job no. sheet no. rev. consulting e n g i n e e r s · coefficient of t.16 bs6399-2 is applied to...

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.

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Structure Design - Steel Portal Frame BS5950 v2015.01.xlsx

Structure Design - Steel Portal Frame 19-08-15Made by Date Chd.

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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


2

Structure Design - Steel Portal Frame 19-08-15

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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;


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Windward Leeward


Structure Design - Steel Portal Frame BS5950 v2015.01.xlsxMade by Date Chd.

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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;

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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

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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


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Eaves and Apex Haunches


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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)


Windward [1.4pWIND,d,windward].sp.s -6.1 kN

Leeward [1.4pWIND,d,leeward].sp.s -10.3 kN


Windward [1.4pWIND,d,windward].s -5.1 kN/m

Leeward [1.4pWIND,d,leeward].s -8.6 kN/m




Combination C (Upward Critical)


Windward [1.4pWIND,u,windward].sp.s -12.0 kN

Leeward [1.4pWIND,u,leeward].sp.s -10.3 kN


Windward [1.4pWIND,u,windward].s -10.0 kN/m

Leeward [1.4pWIND,u,leeward].s -8.6 kN/m




Combination D (Downward Critical)










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



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SLS Load Combinations

Note all loads downwards or rightwards if positive and vice versa;

Combination SLS (Downward Critical)










Combination SLS (Upward Critical)


Windward [1.0pWIND,u,windward].sp.s -8.6 kN

Leeward [1.0pWIND,u,leeward].sp.s -7.3 kN


Windward [1.0pWIND,u,windward].s -7.2 kN/m

Leeward [1.0pWIND,u,leeward].s -6.1 kN/m




Purlin WP,SLS

Rafter ωR,SLS

Stanchion PS,SLS and

ωS,SLS

Stanchion PS,SLS and

ωS,SLS




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Purlin WP,SLS

Rafter ωR,SLS

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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




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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;


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ULS Structural (Elastic) Analysis (Any Combination Case Including Wind Loadcases)

Note sign convention for bending

moment is positive for tension

within frame;

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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


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


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



between intermediate restraints (max is L m,r );

Frame rafter ULS (apex) (-ve) Mp required, Mp,rafter = MIN(0, MC) -36 kNm OK



between full torsional restraints L t,u,r ;

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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


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


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 ;

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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


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

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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


ωR,ULS,leeward (kN/m) -8.6


Reaction (kN)

PS,ULS (kN)


ωR,ULS,windward (kN/m) -5.1

ULS Load Combination BDirection Bending Moment (kNm) at Position


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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


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

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Structure Design - Steel Portal Frame



19-08-15

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ULS Load Combination CDirection

Bending Moment (kNm) at Position


PS,ULS (kN)



Reaction (kN)

Direction

Bending Moment (kNm) at Position


Reaction (kN)





ULS Load Combination D

PS,ULS (kN)


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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;




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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


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


Haunch depth, Dh 530.9 mm

Rafter section depth including inclination, Ds = dr/cosα 530.9 mm

1.25



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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;



19-08-15

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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





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


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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


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


K1 = 1.00 1.00

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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;


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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



Rafter total developed length, Lr = L/cosα 10.050 m

Rafter design strength, py,r 275 N/mm2

Effective frame span 9.000 m



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;




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B. Amplified Moment Method BS5950

Frame elastic critical load factor, λcr 104.9 5.5.4.4

Elastic modulus, E 205 GPa




Stanchion stiffness / rafter stiffness ratio, R = Ic/Ir 1.00


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





Rafter ULS compression force, Pc,rafter 44 kN

Stanchion ULS compression force, Pc,stanchion 37 kN


Frame load factor for frame stability, λr 1.00 OK



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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



Rafter total developed length, Lr = L/cosα 10.050 m




Frame pitch angle, θ = α 5.7 degrees

Effective frame span 9.000 m



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




Rafter length, Lr = q 5.025 m

Stanchion stiffness / rafter stiffness ratio, R = Ic/Ir 1.00


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

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SLS Deflection Criteria

Eaves horizontal deflection 6.2 <=h/300 20.0 mm OK



Rafter section depth, dr 528.3 mm


Eaves deflection factor, D 0.30

Frame span to frame eaves height ratio, L/h 1.7


Ridge deflection, dRE 62.5 mm




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