Job No. Sheet No. Rev. CONSULTING Engineering Calculation Sheet

Transcription

1 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 1 Structural Description 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 is provided by the roof diaphragm or wind girder spanning onto orthogonal walls or bracing. Material Properties Steel grade Modulus of elasticity, E N/mm 2 Scheme Design

2 E N G I N E E R S Consulting Engineers jxxx 2 Wind Loading Definition Wind net drag pressure, p WIND = q s.i.c p.c a 0.65 I.C p kpa Site (mean) wind speed (10m mean hourly or gust / 1.62), V s 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, S b 1.62 Effective height, H e m Effective (3s-gust) wind speed, V e = V s.s b 32.6 m/s 2 Dynamic wind pressure, q s = 0.613V e 0.65 kpa BS Size effect factor for external and internal pressures, C a (note cl cl.2.6.1, cl.2.6

3 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 3 Roof Loading (On Slope Where Relevant) Roof covering, p SDL,1 (usually 0.10kPa to 0.20kPa) 0.42mm BMT 0.04 kpa Purlins, p SDL,2 = ω SDL,2 /s p 0.06 kpa Purlins dead load UDL, ω SDL,2 C kn/m 3]; Purlins spacing, s p (usually 1.500m to 2.000m) m Ceiling and services, p SDL,3 (usually 0.10kPa to 0.30kPa) 0.00 kpa Additional super dead load, p SDL, kpa 6.2 Total super dead load, p ΣSDL =p SDL,1 +p SDL,2 +p SDL,3 +p SDL, kpa Live load, p LL 0.25 kpa Snow load, p SNOW (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, I R BS Wind pressure coefficients, I R.C p 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 BS Ratio of dominant opening area to remaining openings (where applicable) T.17 α Windward BS (degrees) I R.C p,d I R.C p,u I R.C p,d I R.C p,u T.10, T BS T.16, T 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; Leeward

4 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 4 Wall Loading Wall covering, p SDL,W1 (usually 0.10kPa to 0.20kPa) Rails, p SDL,W2 = ω SDL,W2 /s r Rails dead load UDL, ω SDL,W2 Rails spacing, s r (usually 1.500m to 2.000m) Additional super dead load, p SDL,W3 Total super dead load, p ΣSDL,W =p SDL,W1 +p SDL,W2 +p SDL,W kpa 0.00 kpa 0.00 kn/m m 0.00 kpa 0.00 kpa Impermeability of wall cladding, I W BS 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, I W.C p,windward, with C p = T.5, T.16, T.1 Leeward wind pressure coefficient, I W.C p,leeward, with C p = T.5, T.16, T.1 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 BS 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 BS is applied to the windward and leeward walls simultaneously; Note +ve C p indicates rightwards action;

5 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 5 Portal Frame Dimensions Frame span, L (usually m to m) m Frame eaves height, h (usually 5.000m to m) m Frame rise, r 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 m Frame length of slope, q = (L 2 /4 + r 2 ) 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, I R.C p,d,windward Windward roof upward wind pressure coefficient, I R.C p,u,windward Leeward roof downward wind pressure coefficient, I R.C p,d,leeward Leeward roof upward wind pressure coefficient, I R.C p,u,leeward -1.04

6 E N G I N E E R S Consulting Engineers jxxx 6 Rafter section Total depth, d r (usually L/60 = 167mm) mm Web thickness, t r 9.6 mm Flange thickness, T r 13.2 mm Design strength, p y,r 275 N/mm 2 Gross area of section, A g,r cm 2 Major plane second moment of area, I r cm 4 Minor plane radius of gyration, r y,r 4.4 cm Major plane plastic modulus, s r 2059 cm 3 Moment capacity (low shear, compact), M c,r = p y,r. s r 566 knm Torsional index, x r 41.6 Rafters dead load UDL, ω DL 0.81 kn/m Rafters dead load pressure, p DL = ω DL /s (usually 0.10kPa to 0.30kPa) 0.09 kpa Stanchion section Total depth, d s (usually L/50 = 200mm) mm Web thickness, t s 9.6 mm Flange thickness, T s 13.2 mm Design strength, p y,s 275 N/mm 2 Gross area of section, A g,s cm 2 Major plane second moment of area, I s cm 4 Minor plane radius of gyration, r y,s 4.4 cm Major plane plastic modulus, s s 2059 cm 3 Moment capacity (low shear, compact), M c,s = p y,s. s s 566 knm Torsional index, x s 41.6 Stanchion dead load UDL, ω DL,S 0.81 kn/m Stanchion dead load, P S,DL = ω DL,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

7 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 7 Eaves and Apex Haunches

8 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 8 ULS Load Combinations Note all loads downwards or rightwards if positive and vice versa; Combination A (Downward Critical) Purlin W P,ULS,A Rafter ω R,ULS,A Stanchion P S,ULS,A and ω S,ULS,A Vertical [1.4p ΣSDL +1.6p LL +1.6p SNOW ].s p.s Windward [0.0p WIND,d,windward ].s p.s Leeward [0.0p WIND,d,leeward ].s p.s Vertical [1.4p DL +1.4p ΣSDL +1.6p LL +1.6p SNOW ].s Windward [0.0p WIND,d,windward ].s Leeward [0.0p WIND,d,leeward ].s Vertical 1.4P S,DL +[1.4p ΣSDL,W ].s.h Windward [0.0p WIND,windward ].s Leeward [0.0p WIND,leeward ].s 5.9 kn 0.0 kn 0.0 kn 6.0 kn/m 0.0 kn/m 0.0 kn/m 7 kn 0.0 kn/m 0.0 kn/m Combination B (Downward Critical) Purlin W P,ULS,B Rafter ω R,ULS,B Stanchion P S,ULS,B and ω S,ULS,B Vertical [1.4p ΣSDL +0.0p LL +0.0p SNOW ].s p.s Windward [1.4p WIND,d,windward ].s p.s Leeward [1.4p WIND,d,leeward ].s p.s Vertical [1.4p DL +1.4p ΣSDL +0.0p LL +0.0p SNOW ].s Windward [1.4p WIND,d,windward ].s Leeward [1.4p WIND,d,leeward ].s Vertical 1.4P S,DL +[1.4p ΣSDL,W ].s.h Windward [1.4p WIND,windward ].s Leeward [1.4p WIND,leeward ].s 1.5 kn -6.1 kn kn 2.4 kn/m -5.1 kn/m -8.6 kn/m 7 kn 1.7 kn/m 9.3 kn/m Combination C (Upward Critical) Purlin W P,ULS,C Rafter ω R,ULS,C Stanchion P S,ULS,C and ω S,ULS,C Vertical [1.0p ΣSDL +0.0p LL +0.0p SNOW ].s p.s Windward [1.4p WIND,u,windward ].s p.s Leeward [1.4p WIND,u,leeward ].s p.s Vertical [1.0p DL +1.0p ΣSDL +0.0p LL +0.0p SNOW ].s Windward [1.4p WIND,u,windward ].s Leeward [1.4p WIND,u,leeward ].s Vertical 1.0P S,DL +[1.0p ΣSDL,W ].s.h Windward [1.4p WIND,windward ].s Leeward [1.4p WIND,leeward ].s 1.1 kn kn kn 1.7 kn/m kn/m -8.6 kn/m 5 kn 1.7 kn/m 9.3 kn/m Combination D (Downward Critical) Purlin W P,ULS,D Rafter ω R,ULS,D Stanchion P S,ULS,D and ω S,ULS,D Vertical [1.2p ΣSDL +1.2p LL +1.2p SNOW ].s p.s Windward [1.2p WIND,d,windward ].s p.s Leeward [1.2p WIND,d,leeward ].s p.s Vertical [1.2p DL +1.2p ΣSDL +1.2p LL +1.2p SNOW ].s Windward [1.2p WIND,d,windward ].s Leeward [1.2p WIND,d,leeward ].s Vertical 1.2P S,DL +[1.2p ΣSDL,W ].s.h Windward [1.2p WIND,windward ].s Leeward [1.2p WIND,leeward ].s 4.6 kn -5.3 kn -8.8 kn 4.8 kn/m -4.4 kn/m -7.3 kn/m 6 kn 1.5 kn/m 8.0 kn/m

9 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 9 SLS Load Combinations Note all loads downwards or rightwards if positive and vice versa; Combination SLS (Downward Critical) Purlin W P,SLS Rafter ω R,SLS Stanchion P S,SLS and ω S,SLS Vertical [1.0p ΣSDL +1.0p LL +1.0p SNOW ].s p.s Windward [1.0p WIND,d,windward ].s p.s Leeward [1.0p WIND,d,leeward ].s p.s Vertical [1.0p DL +1.0p ΣSDL +1.0p LL +1.0p SNOW ].s Windward [1.0p WIND,d,windward ].s Leeward [1.0p WIND,d,leeward ].s Vertical 1.0P S,DL +[1.0p ΣSDL,W ].s.h Windward [1.0p WIND,windward ].s Leeward [1.0p WIND,leeward ].s 3.8 kn -4.4 kn -7.3 kn 4.0 kn/m -3.6 kn/m -6.1 kn/m 5 kn 1.2 kn/m 6.7 kn/m Combination SLS (Upward Critical) Purlin W P,SLS Rafter ω R,SLS Stanchion P S,SLS and ω S,SLS Vertical [1.0p ΣSDL +0.0p LL +0.0p SNOW ].s p.s Windward [1.0p WIND,u,windward ].s p.s Leeward [1.0p WIND,u,leeward ].s p.s Vertical [1.0p DL +1.0p ΣSDL +0.0p LL +0.0p SNOW ].s Windward [1.0p WIND,u,windward ].s Leeward [1.0p WIND,u,leeward ].s Vertical 1.0P S,DL +[1.0p ΣSDL,W ].s.h Windward [1.0p WIND,windward ].s Leeward [1.0p WIND,leeward ].s 1.1 kn -8.6 kn -7.3 kn 1.7 kn/m -7.2 kn/m -6.1 kn/m 5 kn 1.2 kn/m 6.7 kn/m

10 E N G I N E E R S Consulting Engineers jxxx 10 ULS Structural (Plastic Collapse) Analysis (Combination Case A Only, No Wind Loadcase) Critical combination case Combination C Critical combination case uniformly distributed ULS load, ω R,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 Frame uniformly distributed ULS load, ω R,ULS,PC = ω R,ULS,A,vertical 6.0 kn/m Frame horizontal base force ratio, H FR 0.15 Frame ULS horizontal base force, H F = H FR.ω R,ULS,PC.L 9 kn

11 E N G I N E E R S Consulting Engineers jxxx 11 Frame rafter M p ratio, M pr Frame rafter ULS (apex) M p required, M p,rafter = M pr.ω R,ULS,PC.L 2 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 distance between intermediate restraints L m,r ; Frame stanchion M p ratio, M pl Frame stanchion ULS (eaves) M p required, M p,stanchion = M pl.ω R,ULS,PC.L 2 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 between full torsional restraints L m,s or L t,s depending on the method adopted;

12 CONSULTING E N G I N E E R S Engineering Calculation Sheet Consulting Engineers jxxx 12 ULS Structural (Elastic) Analysis (Any Combination Case Including Wind Loadcases) Note sign convention for bending moment is positive for tension within frame;

13 E N G I N E E R S Consulting Engineers jxxx 13 Stanchion major plane second moment of area, I 1 = I s cm 4 Rafter major plane second moment of area, I 2 = I r cm 4 Frame eaves height, h m Rafter length, s = q m Coefficient, k = (I 2 /I 1 ).(h/s) 1.19 Frame rise, f = r 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 m Frame ULS horizontal (inward) base force, H F,inward = MAX(0, H A, H E ) Frame ULS horizontal (outward) base force, H F,outward = MIN(0, H A, H E ) Frame ULS vertical (upward) base force, V F,upward = MAX(0, V A, V E ) Frame ULS vertical (downward) base force, V F,downward = MIN(0, V A, V E ) Note a negative V F indicates uplift; 41 kn -29 kn 37 kn -54 kn Frame rafter ULS (eaves) (-ve) M p required, M p,rafter = MIN(0, M B, M D ) -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 distance between full torsional restraints (max is L m,r or L t,r depending on the method adopted); Frame rafter ULS (apex) (+ve) M p required, M p,rafter = MAX(0, M C ) 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 between intermediate restraints (max is L m,r ); Frame rafter ULS (eaves) (+ve) M p required, M p,rafter = MAX(0, M B, M D ) 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 between intermediate restraints (max is L m,r ); Frame rafter ULS (apex) (-ve) M p required, M p,rafter = MIN(0, M C ) -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 between full torsional restraints L t,u,r ;

14 E N G I N E E R S Consulting Engineers jxxx 14 Made by Date Frame rafter ULS compression P c required, P c,rafter = H F,inward.cosα+V F,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 P t required, P t,rafter = H F,outward.cosα+V F,downward.sinα -34 kn Note rafter axial tension capacity should be at least λ r.p t,rafter ; Frame stanchion ULS (eaves) (-ve) M p required, M p,stanchion = MIN(0, M A, M B, 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 full torsional restraints (max is L m,s or L t,s depending on the method adopted); Frame stanchion ULS (eaves) (+ve) M p required, M p,stanchion = MAX(0, M A, M B, 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 intermediate restraints (max is L m,s ); Frame stanchion ULS compression P c required, P c,stanchion = V F,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 P t required, P t,stanchion = V F,downward -54 kn Note stanchion axial tension capacity should be at least λ r.p t,stanchion ; Frame eaves connection ULS (+ve) moment, CM EAVES,+ = MAX(0, M B, M D ) 144 knm Frame eaves connection ULS (-ve) moment, CM EAVES,- = MIN(0, M B, M D ) -83 knm Frame eaves connection ULS shear, CV EAVES = MAX(ABS(V A -P S,ULS ), ABS(V E -P S 59 kn Frame apex connection ULS (+ve) moment, CM APEX,+ = MAX(0, M C ) 37 knm Frame apex connection ULS (-ve) moment, CM APEX,- = MIN(0, M C ) -36 knm Maximum frame load factor for frame stability, MAX(λ r ) 1.01 Note all connection forces should be factored by λ r ;

15 E N G I N E E R S Consulting Engineers jxxx 15 Made by Date ULS Load Combination A Direction Bending Moment (knm) at Position Vertical Horizontal A B C D E ω R,ULS,vertical (kn/m) ω R,ULS,windward (kn/m) ω R,ULS,leeward (kn/m) P S,ULS (kn) ω S,ULS,windward (kn/m) ω S,ULS,leeward (kn/m) Reaction (kn) H A H E V A V E ULS Load Combination B Direction Bending Moment (knm) at Position Vertical Horizontal A B C D E ω R,ULS,vertical (kn/m) ω R,ULS,windward (kn/m) ω R,ULS,leeward (kn/m) P S,ULS (kn) ω S,ULS,windward (kn/m) ω S,ULS,leeward (kn/m) Reaction (kn) H A H E V A V E

16 E N G I N E E R S Consulting Engineers jxxx 16 Structure Design - Steel Portal Frame XX Made by Date Chd. ULS Load Combination C Direction Bending Moment (knm) at Position Vertical Horizontal A B C D E ω R,ULS,vertical (kn/m) ω R,ULS,windward (kn/m) ω R,ULS,leeward (kn/m) P S,ULS (kn) ω S,ULS,windward (kn/m) ω S,ULS,leeward (kn/m) Reaction (kn) H A H E V A V E ULS Load Combination D Direction Bending Moment (knm) at Position Vertical Horizontal A B C D E ω R,ULS,vertical (kn/m) ω R,ULS,windward (kn/m) ω R,ULS,leeward (kn/m) P S,ULS (kn) ω S,ULS,windward (kn/m) ω S,ULS,leeward (kn/m) Reaction (kn) H A H E V A V E

17 E N G I N E E R S Consulting Engineers jxxx 17 Made by 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;

18 E N G I N E E R S Consulting Engineers jxxx 18 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, L m,r m 5.3.3(a) Minor plane radius of gyration, r y,r 44 mm ULS compression stress, f c,r = P c,rafter /A g,r 4.2 N/mm 2 ULS compression force, P c,rafter 44.4 kn Gross area of section, A g,r cm 2 Design strength, p y,r 275 N/mm 2 Torsional index, x r 41.6 A.2 Method 2 (Includes Intermediate Restraint(s), Less Conservative) BS5950 Maximum distance between intermediate restraints, L i,r = L m,r m Maximum distance between full torsional restraints, L t,r = L s,r m Minor plane radius of gyration, r y,r 44 mm Torsional index, x r 41.6 Haunch depth, D h mm Rafter section depth including inclination, D s = d r /cosα mm 1.25

19 E N G I N E E R S Consulting Engineers jxxx 19 Structure Design - Steel Portal Frame XX Made by Date Chd. 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;

20 E N G I N E E R S Consulting Engineers jxxx 20 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, L t,u,r m

21 E N G I N E E R S Consulting Engineers jxxx 21 Structure Design - Steel Portal Frame 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, L m,s m 5.3.3(a) Minor plane radius of gyration, r y,s 44 mm ULS compression stress, f c,s = P c,stanchion /A g,s 3.5 N/mm 2 ULS compression force, P c,stanchion 37.0 kn Gross area of section, A g,s cm 2 Design strength, p y,s 275 N/mm 2 Torsional index, x s 41.6 A.2 Method 2 (Includes Intermediate Restraint(s), Less Conservative) BS5950 Maximum distance between intermediate restraints, L i,s = L m,s m Maximum distance between full torsional restraints, L t,s = L s,s m Minor plane radius of gyration, r y,s 44 mm Torsional index, x s 41.6 K 1 =

22 E N G I N E E R S Consulting Engineers jxxx 22 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;

23 E N G I N E E R S Consulting Engineers jxxx 23 ULS In-Plane Single Bay Frame Sway Instability A. Sway Check Method BS Sway check criterion 17.0 <= OK (critical gravity) Sway check criterion (critical wind uplift) Rafter section depth, D = d r mm Frame span, L m Frame eaves height, h m Rafter total developed length, L r = L/cosα m Rafter design strength, p y,r 275 N/mm 2 Effective frame span m Rafter section depth including inclination, D s = d r /cosα Haunch depth, D h Haunch length, L h mm mm m Arching ratio 0.07 Frame uniformly distributed ULS load, ω R,ULS,A,vertical 6.0 kn/m Frame total ULS load, W r = ω R,ULS,A,vertical.L 60 kn Rafter major plane plastic modulus, s r 2059 cm 3 Frame total ULS load for plastic failure of rafters as fixe 906 kn Ratio 3.3 Stanchion major plane second moment of area, I c = I s cm 4 Rafter major plane second moment of area, I r cm 4 Frame load factor for frame stability (critical gravity), λ r 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), λ r 1.01 Note if λ sc >= 5.00, then λ r = λ sc / ( λ sc -1), otherwise use amplified moment method;

24 E N G I N E E R S Consulting Engineers jxxx 24 B. Amplified Moment Method BS5950 Frame elastic critical load factor, λ cr Elastic modulus, E 205 GPa Rafter major plane second moment of area, I r cm 4 Stanchion major plane second moment of area, I c = I s cm 4 Rafter length, s = q m Stanchion stiffness / rafter stiffness ratio, R = I c /I r 1.00 Frame eaves height, h m Stanchion ULS compression force, P c,stanchion 37.0 kn Rafter ULS compression force, P c,rafter 44.4 kn Frame elastic critical load factor, λ cr kn kn Stanchion major plane second moment of area, I c = I s cm 4 Rafter major plane second moment of area, I r cm 4 Frame eaves height, h m Rafter length, s = q m Rafter ULS compression force, P c,rafter 44 kn Stanchion ULS compression force, P c,stanchion 37 kn Elastic modulus, E 205 GPa Frame load factor for frame stability, λ r 1.00 OK

25 E N G I N E E R S Consulting Engineers jxxx 25 Structure Design - Steel Portal Frame XX ULS In-Plane Multi Bay Frame Snap Through Instability A. Snap Through Check Method BS Snap through check criterion 17.0 <= OK Rafter section depth, D = d r mm Frame span, L m Frame eaves height, h m Rafter total developed length, L r = L/cosα m Rafter design strength, p y,r 275 N/mm 2 Stanchion major plane second moment of area, I c = I s cm 4 Rafter major plane second moment of area, I r cm 4 Frame pitch angle, θ = α 5.7 degrees Effective frame span m Rafter section depth including inclination, D s = d r /cosα Haunch depth, D h Haunch length, L h mm mm m Arching ratio 0.07 Frame uniformly distributed ULS load, ω R,ULS,A,vertical 6.0 kn/m Frame total ULS load, W r = ω R,ULS,A,vertical.L 60 kn Rafter major plane plastic modulus, s r 2059 cm 3 Frame total ULS load for plastic failure of rafters as fixe 906 kn Frame load factor for frame stability, λ r 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, λ cr Elastic modulus, E 205 GPa Rafter major plane second moment of area, I r cm 4 Stanchion major plane second moment of area, I c = I s cm 4 Rafter length, L r = q m Stanchion stiffness / rafter stiffness ratio, R = I c /I r 1.00 Frame eaves height, h m Stanchion ULS compression force, P c,stanchion 37.0 kn Rafter ULS compression force, P c,rafter 44.4 kn Frame load factor for frame stability, λ r 1.00 OK

26 E N G I N E E R S Consulting Engineers jxxx 26 SLS Deflection Criteria Eaves horizontal deflection 6.2 <=h/ mm OK Frame eaves height, h m Frame span, L m Rafter section depth, d r mm Rafter design strength, p y,r 275 N/mm 2 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, d RE 62.5 mm Frame pitch angle, θ = α 5.7 degrees