Job No. Sheet No. Rev.
Job Title
XX
Structural Description
Material Properties
Steel grade
Modulus of elasticity, E 205000 N/mm2
Scheme Design
The two pinned (at the bases) portal frame is stable in its plane due to the moment connection(possibly haunch member) at the eaves and apex. Lateral stability in the orthogonal direction isprovided by the roof diaphragm or wind girder spanning onto orthogonal walls or bracing.
Engineering Calculation Sheet Consulting Engineers jXXX 1
CONSULTING
E N G I N E E R S
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
Structure Design - Steel Portal Frame 19-08-15Made by Date Chd.
Drg. Ref.
Member/Location
Job No. Sheet No. Rev.
Job Title
XX
Wind Loading Definition
Wind net drag pressure, pWIND = qs.I.Cp.Ca 0.65 I.Cp kPa
Site (mean) wind speed (10m mean hourly or gust / 1.62), Vs 20.1 m/s
Note that V s=V b .S a .S d .S s .S p , V b=basic (mean) wind speed (London 21m/s) [BS6399-2];
Note that V s=(V S /S b ).M d .M z,cat .M s .M h , V S=station (3s-gust) wind speed (KL 33.5m/s) [MS1553];
Terrain factor, Sb 1.62
Effective height, He 6.500 m
Effective (3s-gust) wind speed, Ve = Vs.Sb 32.6 m/s
Dynamic wind pressure, qs = 0.613Ve2 0.65 kPa BS6399-2
Size effect factor for external and internal pressures, Ca (note 1.000 is conservative)1.000 cl.2.1.3.4
cl.2.6.1, cl.2.6.2
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
2
Structure Design - Steel Portal Frame 19-08-15
CONSULTING
E N G I N E E R S
Engineering Calculation Sheet Consulting Engineers jXXX
Made by Date Chd.
Drg. Ref.
Member/Location
Job No. Sheet No. Rev.
Job Title
XX
Roof Loading (On Slope Where Relevant)
Roof covering, pSDL,1 (usually 0.10kPa to 0.20kPa) 0.42mm BMT 0.04 kPa
Purlins, pSDL,2 = ωSDL,2/sp 0.06 kPa
Purlins dead load UDL, ωSDL,2 C20024 0.07 kN/m
=station (3s-gust) wind speed (KL 33.5m/s) [MS1553]; Purlins spacing, sp (usually 1.500m to 2.000m) 1.200 m
Ceiling and services, pSDL,3 (usually 0.10kPa to 0.30kPa) 0.00 kPa
Additional super dead load, pSDL,4 0.00 kPa
cl.2.6.1, cl.2.6.2
Total super dead load, pΣSDL=pSDL,1+pSDL,2+pSDL,3+pSDL,4 0.10 kPa
Live load, pLL 0.25 kPa
Snow load, pSNOW (usually 0.60kPa to 0.75kPa) 0.00 kPa
Note for the design of the roof (and only the roof) the greater of the live load and snow load is adopted,
with the lesser value put to zero in view of the fact that design live and snow loads are not simultaneous;
Impermeability of roof cladding, IR BS6399-2
Wind pressure coefficients, IR.Cp T.10, T.14
Include internal wind pressure coefficient (T.10 applicable, T.14 not applicable) ? T.16, T.17
Enclosed building or building with dominant openings ? T.16, T.17
Case A: No Dominant Openings
Internal pressure as max positive or min negative ? T.16
Case B: With Dominant Openings
Wall with dominant opening BS6399-2
Ratio of dominant opening area to remaining openings (where applicable) T.17
α BS6399-2
(degrees) IR.Cp,d IR.Cp,u IR.Cp,d IR.Cp,u T.10, T.14
5 -0.64 -1.24 -1.04 -1.04 BS6399-2
15 -0.44 -1.04 -1.14 -1.14 T.16, T.17
30 -0.24 -0.84 -1.14 -1.14
45 0.06 -0.64 -0.94 -0.94
60 0.16 0.16 -1.24 -1.24
75 0.16 0.16 -1.44 -1.44
Note that the pressure coefficient, C p is the net pressure coefficient, C p=C pe -C pi
where C pe is the external and C pi the internal pressure coefficients, respectively;
Note − ve C p indicates uplift;
Structure Design - Steel Portal Frame 19-08-15
CONSULTING
E N G I N E E R S
Windward Leeward
Engineering Calculation Sheet Consulting Engineers jXXX 3
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsxMade by Date Chd.
Drg. Ref.
Member/Location
Job No. Sheet No. Rev.
Job Title
XX
Wall Loading
Wall covering, pSDL,W1 (usually 0.10kPa to 0.20kPa) 0.00 kPa
Rails, pSDL,W2 = ωSDL,W2/sr 0.00 kPa
Rails dead load UDL, ωSDL,W2 0.00 kN/m
Rails spacing, sr (usually 1.500m to 2.000m) 1.500 m
Additional super dead load, pSDL,W3 0.00 kPa
Total super dead load, pΣSDL,W=pSDL,W1+pSDL,W2+pSDL,W3 0.00 kPa
Impermeability of wall cladding, IW BS6399-2
Include wind internal pressure coefficient ? T.16, T.17
Enclosed building or building with dominant openings ? T.16, T.17
Case A: No Dominant Openings
Internal pressure as max positive or min negative ? T.16
Case B: With Dominant Openings
Wall with dominant opening
Ratio of dominant opening area to remaining openings (where applicable) T.17
Windward wind pressure coefficient, IW.Cp,windward, with Cp = 0.21 0.21 T.5, T.16, T.17
Leeward wind pressure coefficient, IW.Cp,leeward, with Cp = 1.14 1.14 T.5, T.16, T.17
Note that the pressure coefficient, C p is the net pressure coefficient, C p=C pe -C pi where C pe
is the external and C pi the internal pressure coefficients, respectively;
Note that in the case of internal pressure without dominant openings, the critical wall pressure
coefficient of T.16 BS6399-2 is applied to the windward and leeward walls simultaneously;
Note that in the case of internal pressure with dominant openings, the critical wall pressure
coefficient of T.17 BS6399-2 is applied to the windward and leeward walls simultaneously;
Note +ve C p indicates rightwards action;
CONSULTING
E N G I N E E R S 4
Engineering Calculation Sheet Consulting Engineers
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
Structure Design - Steel Portal Frame 19-08-15
jXXX
Made by Date Chd.
Drg. Ref.
Member/Location
Job No. Sheet No. Rev.
Job Title
XX
Portal Frame Dimensions
T.5, T.16, T.17
T.5, T.16, T.17
Frame span, L (usually 15.000m to 50.000m) 10.000 m
Frame eaves height, h (usually 5.000m to 15.000m) 6.000 m
Frame rise, r 0.500 m
Frame span to frame rise ratio, L/r 20.0
Frame spacing, s (usually 5.000m to 8.000m, commonly 6.000mm or 7.500m) 9.000 m
Frame length of slope, q = √(L2/4 + r2) 5.025 m
Frame pitch angle, α = arctan (2r/L) (usually 5.0° to 10.0°, commonly 6.0°) 5.7 degrees OK
Note that the minimum rafter slope is 2.5° whilst the maximum is 25.0°;
Windward roof downward wind pressure coefficient, IR.Cp,d,windward -0.62
Windward roof upward wind pressure coefficient, IR.Cp,u,windward -1.22
Leeward roof downward wind pressure coefficient, IR.Cp,d,leeward -1.04
Leeward roof upward wind pressure coefficient, IR.Cp,u,leeward -1.04
CONSULTING
E N G I N E E R S
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
Structure Design - Steel Portal Frame 19-08-15
Engineering Calculation Sheet Consulting Engineers jXXX 5
Made by Date Chd.
Drg. Ref.
Member/Location
Job No. Sheet No. Rev.
Job Title
XX
Rafter section
Total depth, dr (usually L/60 = 167mm) 528.3 mm
Web thickness, tr 9.6 mm
Flange thickness, Tr 13.2 mm
Design strength, py,r 275 N/mm2
Gross area of section, Ag,r 105.0 cm2
Major plane second moment of area, Ir 47539 cm4
Minor plane radius of gyration, ry,r 4.4 cm
Major plane plastic modulus, sr 2059 cm3
Moment capacity (low shear, compact), Mc,r = py,r . sr 566 kNm
Torsional index, xr 41.6
Rafters dead load UDL, ωDL 0.81 kN/m
Rafters dead load pressure, pDL = ωDL/s (usually 0.10kPa to 0.30kPa) 0.09 kPa
Stanchion section
Total depth, ds (usually L/50 = 200mm) 528.3 mm
Web thickness, ts 9.6 mm
Flange thickness, Ts 13.2 mm
Design strength, py,s 275 N/mm2
Gross area of section, Ag,s 105.0 cm2
Major plane second moment of area, Is 47539 cm4
Minor plane radius of gyration, ry,s 4.4 cm
Major plane plastic modulus, ss 2059 cm3
Moment capacity (low shear, compact), Mc,s = py,s . ss 566 kNm
Torsional index, xs 41.6
Stanchion dead load UDL, ωDL,S 0.81 kN/m
Stanchion dead load, PS,DL = ωDL,S.h 4.8 kN
Note that the additional section capacity provided by the haunches has been ignored, their other
beneficial stability enhancements have however been considered;
Utilisation Summary
Utilisations and criteria OK
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
Engineering Calculation Sheet Consulting Engineers jXXX
CONSULTING
E N G I N E E R S
Structure Design - Steel Portal Frame 19-08-15
6
Made by Date Chd.
Drg. Ref.
Member/Location
Job No. Sheet No. Rev.
Job Title
XX
Eaves and Apex Haunches
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
CONSULTING
E N G I N E E R S
Engineering Calculation Sheet Consulting Engineers jXXX 7
Structure Design - Steel Portal Frame 19-08-15Made by Date Chd.
Drg. Ref.
Member/Location
Job No. Sheet No. Rev.
Job Title
XX
ULS Load Combinations
Note all loads downwards or rightwards if positive and vice versa;
Combination A (Downward Critical)
Vertical [1.4pΣSDL+1.6pLL+1.6pSNOW].sp.s 5.9 kN
Windward [0.0pWIND,d,windward].sp.s 0.0 kN
Leeward [0.0pWIND,d,leeward].sp.s 0.0 kN
Vertical [1.4pDL+1.4pΣSDL+1.6pLL+1.6pSNOW].s 6.0 kN/m
Windward [0.0pWIND,d,windward].s 0.0 kN/m
Leeward [0.0pWIND,d,leeward].s 0.0 kN/m
Vertical 1.4PS,DL+[1.4pΣSDL,W].s.h 7 kN
Windward [0.0pWIND,windward].s 0.0 kN/m
Leeward [0.0pWIND,leeward].s 0.0 kN/m
Combination B (Downward Critical)
Vertical [1.4pΣSDL+0.0pLL+0.0pSNOW].sp.s 1.5 kN
Windward [1.4pWIND,d,windward].sp.s -6.1 kN
Leeward [1.4pWIND,d,leeward].sp.s -10.3 kN
Vertical [1.4pDL+1.4pΣSDL+0.0pLL+0.0pSNOW].s 2.4 kN/m
Windward [1.4pWIND,d,windward].s -5.1 kN/m
Leeward [1.4pWIND,d,leeward].s -8.6 kN/m
Vertical 1.4PS,DL+[1.4pΣSDL,W].s.h 7 kN
Windward [1.4pWIND,windward].s 1.7 kN/m
Leeward [1.4pWIND,leeward].s 9.3 kN/m
Combination C (Upward Critical)
Vertical [1.0pΣSDL+0.0pLL+0.0pSNOW].sp.s 1.1 kN
Windward [1.4pWIND,u,windward].sp.s -12.0 kN
Leeward [1.4pWIND,u,leeward].sp.s -10.3 kN
Vertical [1.0pDL+1.0pΣSDL+0.0pLL+0.0pSNOW].s 1.7 kN/m
Windward [1.4pWIND,u,windward].s -10.0 kN/m
Leeward [1.4pWIND,u,leeward].s -8.6 kN/m
Vertical 1.0PS,DL+[1.0pΣSDL,W].s.h 5 kN
Windward [1.4pWIND,windward].s 1.7 kN/m
Leeward [1.4pWIND,leeward].s 9.3 kN/m
Combination D (Downward Critical)
Vertical [1.2pΣSDL+1.2pLL+1.2pSNOW].sp.s 4.6 kN
Windward [1.2pWIND,d,windward].sp.s -5.3 kN
Leeward [1.2pWIND,d,leeward].sp.s -8.8 kN
Vertical [1.2pDL+1.2pΣSDL+1.2pLL+1.2pSNOW].s 4.8 kN/m
Windward [1.2pWIND,d,windward].s -4.4 kN/m
Leeward [1.2pWIND,d,leeward].s -7.3 kN/m
Vertical 1.2PS,DL+[1.2pΣSDL,W].s.h 6 kN
Windward [1.2pWIND,windward].s 1.5 kN/m
Leeward [1.2pWIND,leeward].s 8.0 kN/m
Purlin WP,ULS,A
Stanchion PS,ULS,A and
ωS,ULS,A
Purlin WP,ULS,B
Stanchion PS,ULS,B and
ωS,ULS,B
Rafter ωR,ULS,A
Rafter ωR,ULS,B
Stanchion PS,ULS,D and
ωS,ULS,D
Rafter ωR,ULS,D
Purlin WP,ULS,C
Stanchion PS,ULS,C and
ωS,ULS,C
Purlin WP,ULS,D
Rafter ωR,ULS,C
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
Structure Design - Steel Portal Frame 19-08-15
CONSULTING
E N G I N E E R S
Engineering Calculation Sheet Consulting Engineers jXXX 8
Made by Date Chd.
Drg. Ref.
Member/Location
Job No. Sheet No. Rev.
Job Title
XX
SLS Load Combinations
Note all loads downwards or rightwards if positive and vice versa;
Combination SLS (Downward Critical)
Vertical [1.0pΣSDL+1.0pLL+1.0pSNOW].sp.s 3.8 kN
Windward [1.0pWIND,d,windward].sp.s -4.4 kN
Leeward [1.0pWIND,d,leeward].sp.s -7.3 kN
Vertical [1.0pDL+1.0pΣSDL+1.0pLL+1.0pSNOW].s 4.0 kN/m
Windward [1.0pWIND,d,windward].s -3.6 kN/m
Leeward [1.0pWIND,d,leeward].s -6.1 kN/m
Vertical 1.0PS,DL+[1.0pΣSDL,W].s.h 5 kN
Windward [1.0pWIND,windward].s 1.2 kN/m
Leeward [1.0pWIND,leeward].s 6.7 kN/m
Combination SLS (Upward Critical)
Vertical [1.0pΣSDL+0.0pLL+0.0pSNOW].sp.s 1.1 kN
Windward [1.0pWIND,u,windward].sp.s -8.6 kN
Leeward [1.0pWIND,u,leeward].sp.s -7.3 kN
Vertical [1.0pDL+1.0pΣSDL+0.0pLL+0.0pSNOW].s 1.7 kN/m
Windward [1.0pWIND,u,windward].s -7.2 kN/m
Leeward [1.0pWIND,u,leeward].s -6.1 kN/m
Vertical 1.0PS,DL+[1.0pΣSDL,W].s.h 5 kN
Windward [1.0pWIND,windward].s 1.2 kN/m
Leeward [1.0pWIND,leeward].s 6.7 kN/m
Purlin WP,SLS
Rafter ωR,SLS
Stanchion PS,SLS and
ωS,SLS
Stanchion PS,SLS and
ωS,SLS
Engineering Calculation Sheet Consulting Engineers jXXX 9
Structure Design - Steel Portal Frame 19-08-15
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
CONSULTING
E N G I N E E R S
Purlin WP,SLS
Rafter ωR,SLS
Made by Date Chd.
Drg. Ref.
Member/Location
Job No. Sheet No. Rev.
Job Title
XX
ULS Structural (Plastic Collapse) Analysis (Combination Case A Only, No Wind Loadcase)
Critical combination case Combination C
Critical combination case uniformly distributed ULS load, ωR,ULS,critical 8.3 kN/m
Note that the critical combination case is that which produces the greatest uniformly distributed load,
i.e. ω R,ULS,critical = MAX(ω R,ULS,A,vertical+windward , ω R,ULS,B,vertical+windward ,
MAX[ABS(ω R,ULS,C,vertical+windward ),ABS(ω R,ULS,C,vertical+leeward )], ω R,ULS,D,vertical+windward );
Critical combination case analysis validity Analysis Not Valid
Frame span to frame eaves height ratio, L/h 1.67
Frame rise to frame span ratio, r/L 0.050
Frame uniformly distributed ULS load, ωR,ULS,PC = ωR,ULS,A,vertical 6.0 kN/m
Frame horizontal base force ratio, HFR 0.15
Frame ULS horizontal base force, HF = HFR.ωR,ULS,PC.L 9 kN
Structure Design - Steel Portal Frame 19-08-15
Engineering Calculation Sheet Consulting Engineers jXXX 10
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
CONSULTING
E N G I N E E R S
Made by Date Chd.
Drg. Ref.
Member/Location
Job No. Sheet No. Rev.
Job Title
XX
Frame rafter Mp ratio, Mpr 0.038
Frame rafter ULS (apex) Mp required, Mp,rafter = Mpr.ωR,ULS,PC.L2 23 kNm OK
Note rafter moment capacity excluding haunch should be at least λ r .M p,rafter with the LTB BS5950
effective length as calculated within the ULS rafter LTB restraint design sections as maximum 5.3.4
distance between intermediate restraints L m,r ;
Frame stanchion Mp ratio, Mpl 0.070
Frame stanchion ULS (eaves) Mp required, Mp,stanchion = Mpl.ωR,ULS,PC.L2 42 kNm OK
Note stanchion moment capacity should be at least λ r .M p,stanchion with the LTB effective length BS5950
as calculated within the ULS stanchion LTB restraint design sections as maximum distance 5.3.4
between full torsional restraints L m,s or L t,s depending on the method adopted;
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
jXXX 11
Engineering Calculation Sheet Consulting Engineers
CONSULTING
E N G I N E E R S
Structure Design - Steel Portal Frame 19-08-15Made by Date Chd.
Drg. Ref.
Member/Location
Job No. Sheet No. Rev.
Job Title
XX
ULS Structural (Elastic) Analysis (Any Combination Case Including Wind Loadcases)
Note sign convention for bending
moment is positive for tension
within frame;
CONSULTING
E N G I N E E R S
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
jXXX
Engineering Calculation Sheet Consulting Engineers 12
Structure Design - Steel Portal Frame 19-08-15Made by Date Chd.
Drg. Ref.
Member/Location
Job No. Sheet No. Rev.
Job Title
XX
Stanchion major plane second moment of area, I1 = Is 47539 cm4
Rafter major plane second moment of area, I2 = Ir 47539 cm4
Frame eaves height, h 6.000 m
Rafter length, s = q 5.025 m
Coefficient, k = (I2/I1).(h/s) 1.19
Frame rise, f = r 0.500 m
Coefficient, φ = f/h 0.08
Coefficient, m = 1+φ 1.08
Coefficient, B = 2(k+1)+m 5.47
Coefficient, C = 1+2m 3.17
Coefficient, N = B+mC 8.90
Frame span, L 10.000 m
Frame ULS horizontal (inward) base force, HF,inward = MAX(0, HA, HE) 41 kN
Frame ULS horizontal (outward) base force, HF,outward = MIN(0, HA, HE) -29 kN
Frame ULS vertical (upward) base force, VF,upward = MAX(0, VA, VE) 37 kN
Frame ULS vertical (downward) base force, VF,downward = MIN(0, VA, VE) -54 kN
Note a negative V F indicates uplift;
Frame rafter ULS (eaves) (-ve) Mp required, Mp,rafter = MIN(0, MB, MD) -83 kNm OK
Note rafter moment capacity excluding haunch should be at least λ r .M p,rafter with the LTB BS5950
effective length as calculated within the ULS rafter LTB restraint design sections as maximum 5.3.4
distance between full torsional restraints (max is L m,r or L t,r depending on the method adopted);
Frame rafter ULS (apex) (+ve) Mp required, Mp,rafter = MAX(0, MC) 37 kNm OK
Note rafter moment capacity excluding haunch should be at least λ r .M p,rafter with the LTB BS5950
effective length as calculated within the ULS rafter LTB restraint design sections as distance 5.3.4
between intermediate restraints (max is L m,r );
Frame rafter ULS (eaves) (+ve) Mp required, Mp,rafter = MAX(0, MB, MD) 144 kNm OK
Note rafter moment capacity excluding haunch should be at least λ r .M p,rafter with the LTB BS5950
effective length as calculated within the ULS rafter LTB restraint design sections as distance 5.3.4
between intermediate restraints (max is L m,r );
Frame rafter ULS (apex) (-ve) Mp required, Mp,rafter = MIN(0, MC) -36 kNm OK
Note rafter moment capacity excluding haunch should be at least λ r .M p,rafter with the LTB BS5950
effective length as calculated within the ULS rafter LTB restraint design sections as distance 5.3.4
between full torsional restraints L t,u,r ;
CONSULTING
E N G I N E E R S
Structure Design - Steel Portal Frame 19-08-15
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
Engineering Calculation Sheet Consulting Engineers jXXX 13
Made by Date Chd.
Drg. Ref.
Member/Location
Job No. Sheet No. Rev.
Job Title
XX
Frame rafter ULS compression Pc required, Pc,rafter = HF,inward.cosα+VF,upward.sin 44 kN
Note rafter axial compression capacity should be at least λ r .P c,rafter with the major plane
flexural buckling effective length as the frame length of slope, q, and the minor plane flexural
buckling effective length as the distance between intermediate restraints (max is L m,r );
Frame rafter ULS tension Pt required, Pt,rafter = HF,outward.cosα+VF,downward.sinα -34 kN
Note rafter axial tension capacity should be at least λ r .P t,rafter ;
Frame stanchion ULS (eaves) (-ve) Mp required, Mp,stanchion = MIN(0, MA, MB, M -83 kNm OK
Note stanchion moment capacity should be at least λ r .M p,stanchion with the LTB effective length BS5950
as calculated within the ULS stanchion LTB restraint design sections as distance between 5.3.4
full torsional restraints (max is L m,s or L t,s depending on the method adopted);
Frame stanchion ULS (eaves) (+ve) Mp required, Mp,stanchion = MAX(0, MA, MB, M 144 kNm OK
Note stanchion moment capacity should be at least λ r .M p,stanchion with the LTB effective length BS5950
as calculated within the ULS stanchion LTB restraint design sections as distance between 5.3.4
intermediate restraints (max is L m,s );
Frame stanchion ULS compression Pc required, Pc,stanchion = VF,upward 37 kN
Note stanchion axial compression capacity should be at least λ r .P c,stanchion with the major plane
flexural buckling effective length as the frame eaves height, h, and the minor plane flexural
buckling effective length as the distance between intermediate restraints (max is L m,s );
Frame stanchion ULS tension Pt required, Pt,stanchion = VF,downward -54 kN
Note stanchion axial tension capacity should be at least λ r .P t,stanchion ;
Frame eaves connection ULS (+ve) moment, CMEAVES,+ = MAX(0, MB, MD) 144 kNm
Frame eaves connection ULS (-ve) moment, CMEAVES,- = MIN(0, MB, MD) -83 kNm
Frame eaves connection ULS shear, CVEAVES = MAX(ABS(VA-PS,ULS), ABS(VE-PS,ULS 59 kN
Frame apex connection ULS (+ve) moment, CMAPEX,+ = MAX(0, MC) 37 kNm
Frame apex connection ULS (-ve) moment, CMAPEX,- = MIN(0, MC) -36 kNm
Maximum frame load factor for frame stability, MAX(λr) 1.01
Note all connection forces should be factored by λ r ;
CONSULTING
E N G I N E E R S
Structure Design - Steel Portal Frame 19-08-15
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
Engineering Calculation Sheet Consulting Engineers jXXX 14
Made by Date Chd.
Drg. Ref.
Member/Location
Made by Date
Job No. Sheet No. Rev.
Job Title
XX
Vertical Horizontal A B C D E
6.0 6.0 0 -36 37 -36 0
0.0 0 0 0 0 0
0.0 0 0 0 0 0
0.0 0 0 0 0 0
0.0 0 0 0 0 0
7 7 0 0 0 0 0
0.0 0.0 0 0 0 0 0
0.0 0.0 0 0 0 0 0
0 -36 37 -36 0
HA HE VA VE
6 6 30 30
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 7 7
0 0 0 0
0 0 0 0
6 6 37 37
Vertical Horizontal A B C D E
2.4 2.4 0 -14 15 -14 0
-5.1 0 15 -16 15 0
-6.1 0 -9 0 9 0
-8.5 0 25 -26 25 0
-10.2 0 15 0 -15 0
7 7 0 0 0 0 0
1.7 1.7 0 15 -2 -16 0
9.3 -9.3 0 87 10 -81 0
0 134 -18 -78 0
HA HE VA VE
2 2 12 12
-3 -3 -19 -6
2 -2 2 -2
-4 -4 -11 -32
-3 3 -3 3
0 0 7 7
-8 3 -3 3
-15 41 -17 17
-28 41 -32 2
CONSULTING
E N G I N E E R S
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
Structure Design - Steel Portal Frame 19-08-15
15
ωS,ULS,windward (kN/m)
ωS,ULS,leeward (kN/m)
ULS Load Combination ADirection Bending Moment (kNm) at Position
ωR,ULS,vertical (kN/m)
Reaction (kN)
PS,ULS (kN)
ωR,ULS,windward (kN/m)
ωR,ULS,leeward (kN/m)
0.0
0.0
jXXX
Engineering Calculation Sheet Consulting Engineers
ωR,ULS,leeward (kN/m) -8.6
ωS,ULS,leeward (kN/m)
Reaction (kN)
PS,ULS (kN)
ωS,ULS,windward (kN/m)
ωR,ULS,windward (kN/m) -5.1
ULS Load Combination BDirection Bending Moment (kNm) at Position
ωR,ULS,vertical (kN/m)
Made by Date
Drg. Ref.
Member/Location
Made by Date Chd.
Job No. Sheet No. Rev.
Job Title
XX
Vertical Horizontal A B C D E
1.7 1.7 0 -10 11 -10 0
-10.0 0 29 -30 29 0
-12.0 0 -18 1 18 0
-8.5 0 25 -26 25 0
-10.2 0 15 0 -15 0
5 5 0 0 0 0 0
1.7 1.7 0 15 -2 -16 0
9.3 -9.3 0 87 10 -81 0
0 144 -36 -50 0
HA HE VA VE
2 2 9 9
-5 -5 -37 -12
3 -3 4 -4
-4 -4 -11 -32
-3 3 -3 3
0 0 5 5
-8 3 -3 3
-15 41 -17 17
-29 36 -54 -12
Vertical Horizontal A B C D E
4.8 4.8 0 -28 29 -28 0
-4.4 0 13 -13 13 0
-5.2 0 -8 0 8 0
-7.3 0 22 -22 22 0
-8.8 0 13 0 -13 0
6 6 0 0 0 0 0
1.5 1.5 0 13 -2 -14 0
8.0 -8.0 0 75 9 -69 0
0 99 2 -83 0
HA HE VA VE
5 5 24 24
-2 -2 -16 -5
1 -1 2 -2
-4 -4 -9 -27
-2 2 -3 3
0 0 6 6
-7 2 -3 3
-12 36 -14 14
-21 38 -14 15
CONSULTING
E N G I N E E R S
Structure Design - Steel Portal Frame
Engineering Calculation Sheet Consulting Engineers
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
19-08-15
jXXX 16
ωS,ULS,leeward (kN/m)
ULS Load Combination CDirection
Bending Moment (kNm) at Position
ωR,ULS,vertical (kN/m)
PS,ULS (kN)
ωS,ULS,windward (kN/m)
ωS,ULS,leeward (kN/m)
Reaction (kN)
Direction
Bending Moment (kNm) at Position
ωR,ULS,vertical (kN/m)
Reaction (kN)
ωR,ULS,windward (kN/m) -4.4
ωR,ULS,leeward (kN/m) -7.3
ωR,ULS,windward (kN/m) -10.0
ωR,ULS,leeward (kN/m) -8.6
ULS Load Combination D
PS,ULS (kN)
ωS,ULS,windward (kN/m)
Made by Date Chd.
Drg. Ref.
Member/Location
Made byMade by Date
Job No. Sheet No. Rev.
Job Title
XX
ULS Rafter LTB Restraint Design (To Critical Gravity Loadcase)
Note purlins attached to the compression flange of the rafter constitutes an LTB restraint,
aka full torsional restraint;
Note rafter stays attached to the compression flange of the rafter together with purlins
attached to the tension flange constitutes an LTB restraint, aka a full torsional restraint;
Note purlins attached to the tension flange of the rafter constitutes a partial torsional restraint;
Structure Design - Steel Portal Frame 19-08-15
Engineering Calculation Sheet Consulting Engineers
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
jXXX 17
CONSULTING
E N G I N E E R S
Made by Date Chd.
Drg. Ref.
Member/Location
Made by
Job No. Sheet No. Rev.
Job Title
XX
A. Zone 1 Haunch Stability
Full torsional restraint at haunch bottom is provided by the combination of a column stiffener
and a CHS or a rail and a column stay;
Full torsional restraint at haunch top is provided by the combination of a purlin and a rafter stay;
Partial torsional restraints (intermediate restraints) are provided by intermediate purlins at max
L i,r allowing the distance between the full torsional restraints to be increased from L m,r to L t,r ;
A.1 Method 1 (Excludes Intermediate Restraint(s), More Conservative) BS5950
Maximum distance between full torsional restraints, Lm,r 1.423 m 5.3.3(a)
Minor plane radius of gyration, ry,r 44 mm
ULS compression stress, fc,r = Pc,rafter/Ag,r 4.2 N/mm2
ULS compression force, Pc,rafter 44.4 kN
Gross area of section, Ag,r 105.0 cm2
Design strength, py,r 275 N/mm2
Torsional index, xr 41.6
A.2 Method 2 (Includes Intermediate Restraint(s), Less Conservative) BS5950
Maximum distance between intermediate restraints, Li,r = Lm,r 1.423 m 5.3.4
Maximum distance between full torsional restraints, Lt,r = Ls,r 2.670 m
Minor plane radius of gyration, ry,r 44 mm
Torsional index, xr 41.6
Haunch depth, Dh 530.9 mm
Rafter section depth including inclination, Ds = dr/cosα 530.9 mm
1.25
Structure Design - Steel Portal Frame 19-08-15
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
Engineering Calculation Sheet Consulting Engineers 18jXXX
CONSULTING
E N G I N E E R S
Made by Date Chd.
Drg. Ref.
Member/Location
Made by Date Chd.
Job No. Sheet No. Rev.
Job Title
XX
B. Zone 2 Rafter Stability
Full torsional restraint at Zone 2 bottom is provided by the combination of a purlin and a rafter stay;
Full torsional restraint at Zone 2 top is provided by the combination of a purlin and a rafter stay;
Maximum distance between full torsional restraints within Zone 2 can be conservatively calculated
as L m,r or L t,r (with intermediate restraints at L i,r ) as calculated within Zone 1;
C. Zone 3 Rafter Stability
Full torsional restraints within Zone 3 are provided by purlins;
D. Zone 4 Rafter Stability
Full torsional restraint at Zone 4 bottom is provided by the combination of a rafter stay and a purlin;
Full torsional restraint at Zone 4 top is provided by the combination of an apex stiffener and a purlin;
Maximum distance between full torsional restraints within Zone 4 can be calculated as L m,r (not L t,r )
as calculated within Zone 1;
Structure Design - Steel Portal Frame
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
19-08-15
jXXX 19
Engineering Calculation Sheet Consulting Engineers
CONSULTING
E N G I N E E R S
Made by Date Chd.
Drg. Ref.
Member/Location
Date Chd.
Job No. Sheet No. Rev.
Job Title
XX
ULS Rafter LTB Restraint Design (To Critical Wind Uplift Loadcase)
A. Zones 1 and 2 Haunch and Rafter Stability
Full torsional restraints within Zones 1 and 2 are provided by purlins;
B. Zones 5 and 6 Rafter Stability
Full torsional restraint at Zone 5 bottom is provided by the combination of a purlin and a rafter stay;
Full torsional restraint at Zone 5 top is provided by the combination of a purlin and a rafter stay;
Full torsional restraint at Zone 6 bottom is provided by the combination of a purlin and a rafter stay;
Full torsional restraint at Zone 6 top is provided by the combination of a purlin and a rafter stay;
Maximum distance between full torsional restraints within Zone 5 and 6 can be calculated as
required to limit effective LTB length to ensure sufficient moment capacity;
Maximum distance between full torsional restraints, Lt,u,r 1.500 m
Structure Design - Steel Portal Frame 19-08-15
CONSULTING
E N G I N E E R S
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
jXXX 20
Engineering Calculation Sheet Consulting Engineers
Made by Date Chd.
Drg. Ref.
Member/Location
Job No. Sheet No. Rev.
Job Title
XX
ULS Stanchion LTB Restraint Design (To Critical Gravity Loadcase)
Note rails attached to the compression flange of the stanchion constitutes an LTB restraint,
aka full torsional restraint;
Note column stays attached to the compression flange of the stanchion together with rails
attached to the tension flange constitutes an LTB restraint, aka a full torsional restraint;
Note rails attached to the tension flange of the stanchion constitutes a partial torsional restraint ;
A. Stanchion Stability Near Haunch
Full torsional restraint at stanchion top (haunch bottom) is provided by the combination of a
column stiffener and a CHS or a rail and a column stay;
Full torsional restraint at stanchion intermediate is provided by the combination of a rail and a
column stay;
Partial torsional restraints (intermediate restraints) are provided by intermediate rails at max
L i,s allowing the distance between the full torsional restraints to be increased from L m,s to L t,s ;
A.1 Method 1 (Excludes Intermediate Restraint(s), More Conservative) BS5950
Maximum distance between full torsional restraints, Lm,s 1.426 m 5.3.3(a)
Minor plane radius of gyration, ry,s 44 mm
ULS compression stress, fc,s = Pc,stanchion/Ag,s 3.5 N/mm2
ULS compression force, Pc,stanchion 37.0 kN
Gross area of section, Ag,s 105.0 cm2
Design strength, py,s 275 N/mm2
Torsional index, xs 41.6
A.2 Method 2 (Includes Intermediate Restraint(s), Less Conservative) BS5950
Maximum distance between intermediate restraints, Li,s = Lm,s 1.426 m 5.3.4
Maximum distance between full torsional restraints, Lt,s = Ls,s 3.337 m
Minor plane radius of gyration, ry,s 44 mm
Torsional index, xs 41.6
K1 = 1.00 1.00
19-08-15
jXXX 21
Engineering Calculation Sheet Consulting Engineers
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
Structure Design - Steel Portal Frame
CONSULTING
E N G I N E E R S
Made by Date Chd.
Drg. Ref.
Member/Location
Job No. Sheet No. Rev.
Job Title
XX
ULS Stanchion LTB Restraint Design (To Critical Wind Uplift Loadcase)
A. Stanchion Stability Near Haunch
Full torsional restraints within stanchion near haunch are provided by rails;
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
jXXX
Structure Design - Steel Portal Frame 19-08-15
22
Engineering Calculation Sheet Consulting Engineers
CONSULTING
E N G I N E E R S
Made by Date Chd.
Drg. Ref.
Member/Location
Job No. Sheet No. Rev.
Job Title
XX
ULS In-Plane Single Bay Frame Sway Instability
A. Sway Check Method BS5950
5.5.4.2
Sway check criterion 17.0 <= 501.4 OK
(critical gravity)
Sway check criterion 147.2
(critical wind uplift)
Rafter section depth, D = dr 528.3 mm
Frame span, L 10.000 m
Frame eaves height, h 6.000 m
Rafter total developed length, Lr = L/cosα 10.050 m
Rafter design strength, py,r 275 N/mm2
Effective frame span 9.000 m
Rafter section depth including inclination, Ds = dr/cosα 530.9 mm
Haunch depth, Dh 530.9 mm
Haunch length, Lh 1.000 m
Arching ratio 0.07
Frame uniformly distributed ULS load, ωR,ULS,A,vertical 6.0 kN/m
Frame total ULS load, Wr = ωR,ULS,A,vertical.L 60 kN
Rafter major plane plastic modulus, sr 2059 cm3
Frame total ULS load for plastic failure of rafters as fixed-ended beam, W906 kN
Ratio 3.3
Stanchion major plane second moment of area, Ic = Is 47539 cm4
Rafter major plane second moment of area, Ir 47539 cm4
Frame load factor for frame stability (critical gravity), λr 1.00
Note if sway check criterion satisfied, then λ r = 1.00, otherwise use amplified moment method;
Frame load factor for frame stability (critical wind uplift), λr 1.01
Note if λ sc >= 5.00, then λ r = λ sc / ( λ sc -1), otherwise use amplified moment method;
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
Structure Design - Steel Portal Frame 19-08-15
Engineering Calculation Sheet Consulting Engineers jXXX 23
CONSULTING
E N G I N E E R S
Made by Date Chd.
Drg. Ref.
Member/Location
Job No. Sheet No. Rev.
Job Title
XX
B. Amplified Moment Method BS5950
Frame elastic critical load factor, λcr 104.9 5.5.4.4
Elastic modulus, E 205 GPa
Rafter major plane second moment of area, Ir 47539 cm4
Stanchion major plane second moment of area, Ic = Is 47539 cm4
Rafter length, s = q 5.025 m
Stanchion stiffness / rafter stiffness ratio, R = Ic/Ir 1.00
Frame eaves height, h 6.000 m
Stanchion ULS compression force, Pc,stanchion 37.0 kN
Rafter ULS compression force, Pc,rafter 44.4 kN
Frame elastic critical load factor, λcr 130.5
0.84
38093 kN
26718 kN
Stanchion major plane second moment of area, Ic = Is 47539 cm4
Rafter major plane second moment of area, Ir 47539 cm4
Frame eaves height, h 6.000 m
Rafter length, s = q 5.025 m
Rafter ULS compression force, Pc,rafter 44 kN
Stanchion ULS compression force, Pc,stanchion 37 kN
Elastic modulus, E 205 GPa
Frame load factor for frame stability, λr 1.00 OK
Structure Design - Steel Portal Frame 19-08-15
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
24
Engineering Calculation Sheet Consulting Engineers
CONSULTING
E N G I N E E R S jXXX
Made by Date Chd.
Drg. Ref.
Member/Location
Job No. Sheet No. Rev.
Job Title
XX
ULS In-Plane Multi Bay Frame Snap Through Instability
A. Snap Through Check Method BS5950
5.5.4.3
Snap through check criterion 17.0 <= 999.0 OK
Rafter section depth, D = dr 528.3 mm
Frame span, L 10.000 m
Frame eaves height, h 6.000 m
Rafter total developed length, Lr = L/cosα 10.050 m
Rafter design strength, py,r 275 N/mm2
Stanchion major plane second moment of area, Ic = Is 47539 cm4
Rafter major plane second moment of area, Ir 47539 cm4
Frame pitch angle, θ = α 5.7 degrees
Effective frame span 9.000 m
Rafter section depth including inclination, Ds = dr/cosα 530.9 mm
Haunch depth, Dh 530.9 mm
Haunch length, Lh 1.000 m
Arching ratio 0.07
Frame uniformly distributed ULS load, ωR,ULS,A,vertical 6.0 kN/m
Frame total ULS load, Wr = ωR,ULS,A,vertical.L 60 kN
Rafter major plane plastic modulus, sr 2059 cm3
Frame total ULS load for plastic failure of rafters as fixed-ended beam, W906 kN
Frame load factor for frame stability, λr 1.00
Note if sway check criterion satisfied, then λ r = 1.00, otherwise use amplified moment method;
B. Amplified Moment Method BS5950
Rafter elastic critical load factor, λcr 848.9 5.5.4.4
Elastic modulus, E 205 GPa
Rafter major plane second moment of area, Ir 47539 cm4
Stanchion major plane second moment of area, Ic = Is 47539 cm4
Rafter length, Lr = q 5.025 m
Stanchion stiffness / rafter stiffness ratio, R = Ic/Ir 1.00
Frame eaves height, h 6.000 m
Stanchion ULS compression force, Pc,stanchion 37.0 kN
Rafter ULS compression force, Pc,rafter 44.4 kN
Frame load factor for frame stability, λr 1.00 OK
19-08-15
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
Structure Design - Steel Portal Frame
jXXX 25
Engineering Calculation Sheet Consulting Engineers
CONSULTING
E N G I N E E R S
Made by Date Chd.
Drg. Ref.
Member/Location
Job No. Sheet No. Rev.
Job Title
XX
SLS Deflection Criteria
Eaves horizontal deflection 6.2 <=h/300 20.0 mm OK
Frame eaves height, h 6.000 m
Frame span, L 10.000 m
Rafter section depth, dr 528.3 mm
Rafter design strength, py,r 275 N/mm2
Eaves deflection factor, D 0.30
Frame span to frame eaves height ratio, L/h 1.7
Frame pitch angle, θ = α 5.7 degrees
Ridge deflection, dRE 62.5 mm
Frame pitch angle, θ = α 5.7 degrees
Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx
Structure Design - Steel Portal Frame 19-08-15
CONSULTING
E N G I N E E R S
Engineering Calculation Sheet Consulting Engineers jXXX 26
Made by Date Chd.
Drg. Ref.
Member/Location