3. Maximum capacity of a point load mid way between nodes is 15kN but overall buckling of the top chord should be
checked if loads are placed other than at restrained loads. Compression chord restraint required at 1.0m c/c4. Factor of Safety = 1.655. Calculations as per BS EN 1999-1-1
Clear span (m)
Clear span (m)
Alan white design
Page 42
Project : Apollo 1.3m X-beamElement : 15m X-Beam ResultsJob Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
15m X-Beam Results
Alan white design
Page 43
Project : Apollo 1.3m X-beamElement : 15m X-Beam Load Combination 1Job Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 1 UDL load 10kN/m applied along beam
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.51 2.04
Shear VRd 32.91 1.54 21.40
Tension No,Rd 90.13 109.43 0.82
Compression Nb,Rd 103.22 328.47 0.31Deflection d 150.00 130.55 1.15Combined Axial (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 0.28
Vertical Moment Mc,Rd 0.91 0.20 4.47
Shear VRd 47.79 0.30 157.20
Tension No,Rd 90.13 1.17 77.04
Compression Nb,Rd 53.80 49.54 1.09Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 0.92
Diagonal Tension No,Rd 60.28 56.88 1.06
Compression Nb,Rd 49.18 66.20 0.74Factor 0.28
Ra Rb
Max Moment= WL2/8
so for ultimate condition W= 1.5*10
15.00 kNapply factor from above
Wf= 15*0.28= 4.20 kN
so maximum moment is as above Ultimate Mu= Wf*15^2/8
= (4.20*15^2)/8= 118.13 kNm
and for allowable valueallowable max moment= 118.13/1.50
= 78.75 kNm
Moment values Ultimate 118.13 kNmAllowable 78.75 kNm
15.00m
Alan white design
w w
Page 44
Project : Apollo 1.3m X-beamElement : 15m X-Beam Load Combination 2Job Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 2 Point load 10kN load applied at midspan of beam
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.09 11.72
Shear VRd 32.91 0.25 131.11
Tension No,Rd 90.13 23.58 3.82
Compression Nb,Rd 103.22 45.98 2.24Deflection d 150.00 16.96 8.84Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 1.96
Vertical Moment Mc,Rd 0.91 0.03 36.28
Shear VRd 47.79 0.03 1,493.40
Tension No,Rd 90.13 2.89 31.19
Compression Nb,Rd 53.80 3.73 14.42Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 11.01
Diagonal Tension No,Rd 60.28 5.10 11.82
Compression Nb,Rd 49.18 7.77 6.33Factor 1.96
W 7.5m
Ra RbMax Moment= WL/4
so for ultimate condition W= 1.50*10
= 15.00 kNapply factor from above
Wf= 15*1.96= 29.40 kN
so maximum moment is as above Ultimate Mu= Wf*15/4
= 29.40*15/4= 110.25 kNm
and for allowable valueallowable max moment= 110.25/1.50
= 73.50 kNm
Moment values Ultimate 110.25 kNmAllowable 73.50 kNm
15.00m
Alan white design
Page 45
Project : Apollo 1.3m X-beamElement : 15m X-Beam Load Combination 3Job Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 3 PL at third points 10kN load applied at each of the two third points
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.10 10.98
Shear VRd 32.91 0.26 127.55
Tension No,Rd 90.13 21.27 4.24
Compression Nb,Rd 103.22 63.89 1.62Deflection d 150.00 26.05 5.76Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 1.46
Vertical Moment Mc,Rd 0.91 0.03 26.68
Shear VRd 47.79 0.05 919.02
Tension No,Rd 90.13 0.26 346.66
Compression Nb,Rd 53.80 6.86 7.84Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 6.40
Diagonal Tension No,Rd 60.28 9.47 6.37
Compression Nb,Rd 49.18 9.78 5.03Factor 1.46
5.0m W W 5.0m
Ra Rb
Max Moment= WL/3
so for ultimate condition W= 1.50*10
15.00 kNapply factor from above
Wf= 15.00*1.46= 21.90 kN
so maximum moment is as above Ultimate Mu= Wf*L/3
= (21.90*15)/3= 109.50 kNm
and for allowable valueallowable max moment= 109.50/1.50
= 73.00 kNm
Moment values Ultimate 109.50 kNmAllowable 73.00 kNm
15.00m
Alan white design
Page 46
Project : Apollo 1.3m X-beamElement : 15m X-Beam Load Combination 4Job Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 4 Load at quarter points10kN load applied at each of the three quarter points
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.12 8.99
Shear VRd 32.91 0.35 93.76
Tension No,Rd 90.13 36.33 2.48
Compression Nb,Rd 103.22 93.86 1.10Deflection d 150.00 37.09 4.04Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 1.01
Vertical Moment Mc,Rd 0.91 0.05 18.14
Shear VRd 47.79 0.08 628.80
Tension No,Rd 90.13 3.13 28.80
Compression Nb,Rd 53.80 9.99 5.39Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 4.38
Diagonal Tension No,Rd 60.28 13.84 4.36
Compression Nb,Rd 49.18 14.27 3.45Factor 1.01
3.75m W 3.75m W 3.75m W 3.75m
15.00m Ra Rb
Max Moment= WL/2
so for ultimate condition W= 1.50*10
15.00 kNapply factor from above
Wf= 15.00*1.01= 15.15 kN
so maximum moment is as above Ultimate Mu= Wf*L/2
= (15.15*15)/2= 113.63 kNm
and for allowable valueallowable max moment= 113.63/1.50
= 75.75 kNm
Moment values Ultimate 113.63 kNmAllowable 75.75 kNm
Alan white design
Page 47
Project : Apollo 1.3m X-beamElement : 15m X-Beam Combination 5Job Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 5 End Shear 10kN load applied at 1.0m distance from the support
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.08 13.91
Shear VRd 32.91 0.24 135.43
Tension No,Rd 90.13 4.25 21.21
Compression Nb,Rd 103.22 12.48 8.27Deflection d 150.00 4.27 35.13Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 5.61
Vertical Moment Mc,Rd 0.91 0.02 50.40
Shear VRd 47.79 0.03 1,911.55
Tension No,Rd 90.13 0.04 2,253.30
Compression Nb,Rd 53.80 7.05 7.63Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 6.85
Diagonal Tension No,Rd 60.28 8.00 7.54
Compression Nb,Rd 49.18 8.49 5.79Factor 5.61
W 1.0m
Ra Rb
Max Shear Rb= W*14/15
so for ultimate condition W= 1.50*10
15.00 kNapply factor from above
Wf= 15.00*5.61= 84.15 kN
so maximum shear is as above Ultimate Qu= Wf*14/15
= (84.15*14)/15= 78.54 kN
and for allowable valueallowable max shear= 78.54/1.50
= 52.36 kN
Shear values Ultimate 78.54 kNAllowable 52.36 kN
15.00m
Alan white design
Page 48
Project : Apollo 1.3m X-beamElement : 15m X-Beam ResultsJob Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Loadcase Ultimate AllowableNo. Moment Moment1 UDL 118.13 78.752 Point 110.25 73.503 Third 109.50 73.004 Quarter 113.63 75.75
Loadcase Ultimate AllowableNo. Shear Shear5 End Shear 78.54 52.36
Max Allowable Moment = 73.00 kNm
Max Allowable Shear = 52.25 kN
15.00m X-BEAM
Alan white design
Page 49
From 15m 1.3m X-Beam Results with restraint to compression chord at 1.0m c/c:
For simply supported Apollo single 1.3m X-BEAM TO EUROCODE EN 1999-1-1
Allowable Bending Moment 73.00 kNmAllowable Shear 52.25 kN
Allowable loads for load distributionsType of Load
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18Uniformly Distributed load kN/m 52.3 34.8 26.1 20.9 16.2 11.9 9.1 7.2 5.8 4.8 4.1 3.5 3.0 2.6 2.3 2.0 1.8Total UDL kN 104.5 104.5 104.5 104.5 97.3 83.4 73.0 64.9 58.4 53.1 48.7 44.9 41.7 38.9 36.5 34.4 32.4Single point load (mid Point) kN 104.5 97.3 73.0 58.4 48.7 41.7 36.5 32.4 29.2 26.5 24.3 22.5 20.9 19.5 18.3 17.2 16.2Two point loads (third points) Each kN 52.3 52.3 52.3 43.8 36.5 31.3 27.4 24.3 21.9 19.9 18.3 16.8 15.6 14.6 13.7 12.9 12.2Three point loads ( quarter points) Each kN 34.8 34.8 34.8 29.2 24.3 20.9 18.3 16.2 14.6 13.3 12.2 11.2 10.4 9.7 9.1 8.6 8.1Type of Load
19 20 21 22 23 24 25 26 27 28 29 30Uniformly Distributed load kN/m 1.6 1.5 1.3 1.2 1.1 1.0 0.9 0.9 0.8 0.7 0.7 0.6Total UDL kN 30.7 29.2 27.8 26.5 25.4 24.3 23.4 22.5 21.6 20.9 20.1 19.5Single point load (mid Point) kN 15.4 14.6 13.9 13.3 12.7 12.2 11.7 11.2 10.8 10.4 10.1 9.7Two point loads (third points) Each kN 11.5 11.0 10.4 10.0 9.5 9.1 8.8 8.4 8.1 7.8 7.6 7.3Three point loads ( quarter points) Each kN 7.7 7.3 7.0 6.6 6.3 6.1 5.8 5.6 5.4 5.2 5.0 4.9
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 15kN but overall buckling of the top chord should be
checked if loads are placed other than at restrained loads. Compression chord restraint required at 1.0m c/c4. Factor of Safety = 1.655. Calculations as per BS EN 1999-1-1
Clear span (m)
Clear span (m)
Alan white design
Page 50
Project : Apollo 1.3m X-beamElement : 18m X-Beam ResultsJob Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
18m X-Beam Results
Alan white design
Page 51
Project : Apollo 1.3m X-beamElement : 18m X-Beam Load Combination 1Job Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 1 UDL load 10kN/m applied along beam
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.64 1.64
Shear VRd 32.91 2.24 14.71
Tension No,Rd 90.13 158.46 0.57
Compression Nb,Rd 103.22 475.56 0.22Deflection d 180.00 258.57 0.70Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 0.20
Vertical Moment Mc,Rd 0.91 0.25 3.63
Shear VRd 47.79 0.38 127.10
Tension No,Rd 90.13 1.85 48.72
Compression Nb,Rd 53.80 58.82 0.91Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 0.77
Diagonal Tension No,Rd 60.28 69.96 0.86
Compression Nb,Rd 49.18 79.82 0.62Factor 0.20
Ra Rb
Max Moment= WL2/8
so for ultimate condition W= 1.5*10
15.00 kNapply factor from above
Wf= 15*0.20= 3.00 kN
so maximum moment is as above Ultimate Mu= Wf*18^2/8
= (3.00*18^2)/8= 121.50 kNm
and for allowable valueallowable max moment= 121.50/1.50
= 81.00 kNm
Moment values Ultimate 121.50 kNmAllowable 81.00 kNm
18.00m
Alan white design
w w
Page 52
Project : Apollo 1.3m X-beamElement : 18m X-Beam Load Combination 2Job Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 2 Point load 10kN load applied at midspan of beam
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.08 12.57
Shear VRd 32.91 0.25 129.56
Tension No,Rd 90.13 27.65 3.26
Compression Nb,Rd 103.22 57.82 1.79Deflection d 180.00 28.09 6.41Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 1.61
Vertical Moment Mc,Rd 0.91 0.02 47.74
Shear VRd 47.79 0.03 1,647.89
Tension No,Rd 90.13 0.20 450.66
Compression Nb,Rd 53.80 5.53 9.73Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 8.43
Diagonal Tension No,Rd 60.28 5.25 11.48
Compression Nb,Rd 49.18 5.46 9.01Factor 1.61
W 9.0m
Ra RbMax Moment= WL/4
so for ultimate condition W= 1.50*10
= 15.00 kNapply factor from above
Wf= 15*1.61= 24.15 kN
so maximum moment is as above Ultimate Mu= Wf*18/4
= 24.15*18/4= 108.68 kNm
and for allowable valueallowable max moment= 108.68/1.50
= 72.45 kNm
Moment values Ultimate 108.68 kNmAllowable 72.45 kNm
18.00m
Alan white design
Page 53
Project : Apollo 1.3m X-beamElement : 18m X-Beam Load Combination 3Job Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 3 PL at third points 10kN load applied at each of the two third points
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.10 10.13
Shear VRd 32.91 0.31 106.85
Tension No,Rd 90.13 25.86 3.49
Compression Nb,Rd 103.22 77.60 1.33Deflection d 180.00 43.39 4.15Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 1.21
Vertical Moment Mc,Rd 0.91 0.04 25.92
Shear VRd 47.79 0.05 901.68
Tension No,Rd 90.13 0.34 265.09
Compression Nb,Rd 53.80 6.94 7.75Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 6.30
Diagonal Tension No,Rd 60.28 9.61 6.27
Compression Nb,Rd 49.18 9.96 4.94Factor 1.21
6.0m W W 6.0m
Ra Rb
Max Moment= WL/3
so for ultimate condition W= 1.50*10
15.00 kNapply factor from above
Wf= 15.00*1.21= 18.15 kN
so maximum moment is as above Ultimate Mu= Wf*L/3
= (18.15*18)/3= 108.90 kNm
and for allowable valueallowable max moment= 108.90/1.50
= 72.60 kNm
Moment values Ultimate 108.90 kNmAllowable 72.60 kNm
18.00m
Alan white design
Page 54
Project : Apollo 1.3m X-beamElement : 18m X-Beam Load Combination 4Job Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 4 Load at quarter points10kN load applied at each of the three quarter points
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.12 8.62
Shear VRd 32.91 0.37 89.67
Tension No,Rd 90.13 40.96 2.20
Compression Nb,Rd 103.22 111.69 0.92Deflection d 180.00 59.42 3.03Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 0.86
Vertical Moment Mc,Rd 0.91 0.06 15.64
Shear VRd 47.79 0.08 575.77
Tension No,Rd 90.13 3.23 27.90
Compression Nb,Rd 53.80 10.07 5.34Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 4.23
Diagonal Tension No,Rd 60.28 13.98 4.31
Compression Nb,Rd 49.18 16.32 3.01Factor 0.86
4.50m W 4.50m W 4.50m W 4.50m
Ra Rb
Max Moment= WL/2
so for ultimate condition W= 1.50*10
15.00 kNapply factor from above
Wf= 15.00*0.86= 12.90 kN
so maximum moment is as above Ultimate Mu= Wf*L/2
= (12.90*18)/2= 116.10 kNm
and for allowable valueallowable max moment= 116.10/1.50
= 77.40 kNm
Moment values Ultimate 116.10 kNmAllowable 77.40 kNm
18.00m
Alan white design
Page 55
Project : Apollo 1.3m X-beamElement : 18m X-beam Load Combination 5Job Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 5 End Shear 10kN load applied at a 1.0m distance from the support
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.08 13.73
Shear VRd 32.91 0.30 109.33
Tension No,Rd 90.13 3.80 23.72
Compression Nb,Rd 103.22 13.31 7.75Deflection d 180.00 6.75 26.67Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 5.35
Vertical Moment Mc,Rd 0.91 0.02 47.74
Shear VRd 47.79 0.03 1,838.03
Tension No,Rd 90.13 0.05 1,802.64
Compression Nb,Rd 53.80 7.23 7.44Combined Axial (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 6.66
Diagonal Tension No,Rd 60.28 8.25 7.31
Compression Nb,Rd 49.18 8.75 5.62Factor 5.35
W 1.0m
Ra Rb
Max Shear Rb= W*17/18
so for ultimate condition W= 1.50*10.0
15.00 kNapply factor from above
Wf= 15.00*5.35= 80.25 kN
so maximum shear is as above Ultimate Qu= Wf*17/18
= (80.25*17)/18= 75.79 kN
and for allowable valueallowable max shear= 75.79/1.50
= 50.53 kN
Shear values Ultimate 75.79 kNAllowable 50.53 kN
18.00m
Alan white design
Page 56
Project : Apollo 1.3m X-beamElement : 18m X-Beam ResultsJob Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Loadcase Ultimate AllowableNo. Moment Moment1 UDL 121.50 81.002 Point 108.68 72.453 Third 108.90 72.604 Quarter 116.10 77.40
Loadcase Ultimate AllowableNo. Shear Shear5 End Shear 75.79 50.53
Max Allowable Moment = 72.50 kNm
Max Allowable Shear = 50.50 kN
18.0m X-BEAM
Alan white design
Page 57
From 18m 1.3m X-Beam Results with restraint to compression chord at 1.0m c/c:
For simply supported Apollo single 1.3m X-BEAM TO EUROCODE EN 1999-1-1
Allowable Bending Moment 72.50 kNmAllowable Shear 50.50 kN
Allowable loads for load distributionsType of Load
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18Uniformly Distributed load kN/m 50.5 33.7 25.3 20.2 16.1 11.8 9.1 7.2 5.8 4.8 4.0 3.4 3.0 2.6 2.3 2.0 1.8Total UDL kN 101.0 101.0 101.0 101.0 96.7 82.9 72.5 64.4 58.0 52.7 48.3 44.6 41.4 38.7 36.3 34.1 32.2Single point load (mid Point) kN 101.0 96.7 72.5 58.0 48.3 41.4 36.3 32.2 29.0 26.4 24.2 22.3 20.7 19.3 18.1 17.1 16.1Two point loads (third points) Each kN 50.5 50.5 50.5 43.5 36.3 31.1 27.2 24.2 21.8 19.8 18.1 16.7 15.5 14.5 13.6 12.8 12.1Three point loads ( quarter points) Each kN 33.7 33.7 33.7 29.0 24.2 20.7 18.1 16.1 14.5 13.2 12.1 11.2 10.4 9.7 9.1 8.5 8.1Type of Load
19 20 21 22 23 24 25 26 27 28 29 30Uniformly Distributed load kN/m 1.6 1.5 1.3 1.2 1.1 1.0 0.9 0.9 0.8 0.7 0.7 0.6Total UDL kN 30.5 29.0 27.6 26.4 25.2 24.2 23.2 22.3 21.5 20.7 20.0 19.3Single point load (mid Point) kN 15.3 14.5 13.8 13.2 12.6 12.1 11.6 11.2 10.7 10.4 10.0 9.7Two point loads (third points) Each kN 11.4 10.9 10.4 9.9 9.5 9.1 8.7 8.4 8.1 7.8 7.5 7.3Three point loads ( quarter points) Each kN 7.6 7.3 6.9 6.6 6.3 6.0 5.8 5.6 5.4 5.2 5.0 4.8
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.3. Maximum capacity of a point load mid way between nodes is 15kN but overall buckling of the top chord should be
checked if loads are placed other than at restrained loads. Compression chord restraint required at 1.0m c/c4. Factor of Safety = 1.655. Calculations as per BS EN 1999-1-1
Clear span (m)
Clear span (m)
Alan white design
Page 58
Project : Apollo 1.3m X-beamElement : 24m X-Beam ResultsJob Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
24m X-Beam Results
Alan white design
Page 59
Project : Apollo 1.3m X-beamElement : 24m X-Beam ResultsJob Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 1 UDL load 10kN/m applied along beam
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.91 1.15
Shear VRd 32.91 3.15 10.45
Tension No,Rd 90.13 284.43 0.32
Compression Nb,Rd 103.22 853.46 0.12Deflection d 240.00 783.56 0.31Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 0.11
Vertical Moment Mc,Rd 0.91 0.35 2.61
Shear VRd 47.79 0.52 91.55
Tension No,Rd 90.13 3.56 25.32
Compression Nb,Rd 53.80 77.40 0.70Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 0.58
Diagonal Tension No,Rd 60.28 96.36 0.63
Compression Nb,Rd 49.18 107.48 0.46Factor 0.11
Ra Rb
Max Moment= WL2/8
so for ultimate condition W= 1.5*10
15.00 kNapply factor from above
Wf= 15*0.11= 1.65 kN
so maximum moment is as above Ultimate Mu= Wf*24^2/8
= (1.65*24^2)/8= 118.80 kNm
and for allowable valueallowable max moment= 118.80/1.50
= 79.20 kNm
Moment values Ultimate 118.80 kNmAllowable 79.20 kNm
24.00m
Alan white design
w w
Page 60
Project : Apollo 1.3m X-beamElement : 24m X-Beam ResultsJob Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 2 Point load 10kN load applied at midspan of beam
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.10 10.98
Shear VRd 32.91 0.27 120.11
Tension No,Rd 90.13 38.14 2.36
Compression Nb,Rd 103.22 80.30 1.29Deflection d 240.00 65.11 3.69Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 1.18
Vertical Moment Mc,Rd 0.91 0.02 41.23
Shear VRd 47.79 0.03 1,448.15
Tension No,Rd 90.13 0.28 321.90
Compression Nb,Rd 53.80 5.45 9.87Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 8.35
Diagonal Tension No,Rd 60.28 5.55 10.86
Compression Nb,Rd 49.18 5.81 8.46Factor 1.18
W 12.00m
Ra RbMax Moment= WL/4
so for ultimate condition W= 1.50*10
= 15.00 kNapply factor from above
Wf= 15*1.18= 17.70 kN
so maximum moment is as above Ultimate Mu= Wf*24/4
= 17.70*24/4= 106.20 kNm
and for allowable valueallowable max moment= 106.20/1.50
= 70.80 kNm
Moment values Ultimate 106.20 kNmAllowable 70.80 kNm
24.00m
Alan white design
Page 61
Project : Apollo 1.3m X-beamElement : 24m X-Beam ResultsJob Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 3 PL at third points 10kN load applied at each of the two third points
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.12 8.77
Shear VRd 32.91 0.34 96.51
Tension No,Rd 90.13 35.35 2.55
Compression Nb,Rd 103.22 106.06 0.97Deflection d 240.00 100.32 2.39Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 0.90
Vertical Moment Mc,Rd 0.91 0.04 25.20
Shear VRd 47.79 0.06 868.89
Tension No,Rd 90.13 0.48 187.78
Compression Nb,Rd 53.80 7.10 7.58Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 6.15
Diagonal Tension No,Rd 60.28 9.91 6.08
Compression Nb,Rd 49.18 10.32 4.77Factor 0.90
8.0m W W 8.0m
Ra Rb
Max Moment= WL/3
so for ultimate condition W= 1.50*10
15.00 kNapply factor from above
Wf= 15.00*0.90= 13.50 kN
so maximum moment is as above Ultimate Mu= Wf*L/3
= (13.50*24)/3= 108.00 kNm
and for allowable valueallowable max moment= 108.00/1.50
= 72.00 kNm
Moment values Ultimate 108.00 kNmAllowable 72.00 kNm
24.00m
Alan white design
Page 62
Project : Apollo 1.3m X-beamElement : 24m X-Beam ResultsJob Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 4 Load at quarter points10kN load applied at each of the three quarter points
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.40 2.59
Shear VRd 32.91 0.46 71.39
Tension No,Rd 90.13 56.08 1.61
Compression Nb,Rd 103.22 152.11 0.68Deflection d 240.00 136.12 1.76Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 0.57
Vertical Moment Mc,Rd 0.91 0.05 17.44
Shear VRd 47.79 0.08 604.92
Tension No,Rd 90.13 0.65 138.66
Compression Nb,Rd 53.80 10.21 5.27Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 4.27
Diagonal Tension No,Rd 60.28 14.26 4.23
Compression Nb,Rd 49.18 14.82 3.32Factor 0.57
6.00m 6.00m 6.00m 6.00m
Ra Rb
Max Moment= WL/2
so for ultimate condition W= 1.50*10
15.00 kNapply factor from above
Wf= 15.00*0.57= 8.55 kN
so maximum moment is as above Ultimate Mu= Wf*L/2
= (8.55*24)/2= 102.60 kNm
and for allowable valueallowable max moment= 102.60/1.50
= 68.40 kNm
Moment values Ultimate 102.60 kNmAllowable 68.40 kNm
24.00m
Alan white design
Page 63
Project : Apollo 1.3m X-beamElement : 24m X-Beam ResultsJob Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 5 End Shear 10kN load applied at a 1.0m distance from the support
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.08 13.37
Shear VRd 32.91 0.31 105.48
Tension No,Rd 90.13 4.55 19.81
Compression Nb,Rd 103.22 16.22 6.36Deflection d 240.00 15.38 15.60Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 4.63
Vertical Moment Mc,Rd 0.91 0.02 45.36
Shear VRd 47.79 0.03 1,706.74
Tension No,Rd 90.13 0.07 1,287.60
Compression Nb,Rd 53.80 7.54 7.14Combined Axial (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 6.38
Diagonal Tension No,Rd 60.28 8.69 6.94
Compression Nb,Rd 49.18 9.20 5.35Factor 4.63
W 1.0m
Ra Rb
Max Shear Rb= W*23/24
so for ultimate condition W= 1.50*10.0
15.00 kNapply factor from above
Wf= 15.00*4.63= 69.45 kN
so maximum shear is as above Ultimate Qu= Wf*23/24
= (69.45*23)/24= 66.56 kN
and for allowable valueallowable max shear= 66.56/1.50
= 44.37 kN
Shear values Ultimate 66.56 kNAllowable 44.37 kN
24.00m
Alan white design
Page 64
Project : Apollo 1.3m X-beamElement : 24m X-Beam ResultsJob Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Loadcase Ultimate AllowableNo. Moment Moment1 UDL 118.80 79.202 Point 106.20 70.803 Third 108.00 72.004 Quarter 102.60 68.40
Loadcase Ultimate AllowableNo. Shear Shear5 End Shear 66.56 44.37
Max Allowable Moment = 68.25 kNm
Max Allowable Shear = 44.25 kN
24.0m X-BEAM
Alan white design
Page 65
From 24m 1.3m X-Beam Results with restraint to compression chord at 1.0m c/c:
For simply supported Apollo single 1.3m X-BEAM TO EUROCODE EN 1999-1-1
Allowable Bending Moment 68.25 kNmAllowable Shear 44.25 kN
Allowable loads for load distributionsType of Load
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18Uniformly Distributed load kN/m 44.3 29.5 22.1 17.7 14.8 11.1 8.5 6.7 5.5 4.5 3.8 3.2 2.8 2.4 2.1 1.9 1.7Total UDL kN 88.5 88.5 88.5 88.5 88.5 78.0 68.3 60.7 54.6 49.6 45.5 42.0 39.0 36.4 34.1 32.1 30.3Single point load (mid Point) kN 88.5 88.5 68.3 54.6 45.5 39.0 34.1 30.3 27.3 24.8 22.8 21.0 19.5 18.2 17.1 16.1 15.2Two point loads (third points) Each kN 44.3 44.3 44.3 41.0 34.1 29.3 25.6 22.8 20.5 18.6 17.1 15.8 14.6 13.7 12.8 12.0 11.4Three point loads ( quarter points) Each kN 29.5 29.5 29.5 27.3 22.8 19.5 17.1 15.2 13.7 12.4 11.4 10.5 9.8 9.1 8.5 8.0 7.6Type of Load
19 20 21 22 23 24 25 26 27 28 29 30Uniformly Distributed load kN/m 1.5 1.4 1.2 1.1 1.0 0.9 0.9 0.8 0.7 0.7 0.6 0.6Total UDL kN 28.7 27.3 26.0 24.8 23.7 22.8 21.8 21.0 20.2 19.5 18.8 18.2Single point load (mid Point) kN 14.4 13.7 13.0 12.4 11.9 11.4 10.9 10.5 10.1 9.8 9.4 9.1Two point loads (third points) Each kN 10.8 10.2 9.8 9.3 8.9 8.5 8.2 7.9 7.6 7.3 7.1 6.8Three point loads ( quarter points) Each kN 7.2 6.8 6.5 6.2 5.9 5.7 5.5 5.3 5.1 4.9 4.7 4.6
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.3. Maximum capacity of a point load mid way between nodes is 15kN but overall buckling of the top chord should be
checked if loads are placed other than at restrained loads. Compression chord restraint required at 1.0m c/c4. Factor of Safety = 1.655. Calculations as per BS EN 1999-1-1
Clear span (m)
Clear span (m)
Alan white design
Page 66
Project : Apollo 1.3m X-beamElement : 30m X-Beam ResultsJob Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
30m X-Beam Results
Alan white design
Page 67
Project : Apollo 1.3m X-beamElement : 30m X-Beam ResultsJob Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 1 UDL load 10kN/m applied along beam
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 1.20 0.87
Shear VRd 32.91 4.12 7.99
Tension No,Rd 90.13 444.73 0.20
Compression Nb,Rd 103.22 1,334.35 0.08Deflection d 300.00 1,867.83 0.16Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 0.07
Vertical Moment Mc,Rd 0.91 0.44 2.06
Shear VRd 47.79 0.67 71.86
Tension No,Rd 90.13 5.73 15.73
Compression Nb,Rd 53.80 95.25 0.56Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 0.47
Diagonal Tension No,Rd 60.28 122.10 0.49
Compression Nb,Rd 49.18 134.64 0.37Factor 0.07
Ra Rb
Max Moment= WL2/8
so for ultimate condition W= 1.5*10
15.00 kNapply factor from above
Wf= 15*0.07= 1.05 kN
so maximum moment is as above Ultimate Mu= Wf*30^2/8
= (1.05*30^2)/8= 118.13 kNm
and for allowable valueallowable max moment= 118.13/1.50
= 78.75 kNm
Moment values Ultimate 118.13 kNmAllowable 78.75 kNm
30.00m
Alan white design
w w
Page 68
Project : Apollo 1.3m X-beamElement : 30m X-Beam ResultsJob Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 2 Point load 10kN load applied at midspan of beam
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.11 9.75
Shear VRd 32.91 0.30 111.18
Tension No,Rd 90.13 49.06 1.84
Compression Nb,Rd 103.22 104.06 0.99Deflection d 300.00 128.15 2.34Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 0.92
Vertical Moment Mc,Rd 0.91 0.02 43.20
Shear VRd 47.79 0.03 1,493.40
Tension No,Rd 90.13 0.37 243.60
Compression Nb,Rd 53.80 5.36 10.04Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 8.53
Diagonal Tension No,Rd 60.28 5.85 10.30
Compression Nb,Rd 49.18 6.15 8.00Factor 0.92
W 15.0m
Ra RbMax Moment= WL/4
so for ultimate condition W= 1.50*10
= 15.00 kNapply factor from above
Wf= 15*0.92= 13.80 kN
so maximum moment is as above Ultimate Mu= Wf*30/4
= 13.80*30/4= 103.50 kNm
and for allowable valueallowable max moment= 103.50/1.50
= 69.00 kNm
Moment values Ultimate 103.50 kNmAllowable 69.00 kNm
30.00m
Alan white design
Page 69
Project : Apollo 1.3m X-beamElement : 30m X-Beam ResultsJob Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 3 PL at third points 10kN load applied at each of the two third points
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.14 7.67
Shear VRd 32.91 0.38 87.76
Tension No,Rd 90.13 45.26 1.99
Compression Nb,Rd 103.22 134.19 0.77Deflection d 300.00 195.94 1.53Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 0.72
Vertical Moment Mc,Rd 0.91 0.04 24.52
Shear VRd 47.79 0.06 853.37
Tension No,Rd 90.13 0.61 147.76
Compression Nb,Rd 53.80 7.26 7.41Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 6.01
Diagonal Tension No,Rd 60.28 10.20 5.91
Compression Nb,Rd 49.18 10.68 4.60Factor 0.72
10.00m W W 10.00m
Ra Rb
Max Moment= WL/3
so for ultimate condition W= 1.50*10
15.00 kNapply factor from above
Wf= 15.00*0.72= 10.80 kN
so maximum moment is as above Ultimate Mu= Wf*L/3
= (10.80*30)/3= 108.00 kNm
and for allowable valueallowable max moment= 108.00/1.50
= 72.00 kNm
Moment values Ultimate 108.00 kNmAllowable 72.00 kNm
30.00m
Alan white design
Page 70
Project : Apollo 1.3m X-beamElement : 30m X-Beam ResultsJob Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 4 Load at quarter points10kN load applied at each of the three quarter points
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.16 6.48
Shear VRd 32.91 0.50 66.35
Tension No,Rd 90.13 71.41 1.26
Compression Nb,Rd 103.22 192.22 0.54Deflection d 300.00 263.65 1.14Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 0.51
Vertical Moment Mc,Rd 0.91 0.06 15.37
Shear VRd 47.79 0.09 562.22
Tension No,Rd 90.13 3.56 25.32
Compression Nb,Rd 53.80 10.34 5.20Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 4.12
Diagonal Tension No,Rd 60.28 14.55 4.14
Compression Nb,Rd 49.18 16.71 2.94Factor 0.51
7.50m W 7.50m W 7.50m W 7.50m
Ra Rb
Max Moment= WL/2
so for ultimate condition W= 1.50*10
15.00 kNapply factor from above
Wf= 15.00*0.51= 7.65 kN
so maximum moment is as above Ultimate Mu= Wf*L/2
= (7.65*30)/2= 114.75 kNm
and for allowable valueallowable max moment= 114.75/1.50
= 76.50 kNm
Moment values Ultimate 114.75 kNmAllowable 76.50 kNm
30.00m
Alan white design
Page 71
Project : Apollo 1.3m X-beamElement : 30m X-Beam ResultsJob Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Load Comb. 5 End Shear 10kN load applied at a 1.0m distance from the support
Element Action Formula Ultimate Calculated Factor
Boom Moment Mc,Rd 1.04 0.08 12.88
Shear VRd 32.91 0.33 101.26
Tension No,Rd 90.13 6.13 14.70
Compression Nb,Rd 103.22 21.11 4.89Deflection d 300.00 31.41 9.55Combined (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 3.78
Vertical Moment Mc,Rd 0.91 0.02 43.20
Shear VRd 47.79 0.03 1,592.96
Tension No,Rd 90.13 0.10 901.32
Compression Nb,Rd 53.80 7.81 6.89Combined Axial (Ned/NRd)
1.3 + [(Med,x/Mrd,x)
1.7]0.6 < 1.0 1.00 6.15
Diagonal Tension No,Rd 60.28 9.07 6.65
Compression Nb,Rd 49.18 9.61 5.12Factor 3.78
W 1.0m
Ra Rb
Max Shear Rb= W*29/30
so for ultimate condition W= 1.50*10.0
15.00 kNapply factor from above
Wf= 15.00*3.78= 56.70 kN
so maximum shear is as above Ultimate Qu= Wf*29/30
= (56.70*29)/30= 54.81 kN
and for allowable valueallowable max shear= 54.81/1.50
= 36.54 kN
Shear values Ultimate 54.81 kNAllowable 36.54 kN
30.00m
Alan white design
Page 72
Project : Apollo 1.3m X-beamElement : 30m X-Beam ResultsJob Number : V0095 By: mo Date: Nov 17Document No : 001C Checked: mmr Date: Nov 17
Loadcase Ultimate AllowableNo. Moment Moment1 UDL 118.13 78.752 Point 103.50 69.003 Third 108.00 72.004 Quarter 114.75 76.50
Loadcase Ultimate AllowableNo. Shear Shear5 End Shear 54.81 36.54
Max Allowable Moment = 69.00 kNm
Max Allowable Shear = 36.50 kN
30.0m X-BEAM
Alan white design
Page 73
From 30m 1.3m X-Beam Results with restraint to compression chord at 1.0m c/c:
For simply supported Apollo single 1.3m X-BEAM TO EUROCODE EN 1999-1
Allowable Bending Moment 69.00 kNmAllowable Shear 36.50 kN
Allowable loads for load distributionsType of Load
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18Uniformly Distributed load kN/m 36.5 24.3 18.3 14.6 12.2 10.4 8.6 6.8 5.5 4.6 3.8 3.3 2.8 2.5 2.2 1.9 1.7Total UDL kN 73.0 73.0 73.0 73.0 73.0 73.0 69.0 61.3 55.2 50.2 46.0 42.5 39.4 36.8 34.5 32.5 30.7Single point load (mid Point) kN 73.0 73.0 69.0 55.2 46.0 39.4 34.5 30.7 27.6 25.1 23.0 21.2 19.7 18.4 17.3 16.2 15.3Two point loads (third points) Each kN 36.5 36.5 36.5 36.5 34.5 29.6 25.9 23.0 20.7 18.8 17.3 15.9 14.8 13.8 12.9 12.2 11.5Three point loads ( quarter points) Each kN 24.3 24.3 24.3 24.3 23.0 19.7 17.3 15.3 13.8 12.5 11.5 10.6 9.9 9.2 8.6 8.1 7.7Type of Load
19 20 21 22 23 24 25 26 27 28 29 30Uniformly Distributed load kN/m 1.5 1.4 1.3 1.1 1.0 1.0 0.9 0.8 0.8 0.7 0.7 0.6Total UDL kN 29.1 27.6 26.3 25.1 24.0 23.0 22.1 21.2 20.4 19.7 19.0 18.4Single point load (mid Point) kN 14.5 13.8 13.1 12.5 12.0 11.5 11.0 10.6 10.2 9.9 9.5 9.2Two point loads (third points) Each kN 10.9 10.4 9.9 9.4 9.0 8.6 8.3 8.0 7.7 7.4 7.1 6.9Three point loads ( quarter points) Each kN 7.3 6.9 6.6 6.3 6.0 5.8 5.5 5.3 5.1 4.9 4.8 4.6
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.3. Maximum capacity of a point load mid way between nodes is 15kN but overall buckling of the top chord should be
checked if loads are placed other than at restrained loads. Compression chord restraint required at 1.0m c/c4. Factor of Safety = 1.655. Calculations as per BS EN 1999-1-1
Clear span (m)
Clear span (m)
Alan white design
Page 74