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ColdSteel/4600 User's Manual

1. ColdSteel User s Manual Version 1 0 PlainUnequalAngle Specify a list of plain unlipped unequal angle sections The profile geometry of a plain unequal angle section is shown in Fig 1 2 Each plain unequal angle section must be defined on a separate line using the following format Format Description Dimension Section name e g 75x50x5 0 UA Section material must be defined in Material e g C450L0 Unit combination code 0 millimetres newtons Thickness 1 Overall leg length of longer vertical leg B Overall leg length of shorter horizontal leg B Internal corner radius for all corners R 5 25 2 Ge kes Fig 1 2 PlainUnequalAngle definition Centre for Advanced Structural Engineering November 1998 The University of Sydney 50 ColdSteel User s Manual Version 1 0 PlainChannel Specify a list of plain unlipped channel sections The profile geometry of a plain channel section is shown in Fig I 3 Each plain channel section must be defined on a separate line using the following format Format Description Dimension 5 Section name e g 300x90x6 0 PFC 5 Section material must be defined in Material e g C450L0 I Unit combination code 0 millimetres newtons F Thickness 1 L F Overall depth D L F Overall flange width B L F Internal corner radius for all corners
2. Memory Used 304444 Fig 52 Main form for check of interior segment in end span under downwards load Governing Mode Nominal Capacities and Overload Factors CHECK Lipped Z Section Equal Flanges Z 20015 0 Governing Load Factor 2 1918 SAFE Member capacity distortional buckling in bending about n axis Mbn AS NZS 4600 1996 Clause 3 3 3 3 Draw Section Full Details Fig 53 Output form for check of interior segment in end span under downwards load Summary From the results determined in this example the maximum load capacities of the three span lapped purlin system shown in Fig 43 are Upwards load lax 2 05 kN m C factor approach Clause 3 3 3 2 a Gos 2 00 kN m Rational buckling analysis approach Clause 3 3 3 2 b Downwards load jy 2 19 KN m Centre for Advanced Structural Engineering November 1998 The University of Sydney 36 ColdSteel User s Manual Version 1 0 Example 8 Lipped Z Section in Combined Bending and Shear Section 6 8 1 of Hancock 1998 Problem In a lapped Z 20015 purlin system the maximum design moment M 20 and shear v5 at the end of the lap computed using the R factor approach are M 7 44 kNm and v 8 26 KN Check the limit state of combined bending and shear at the end of the lap Solution The Z 20015 section is shown in Fig 40 and is a specific instance of the LippedZed section class defined i
3. The University of Sydney Department of Civil Engineering Centre for Advanced Structural Engineering ColdSteel 4600 Version 1 0 Cold Formed Steel Design to AS NZS 4600 1996 User s Manual November 1998 Version 0 22 48 63 66 70 72 ColdSteel User s Manual Contents 1 Introduction 2 Scope of Software 3 Program Operation 4 Design Examples The ColdSteel Database Section Properties Summary of Member Design Checks Error and Warning Codes References Appendix I Appendix IT Appendix III Appendix IV Appendix V The software described in this document is distributed under licence and may be used or copied only in accordance with the terms of such licence While every effort has been made to ensure its reliability the authors are not liable for damages which result from the use or misuse of the software The ultimate responsibility for checking and correctly interpreting the results rests with the user November 1998 All queries should be directed to Dr Murray Clarke Department of Civil Engineering The University of Sydney NSW 2006 02 9351 2115 02 9351 3343 M Clarke civil usyd edu au Phone Fax Email Centre for Advanced Structural Engineering The University of Sydney November 1998 Centre for Advanced Structural Engineering The University of Sydney ColdSteel User s Manual Version 1 0 1 Introduction ColdSteel is a computer program for the design of co
4. C 20019 96450 0 1 9 0 690 50 60 20024 96450 0 2 4 203 0 7620 210 0 96 25019 90450 0 1 9 254 0 16 0 18 5 9 2 0 C 25024 G450 0 2 4 254 0 76 0 20 5 5 0 E 30024 G450 0 2 4 300 0 960 5 3 20 C 30030 G450 0 3 0 300 0 9650 32 5 3 20 35030 G450 Q 320 9350 0 1250 30 0 0 LippedZed Narrow flange on top gt 2 10010 96450 0 lt 0 102 0 53 0 49 10 12 5 0 Z 10012 96450 0 2 0 0 1920 1225 0 92 10015 96450 0 L 5 102 0 53 0 49 0 135 25 0 Z 10019 96450 0 L 9 102 0 53 0 49 0 14 5 5 0 Z 15012 G450 0 Led 25 2 0 65 0 61 0 15 5 0 Z 15015 96450 0 Pd P5220 65 0 61 0 165 0 Z 15019 96450 0 LeG L520 65 0 61 0 1745 5 0 Z 15024 96450 0 2 4 152 0 65 0 60 0 19 5 5 0 Z 20015 96450 0 L 5 203 0 79 0 74 0 15 0 5 0 Z 20019 G450 0 1 9 203 0 79 0 74 0 18 5 5 0 Z 20024 96450 0 2 4 203 0 79 0 73 0 2145 0 7 25019 96450 0 1 9 254 0 79 0 74 0 18 0 5 0 Z 25024 96450 0 2 4 254 0 79 0 73 0 2120 5 0 92 30024 96450 0 2 4 300 0 100 0 93 0 270 5 0 Z 30030 96450 0 3 0 300 0 100 0 93 0 31 0 5 0 Z 35030 96450 0 320 2350 0 12920 12120 300 5 10 Centre for Advanced Structural Engineering November 1998 The University of Sydney 62 ColdSteel User s Manual Version 1 0 Appendix Il Section Properties The calculation of full and effective section properties in ColdSteel is in accordance w
5. Cmy ft Cmy fi Vx kN Zz Lez m 1 Bearing Tension Factors Clause 3 3 3 2 b Lb y m 4 vy kN oS ension Factors kt f fi cy m 31 Ry ch 7 brim f 900 fpa L ad Ls J Memory Used 324952 Fig 66 Main form pertaining to Example 12 Governing Mode Nominal Capacities and Overload Factors CHECK Lipped Channel Ex7 6 3 0 Governing Load Factor 57 5601 SAFE Member capacity flexural or flexural torsional buckling in compression Neft AS NZS 4600 1996 Clause 3 4 1 Draw Section Full Details Fig 67 Output form pertaining to Example 12 Example 13 Unlipped Channel Beam Column Bent in Plane of Symmetry Section 8 5 1 of Hancock 1998 Problem Calculate the maximum design axial compressive load in the unlipped channel shown in Fig 61 assuming the channel is loaded with an axial force on the line of the x axis at a point in line with the flange tips As in the previous example the effective lengths in flexure L L and torsion L are 1500 mm and the nominal yield stress f is 240 MPa ex Solution The relevant unlipped channel section Ex 7 6 2 is the same as that used in Example 11 It can be seen from the Full Details output given in Fig 68 that the dimension from the full section centroid to the extreme fibre in the positive x axis direction is 0 03869 m Thus in this example a compressive load of N 1 0 kN co exists
6. Full section modulus yield at extreme negative x ordinate m3 Zy Full section modulus yield at extreme positive y ordinate m3 Zy Full section modulus yield at extreme negative y ordinate m4 J torsion constant full section m rol full section m betax monosymmetry parameter referred to principal axes m betay monosymmetry parameter referred to principal axes m6 Iw warping constant full section kg m Mass per unit length m Profile distance m2 kg Profile surface area Area Mass 0 24148 0 000772735 0 000772735 0 0097073 0 0 0255392 0 2 51948E 6 1 69059E 7 0 0 0571005 0147912 0113073 0386927 O50 76 0 076 3 31518 5 31 4 6 1 7 5 2 6376E 9 0 0645648 0 0 168364 6 74926E 10 6 06597 0 489359 0 0806729 Fig 68 Full section properties for PlainChannel section Ex 7 6 2 used in Examples 11 13 and 14 AS NZS 4600 1996 Cold Formed Steel Structures File Options Help k a Check Design Options Exit i 1 Axis System Section Plain Channel Principal 3 8 Ex 7 6 2 Non principal n p Material C240 M Use default material Design Actions 1st Order Lengths Ch Cm Factors Mo Cm Factors N M N kN fa L m 1 5 Clause 3 3 3 2 a Clause 3 5 1 Mx kN m jo Lex m 1 5 j Cmx ft My kN m 0 03869 Ley m 1 5 Cmy ft Cmy ft Vx kN po Lez m 5 jBearing 7 Tension Factors clau
7. Zy Full section modulus yield at extreme negative x ordinate 3 04382E 10 m4 J torsion constant full section 0 082889 m rol full section Om betax monosymmetry parameter referred to principal axes 0 159306 m betay monosymmetry parameter referred to principal axes 7 52148E 10 m6 Iw warping constant full section 3 18587 kg m Mass per unit length 0 544124 m Profile distance 0 170793 m2 kg Profile surface area Area Mass Fig 73 Full section properties for LippedChannel section Ex 7 6 3 used in Examples 12 and 15 0 00478201 m x ordinate of C full gt C effective fy Om y ordinate of C full gt C effective fy 0 SOS oom x ordinate of C full gt C effective fn Om y ordinate of C full gt C effective fn Fig 74 Shift of effective centroid from full section centroid for the two cases of uniform compressive stresses f and f for the LippedChannel section Ex 7 6 3 used in Examples 12 and 15 Centre for Advanced Structural Engineering November 1998 The University of Sydney 46 Version 0 November 1998 x Exit Cm Factors N M Clause 3 5 1 Cmx Cmy Bearing 90 fat c y m 3 em pa L Axis System 6 Principal y Non principal n p ColdSteel User s Manual AS NZS 4600 1996 Cold Formed Steel Structures v Check Design Options Lipped Channel z V Use default material Ch Cm Factors Mo Cl
8. Centre for Advanced Structural Engineering November 1998 The University of Sydney 54 ColdSteel User s Manual Version 1 0 PlainHat Specify a list of plain unlipped hat sections The profile geometry of a plain hat section is shown in Fig I 7 Each plain hat section must be defined on a separate line using the following format Format Description Dimension 5 Section name e g PH 10010 5 Section material must be defined in Material e g G450 I Unit combination code 0 millimetres newtons degrees F Thickness f L F Overall depth D L F Overall width of top flange B L F Width of bottom flanges F L F Internal corner radius for all bends R L F Angle of webs from the vertical A 7 1 2 3 4 5 6 t D B F R fodx Fig I 7 PlainHat definition Centre for Advanced Structural Engineering November 1998 The University of Sydney 55 ColdSteel User s Manual Version 1 0 VeePlainHat Specify a list of plain unlipped hat sections with intermediate V stiffener The profile geometry of a plain hat section with an intermediate V stiffener is shown in Fig I 8 Each plain hat section with an intermediate V stiffener must be defined on a separate line using the following format Format Description Dimension 5 Section name e g VPH 10010 5 Section material must be defined in Materia
9. ColdSteel User s Manual Version 1 0 Example 10 Square Hollow Section Column Section 7 6 1 of Hancock 1998 Problem Determine the maximum design compressive axial force for the 76x76x2 0 SHS cold formed square hollow section column shown in Fig 58 Assume that the effective lengths L L and L are all equal to 3 0 m The nominal yield strength of the material is 350 MPa ex Solution The 76x76x2 0 SHS section is a specific instance of the SHS section class defined in the ColdSteel database see Appendix I The 350 MPa yield material is defined as C350 in the ColdSteel database In this example the maximum design axial compressive force N corresponds to the design compression capacity N which is equal to the computed load factor when a reference load of N 1 KN is input to ColdSteel The Main and Output forms of ColdSteel pertaining to this example are shown in Figs 59 and 60 respectively from which it can be seen that the maximum design compression force is N 0 82 0KN 76 mm E 7 76 mm f 350 MPa Fig 58 Square hollow section for Example 10 AS NZS 4600 1996 Cold Formed Steel Structures j_ lof x File Options Help Check Design Options Exit Section SHSSecion H pew 6 Principal y E 76 x 76 x 2 0 SHS v Non principal n p Material 0 M Use default material Design Actions 1st Order Lengths Ch Cm Factors Mo Cm Factors N M N kN fr L m B Clause 3 3
10. Fig 42 Effective section properties for Z 20015 equal flanges section of Example 6 November 1998 Centre for Advanced Structural Engineering The University of Sydney 30 ColdSteel User s Manual Version 1 0 Example 7 Continuous Lapped Z Section Purlin Section 5 8 3 of Hancock 1998 Problem Determine the upwards and downwards design load capacity kN m of the Z section purlin Z 20015 system shown in Fig 43 The purlin is continuous over three 7 m spans with interior lap lengths of 900 mm and has sheeting screw fastened to the top flange Each span has one brace and in the exterior spans this brace is positioned 2800 mm from the outer support as shown in Fig 43 q 1kN m x Brace Lap 900 mm 2800 4200 3500 3500 4200 0 all dimensions in mm Fig 43 Three span lapped purlin system Solution The first step in solving the problem is to perform the structural analysis using a suitable program Lapped regions may be modelled using elements with double the flexural stiffness of those employed in unlapped regions Based on this assumption and the application of a uniformly distributed load of q 1 0 kN m the bending moment and shear force diagrams for the three span purlin system are shown in Fig 44 In the ColdSteel member strength checks which follow it is assumed that the flanges of the Z 20015 section are averaged and equal in length 3 79 kNm at brace point Includes do
11. Mox from rational buckling analysis KN m fo Combined bending and compression strength check Calculation of Mcx Clause 3 3 3 2 8 x Calculation of Mox Clause 3 3 3 2 a nd Fig 9 Bending Options Distortional Buckling Options For some sections design against distortional buckling in pure compression Clause 3 4 6 and or bending Clause 3 3 3 3 is required The elastic distortional buckling stress in pure compression or bending can be calculated using a simple analytical model such as that given in Appendix D of AS NZS 4600 1996 for flange distortional buckling or that given by Serette amp Pek z 1995 for web distortional buckling Alternatively a rational elastic buckling analysis of the whole plate assemblage such as that performed by program ThinWall CASE 1997b can be used The Distortional Buckling Options form shown in Fig 10 enables the user to select whether the distortional buckling stresses in both compression and bending should be based on a simplified analytical model or a rational elastic buckling analysis of the complete plate assemblage In ColdSteel the simple model given in Appendix D is used for flange distortional buckling for lipped channels and Z sections for example while the model proposed by Serette amp Pek z 1995 is used for the web distortional buckling of hat sections in bending about a horizontal axis If the simple analytical model option is chosen distortional buck
12. corresponds to the design compression capacity N which is equal to the computed load factor when a reference load of N 1 kN is input to ColdSteel The fact that the channel is loaded through the effective centroid rather than the full centroid is indicated by setting the appropriate option in the Options Compression form as shown in Fig 62 The Main and Output forms of ColdSteel pertaining to this example are shown in Figs 66 and 67 respectively from which it can be seen that the maximum design compression force is N 2 57 6kN It is interesting to note that if the member is assumed to be loaded through the full section centroid rather ax 50 2 KN due to the eccentricity of the full and effective section centroids and the consequent additional bending moment that is introduced than the effective section centroid then the maximum capacity reduces to N nax Centre for Advanced Structural Engineering November 1998 The University of Sydney 42 Version 0 ixi Exit ColdSteel User s Manual AS NZS 4600 1996 Cold Formed Steel Structures File Options Help Check Design Options A Axis System Section Lipped Channel z Ex 7 6 3 Non principal np Material C300 vy M Use default material Design Actions 1st Order Lengths Cb Cm Factors Mo Cm Factors N M N kN 1 L m 2 Clause 3 3 3 2 a Clause 3 5 1 Mx kNm 0 Lex m 2 j Cmx it My kNm f0 Ley m j1
13. have suggested CCFSS 1992 that the unbraced length L L should be taken as the distance from the inflection point to the end of the lap with C 1 75 In this case L L 1050 mm Based on a unit uniformly distributed load the maximum design moment M in the physical segment remains 3 79 kNm The Main form with relevant input parameters is shown in Fig 52 The result of the strength check is shown in Fig 53 from which it can be seen that distortional buckling governs and the maximum design load is 2 19 kN m Centre for Advanced Structural Engineering November 1998 The University of Sydney 35 ColdSteel User s Manual Version 1 0 Inspection of the Full Details output reveals that the maximum design load based on lateral buckling failure is 2 55 kN m AS NZS 4600 1996 Cold Formed Steel Structures _ ol x File Options Help Check Design Options Exit l Axis System Section lipped Z Section Equal Flanges v Principal x y 220015 Me Material G450 M Use default material gt Non principal n p Design Actions 1st Order Lengths r Ch Cm Factors Mo Cm Factors N M N kN p kim Clause 3 3 3 2 a Clause 3 5 1 Mnt kNm 3 79 Lex m 0 Cbs fiai Cmn f Mp kN m jo Ley m 5 Chy j Cmp ft Lez m 5 Bearing Vn kN jo Tension Factors Cl use 3 3 3 2 b Lb p m jo nie tf lcm p mm po I brim f epim fpa
14. r e the warping constant I e the monosymmetry parameters 3 and 3 Using the simplified section geometry the above parameters are calculated according to Vlasov s theory Vlasov 1961 for thin walled beams All the above parameters relate to the full section For effective width calculations each element of the cross section is assumed to be of a specific type Examples of different types of elements include unstiffened elements stiffened elements elements with an edge stiffener and elements with one or more intermediate stiffeners In the case of a plain unlipped channel section for example each flange is assumed to be an unstiffened element and the web is assumed to be a stiffened element Furthermore the effective width rules to be applied to such elements may vary depending on whether the element is in uniform compression or is subjected to a stress gradient The corner regions are always fully effective It should be noted that ColdSteel has enormous flexibility and power in modelling the complex geometries of some commercial profiles The modelling is performed in such a manner that the physical purpose of the element is understood and effective width calculations are facilitated even if the complex element comprises many sub elements The philosophy and procedures pertaining to effective width calculations differ between stiffened and unstiffened elements In both cases the starting point for calculations
15. which will also be the computed load factor 4 when a unit design moment M is used The Main form of ColdSteel with all relevant input parameters is shown in Fig 30 Upon clicking the Check button the Output form is displayed as shown in Fig 31 The maximum design bending moment is thus 8 84 kNm November 1998 Centre for Advanced Structural Engineering The University of Sydney 205 100 1s All dimensions in mm All internal radii 3 mm fy 350 MPa Fig 29 Lipped hat section with intermediate V stiffener in bending i0 xl AS NZS 4600 1996 Cold Formed Steel Structures Eile Options Help Check Design Options Exit Section v Stiffened Lipped Hat z ey ro Ex 4 6 2 5 Non principal n p Material G350 M Use default material Design Actions 1st Order Lengths Cb Cm Factors Mo Cm Factors N M N kN jo L m 0 Clause 3 3 3 2 a Clause 3 5 1 Mx kNm f Lex m fo cmx fi Cmx ii My kN im fo Ley m 0 Chy fi Cmy fi Lez m Bearing V jo Felel Tenson Faces Clause 3 3 3 2 b Lb y m 3 vy kN bl ension Factors kt ft Cmx a ciy m 3 jo bs br m jo e y m jo Memory Used 299080 Fig 30 Main form pertaining to Example 2 Governing Mode Nominal Capacities and Overload Factors CHECK V 8Stiffened Lipped Hat Ex4 6 2 0 Governing Load Factor 8 8372 SAFE Section capacity in bending about x axis Msx AS NZS
16. 0 000255211 m2 Ae fy Effective area for uniform stress fy 0 000255211 m2 Ae fn Effective area for uniform stress fn 2 75207E 6 m4 16 effective 2nd moment of area x bending extreme fibre at yield 2 75207E 6 m4 16 effective 2nd moment of area x bending extreme fibre at yield 3 9039E 7 m4 effective 2nd moment of area y bending extreme fibre at yield H oO K 2 82068E 7 4 Iey effective 2nd moment of area y bending extreme fibre at yield 2 41586E 5 3 Zext effective section modulus at yield x bending 2 41586E 5 m3 Zex effective section modulus at yield x bending 7 20052E 6 m3 26 effective section modulus at yield y bending 6 353158 6 m3 Zey effective section modulus at yield y bending Fig 35 Effective section properties for MC 20015 section of Example 3 Centre for Advanced Structural Engineering November 1998 The University of Sydney 26 ColdSteel User s Manual Version 1 0 Example 4 Simply Supported Lipped Channel Section Purlin Section 5 8 1 of Hancock 1998 Problem Determine the design load on the purlin section in Example 3 simply supported over a 7 m span with one brace at the centre and loaded on the tension flange as shown in Fig 36 Use both the lateral buckling method Clause 3 3 3 2 and the R factor method Clause 3 3 3 4 Distortional buckling should also be checked according to Clause 3 3 3 3 Uplift q on tension flange X La
17. 2 of Hancock 1998 Problem Determine the distortional buckling stress f of the lipped channel section in Example 4 Fig 32 when subjected to bending about the major principal axis Use Appendix D of AS NZS 4600 1996 Solution The lipped channel section shown in Fig 32 is termed MC 20015 and is a specific instance of the LippedChannel section class defined in the ColdSteel database see Appendix I Centre for Advanced Structural Engineering November 1998 The University of Sydney 28 ColdSteel User s Manual Version 1 0 The distortional buckling stress f in bending about the x axis is computed by ColdSteel irrespective of the given design actions or other input parameters The MC 20015 channel section has symmetry about the x axis so there is no need to distinguish between positive and negative bending The Main form of ColdSteel with all relevant input parameters is shown in Fig 33 Upon clicking the Check button the Output form is displayed as shown in Fig 34 As no design actions were input there is no governing failure mode or load factor Clicking on the Full Details button produces a full listing of calculated quantities The relevant output from the Miscellaneous Properties portion of the listing is reproduced in Fig 39 from which it can be seen that distortional buckling stress in bending is fa 04 245 0 MPa This value is slightly above the distortional buckling stress of 241 4
18. 3 2 a Clause 3 5 1 Mx kN m fo Lex m B Cx Cmx f Leyim BO Cy Cmy ft Vx kN po Lez m Boo Bearing Clause 3 3 3 2 b Loy mot es kt Mo fF a 8 Bear Poo ewm pi LL Memory Used 272072 Fig 59 Main form pertaining to Example 10 Centre for Advanced Structural Engineering November 1998 The University of Sydney 39 ColdSteel User s Manual Version 1 0 Governing Mode Nominal Capacities and Overload Factors x CHECK SHS Section 76576 2 0 85H85 0 Governing Load Factor 81 9729 SAFE Member capacity flexural or flexural torsional buckling in compression Neft AS NZS 4600 1996 Clause 3 4 1 Draw Section Full Details Fig 60 Output form pertaining to Example 10 Example 11 Unlipped Channel Column Section 7 6 2 of Hancock 1998 Problem Determine the maximum design compressive axial force for the unlipped channel section shown in Fig 61 assuming the channel is loaded concentrically through the centroid of the effective section and the effective lengths in flexure L L and torsion L are 1500 mm The nominal yield stress f is 240 MPa ex Ay All dimensions in mm f y 240 MPa 152 x Fig 61 Unlipped channel section for Example 11 Solution The unlipped channel section depicted in Fig 61 and termed Ex 7 6 2 is a specific instance of the PlainChannel section class defin
19. 3 5 1 a Draw Section Full Details Fig 72 Output form pertaining to Example 14 Centre for Advanced Structural Engineering November 1998 The University of Sydney 45 ColdSteel User s Manual Version 1 0 Example 15 Lipped Channel Beam Column Bent in Plane of Symmetry Section 8 5 3 of Hancock 1998 Problem Calculate the maximum design axial compressive load in the lipped channel shown in Fig 65 assuming the channel is loaded with an axial force at the intersection of the x axis with the outer edge of the web As in Example 12 the effective lengths are L 2000 mm L 1000 mm and L 1000 mm and the nominal yield stress f is 300 MPa Solution The relevant lipped channel section Ex 7 6 3 is the same as that used in Example 12 It can be seen from the Full Details output given in Fig 73 that the dimension from the full section centroid to the extreme fibre in the negative x axis direction is 0 028400 m Furthermore Fig 74 indicates that under a uniform stress f the effective section centroid is 0 003394 m closer to the web than the full section centroid measured along the axis of symmetry Thus in this example a compressive load of N 1 0 KN co exists with a bending moment about the minor y axis of M 0 028400 0 003394 0 025006 kNm The beam is in uniform bending and therefore the moment modification coefficients C used in lateral buckling calculations and in the beam column strength intera
20. 4600 1996 Clause 3 3 2 a Draw Section Full Details Fig 31 Output form pertaining to Example 2 24 ColdSteel User s Manual Version 1 0 Example 3 Lipped Channel Section in Bending Section 4 6 3 of Hancock 1998 Problem Determine the effective section modulus 2 for bending about the horizontal axis for the metric C 20015 lipped channel purlin section shown in Fig 32 The yield stress of the material is 450 MPa Assume elements lie along their centrelines and eliminate thickness effects The effective section modulus Z should be computed assuming the section is fully stressed f f AY 1 200 x All dimensions in mm fy 450 MPa fiss 0 J Fig 32 Metric C 20015 lipped channel section purlin Solution The metric lipped channel section shown in Fig 32 is termed MC 20015 and is a specific instance of the LippedChannel section class defined in the ColdSteel database see Appendix I The 450 MPa yield material is defined as G450 in the ColdSteel database The effective section modulus at yield 2 is computed by ColdSteel irrespective of the given design actions or other input parameters The MC 20015 channel section has symmetry about the x axis so there is no need to distinguish between positive and negative bending The Main form of ColdSteel with all relevant input parameters is shown in Fig 33 Upon clicking the Check butto
21. Effective Cross Se Section C 20015 Material 6450 5 552E 04 m2 3 525E 06 4 3 963E 07 m4 0 000E 00 m4 0 000 deg 3 593E 05 kPa Fig 22 Display after selecting the Effective Section Mbly button Full and Effective Cross Sections Section C 20015 Material 0 3 541E 04 m2 3 224E 06 4 2 710E 07 m4 0 000E 00 m4 0 000 deg 4 5008 05 kPa Fig 24 Display after selecting the Effective Section Mbly button November 1998 ColdSteel User s Manual Full and Effective Cross Sections Section C 20015 Material G450 4 659E 04 m2 2 8125 06 4 2 942E 07 m4 1 737E 07 m4 0 000 deg 4 5008 05 kPa Fig 19 Display after selecting the Effective Section Msx button Full and Effective Cross Sections Section C 20015 Material 6450 5 5528 04 m2 3 525E 06 4 3 963E 07 m4 0 000E 00 m4 0 000 deg 4 5008 05 kPa Fig 21 Display after selecting the Effective Section Msy button Full and Effective Cross Sections Section C 20015 Material 0 3 707E 04 m2 3 292E 06 m4 2 864E 07 m4 0 000E 00 m4 0 000 deg 4 5008 05 kPa Fig 23 Display after selecting the Effective Section Msy button Centre for Advanced Structural Engineering The University of Sydney 20 ColdSteel User s Manual Version 1 0 3 6 Viewing Full Calculation Details After a member strength check or design has been performed a full report of all quanti
22. Engineering November 1998 The University of Sydney 33 ColdSteel User s Manual Version 1 0 Governing Mode Nominal Capacities and Overload Factors CHECK Lipped Z Section Equal Flanges Z 20015 0 Governing Load Factor 2 1106 SAFE Member capacity lateral buckling in bending about n axis Mbn AS NZS 4600 1996 Clause 3 3 2 b Draw Section Full Details Fig 48 Output form for check of interior segment in end span under uplift load System capacity based on rational elastic buckling analysis A rational elastic lateral buckling analysis of the whole purlin system under uplift load has been performed by Hancock 1998 From this analysis it can be deduced that the elastic critical buckling moment M is 13 34 kNm This result can be used to determine the maximum design load as described hereafter The Options Bending form of ColdSteel needs to be set to indicate that the critical moment M will be computed according to Clause 3 3 3 2 b of AS NZS 4600 1996 the elastic buckling moment M will be determined using a rational elastic buckling analysis and the value of M is 13 34 kNm The completed Options Bending form is shown in Fig 49 The corresponding Main and Output forms are shown in Figs 50 and 51 respectively from which it can be deduced that the maximum upwards design load is 2 00 kN m which is very close to Hancock s 1998 result of 1 98 kN m AS NZS 4600 1996 Options x General Compres
23. MPa reported by Hancock 1998 since ColdSteel assumes that the elastic critical buckling load in compression of the flange lip assembly acts at the centroid of the assembly rather than at the midline fibre of the flange as assumed by Hancock 1998 8 5000 Distortional buckling stress in pure compression 244990 kPa fodx Distortional buckling stress in bending 244990 kPa fodx Distortional buckling stress in bending 290645 kPa fody Distortional buckling stress in bending 8 fody Distortional buckling stress in bending Fig 39 Distortional buckling parameters for MC 20015 section of Example 5 Example 6 Lipped Z Section in Bending Section 5 8 4 of Hancock 1998 Problem Determine the effective section modulus Z for bending about the horizontal axis for the Z 20015 lipped Z section purlin shown in Fig 40 The yield stress of the material is 450 MPa Assume elements lie along their centrelines and eliminate thickness effects The effective section modulus Z should be computed assuming the section is fully stressed f f Solution The lipped Z section shown in Fig 40 is termed Z 20015 and is a specific instance of the LippedZed section class defined in the ColdSteel database see Appendix I The 450 MPa yield material is defined as G450 in the ColdSteel database The effective section modulus at yield Z for bending about the horizontal n non principal axis is computed by C
24. R L 1 4 t 8 Fig 1 3 PlainChannel definition Centre for Advanced Structural Engineering November 1998 The University of Sydney 51 ColdSteel User s Manual Version 1 0 LippedChannel Specify a list of lipped channel sections The profile geometry of a lipped channel section is shown in Fig I 4 Each lipped channel section must be defined on a separate line using the following format Format Description Dimension 5 Section name e g C 10010 5 Section material must be defined in Material e g G450 I Unit combination code 0 millimetres newtons F Thickness f L F Overall depth D L F Overall flange width B L F Overall lip depth L L F Internal corner radius for all corners R L F Distortional buckling stress for bending about x axis f4 F L 2 3 4 5 6 tID BIL R Fig I 4 LippedChannel definition Centre for Advanced Structural Engineering November 1998 The University of Sydney 52 ColdSteel User s Manual Version 1 0 PlainZed Specify a list of Plain Z sections The profile geometry of a plain Z section is shown in Fig I 5 Each plain Z section must be defined on a separate line using the following format Format Description Dimension 5 Section name e g PZ 10010 5 Section material must be defined in Material e g G450 I Unit combination code 0 millimetres ne
25. checked then for the purposes of calculating the torsion related section properties of shear centre x y warping constant I monosymmetry parameters B and B and polar radius of gyration r a simplified model of the cross section whereby the bends are eliminated and the section is represented by straight midlines is employed A simplified model of this nature is permitted by Clause 2 1 2 1 of AS NZS 4600 1996 If this option is not checked then a thin walled midline model in which the bends are modelled exactly is used Primarily through its influence on the warping constant the use of a simplified square corner model rather than an accurate one which models the bends may lead to slightly improved values of design capacities which involve flexural torsional or lateral buckling Centre for Advanced Structural Engineering November 1998 The University of Sydney 12 ColdSteel User s Manual Version 1 0 e Effective width of unstiffened elements with stress gradient Clause 2 3 2 2 of AS NZS 4600 1996 outlines the rules for the effective width of unstiffened elements and edge stiffeners for capacity calculations These procedures implicitly assume that the element is subjected to a uniform compressive stress and do not consider the beneficial effect of a stress gradient on the resulting effective width The effective width formulation described in Appendix F of AS NZS 4600 1996 takes into account the effect
26. from the list of available materials The available Centre for Advanced Structural Engineering November 1998 The University of Sydney ColdSteel User s Manual Version 1 0 materials are specified in the Material section of the ColdSteel database as described in Appendix I It is possible for the user to define their own materials Axis System For some cross sectional shapes such as Z sections and angle sections the principal x y axes are rotated from the so called non principal or rectangular n p axes yet it is often the case that such members are constrained to bend about a non principal axis For example Z section purlins attached to sheeting are usually constrained to bend about an axis perpendicular to the web the n axis ColdSteel then uses a stress distribution based on this assumption to calculate the effective sections in bending In ColdSteel the Axis System option will only be enabled if the currently chosen section class is one for which it is relevant to consider bending about non principal n p axes If the n p axis system is chosen the subscripts on the design actions and equivalent moment coefficients displayed on the main form alter from x to n and y to p accordingly Design Actions Clause 1 6 2 Structural Analysis and Design of AS NZS 4600 1996 does not mention whether the design actions should be based on first order or second order elastic analysis However the terms C a and C in the member s
27. is the monosymmetry section constant defined by 1 2 3 X X dA 2x 6 where x is the shear centre position relative to the centroid and C is a coefficient which is equal to 1 depending on the direction of bending about the y axis Caution is advised when using ColdSteel to calculate the lateral buckling capacities of hat sections bent about the horizontal non symmetry axis This is because there is a large monosymmetry section constant B associated with hat sections and the shear centre y is eccentric from the section centroid The lateral buckling moments for hat sections may differ by an order of magnitude between positive and negative bending and there is also a strong load height effect Neither of these factors is considered adequately in Clauses 3 3 3 2 a or 3 3 3 2 b of AS NZS 4600 1996 In view of the preceding comments it is recommended that elastic lateral buckling moments for hat sections be determined using a rational elastic buckling analysis CASE 1997a as it is only in this way that the effects of support conditions moment distribution and load height can be considered with a degree of accuracy C Factors for use in Interaction Formulae for Combined Compression and Bending When compression and bending co exist AS NZS 4600 1996 requires the specification of coefficients C and C which account for an unequal distribution of bending moment for bending about the x and y axes of the cross section respectively Th
28. stress gradient parameter y After the plate buckling coefficients have been determined the effective widths for the plate elements in the cross section can be calculated For this purpose the stress f used in calculating the element slenderness A 2 5 Jk 11 5 tN is equal to the maximum compressive stress in the element as shown in Fig 11 1 for stiffened elements ree f Based on the resulting effective section effective cross sectional properties such as area centroid and second moments of area can be determined If the centroid of the effective section differs from the centroid of the gross section then the ratio y of the stresses at the ends of each element may change this leads to Centre for Advanced Structural Engineering November 1998 The University of Sydney 64 ColdSteel User s Manual Version 1 0 the question of whether a new plate buckling coefficient k and hence new effective lengths should be computed for the various elements in the cross section If so the whole effective section computation procedure is iterative until convergence is achieved In relation to AS NZS 4600 1996 the following philosophy is adopted for stiffened and unstiffened elements e For stiffened elements effective width calculations are iterative i e the plate buckling coefficient is computed based on the current effective section or full section if it s the first iteration which in turn leads to
29. the units and data values displayed MEE Exit Axis System Section C20015 v Non principal np Material G450 gt M Use default material Design Actions 1st Order Lengths Ch Cm Factors Mo Cm Factors N M N kN fo L m 6 Clause 3 3 3 2 a Clause 3 5 1 Mx kNm f5 Lex m f chx i Cmx fi My kN m fo Ley m 5 Cmy ft Cmy Vx kN gt Lez m Bearing _ Clause 3 3 3 2 b Lb y m 41 Vy kN oS ension Factors kt fi Cmx fi 66 m 0 1 fo Ry en br m fo e y m 41 Memory Used 190944 on the Main form alter correspondingly AS NZS 4600 1996 Cold Formed Steel Structures File Options Help Check Design Options Fig 1 Main form of ColdSteel November 1998 Centre for Advanced Structural Engineering The University of Sydney ColdSteel User s Manual Version 1 0 The physical problem represented by the data on the Main form shown in Fig 1 corresponds to a C 20015 Grade 450 lipped channel section in uniform bending about the major x axis as shown in Fig 2 The span of the member is 6 m and it has lateral and torsional restraints at the supports and at midspan The data required for ColdSteel comprises the following e effective lengths L L 3m e moment modification coefficient C 1 0 e design moment M 5 kNm The above problem and data will constitute the basis of many of the figures pres
30. 0 AS 4100 1990 Steel Structures Standards Australia Sydney 1990 SA SNZ 1996 AS NZS 4600 1996 Cold Formed Steel Structures Standards Australia Standards New Zealand 1996 SA SNZ 1998 AS NZS 4600 Supplement 1 1998 Cold Formed Steel Structures Commentary Supplement 1 to AS NZS 4600 1996 Standards Australia Standards New Zealand 1998 Trahair N S 1993 Flexural Torsional Buckling of Structures Chapman amp Hall First Edition London Vlasov V Z 1961 Thin walled Elastic Beams 2nd edition Israel Program for Scientific Translations Jerusalem Centre for Advanced Structural Engineering November 1998 The University of Sydney 72
31. 0 Invalid factor for tension capacity E 151 Invalid amount of material removed b for tension capacity E 152 Invalid amount of material removed for tension capacity b gt b E 160 Invalid member actual length L E 161 Invalid member effective length L E 162 Invalid member effective length L E 163 Invalid member effective length L E 164 Elastic critical buckling load N from rational buckling analysis is zero W 165 Invalid effective length L r gt 200 W 166 Invalid effective length L r gt 200 E 167 Invalid set of effective lengths L La Le fa is negative Centre for Advanced Structural Engineering November 1998 The University of Sydney 70 ColdSteel User s Manual Version 1 0 E 170 Invalid moment factor C for calculation of M Clause 3 3 3 2 a E 171 Invalid moment factor C for calculation of M Clause 3 3 3 2 a E 172 Invalid moment factor C for calculation of M Clause 3 3 3 2 a E 173 Invalid moment factor C for calculation of M Clause 3 3 3 2 a E 174 Invalid moment factor C for calculation of M Clause 3 3 3 2 b E 175 Invalid moment factor C for calculation of M Clause 3 3 3 2 b E 176 Invalid moment factor C for use in combined actions E 177 Invalid moment factor C for use in combined actions E 178 Elastic critical buckling moment M from rational buckling analysis is zero E 180 Invalid bearing length E 181 Invalid bearing length c E 182 Invali
32. Factor 5 4057 SAFE Section capacity in bending about x axis Msx AS NZS 4600 1996 Clause 3 3 2 a Draw Section Full Details Fig 28 Output form pertaining to Example 1 Example 2 Hat Section in Bending with Intermediate Stiffener in Compression Flange Section 4 6 2 of Hancock 1998 Problem Determine the maximum design positive bending moment for bending about a horizontal axis of the hat section shown in Fig 29 when an intermediate stiffener is added to the centre of the compression flange as shown in Fig 29 Solution The hat section shown in Fig 29 is termed Ex 4 6 2 and is a specific instance of the VeeLippedHat section class see Appendix I In the notation of this example a positive bending moment about the horizontal axis is one causing compression in the top flange of the hat section In the notation and terminology of ColdSteel this corresponds to a negative moment M To determine the design moment capacity a reference value of M 1 is input to ColdSteel with all other design actions zero To reflect the fact that a section Centre for Advanced Structural Engineering November 1998 The University of Sydney 23 Version 0 ColdSteel User s Manual rather than member capacity is being calculated all member effective lengths are also input as zero The maximum design moment capacity will then correspond to the relevant design section capacity in bending M
33. OM Any lt 1 0 1 18 where it should be borne in mind that gt b M and 0 M gt pM In essence Eq 111 17 constitutes the critical strength check where the moment amplification is not sufficient to cause the maximum moments within the length of the member to exceed the maximum first order values If there are no transverse loads on the member the position of maximum moment will be at one of the member ends Equation III 18 allows for the effects of moment amplification on the design moment distributions about the x and y axes Centre for Advanced Structural Engineering November 1998 The University of Sydney 68 ColdSteel User s Manual Version 1 0 If N b N gt 0 15 the following interaction may be used in lieu of Eqs 111 17 and III 18 4 5 gt lt 10 III 19 ON PM yx DM oy 11 9 Combined Axial Tensile Load and Bending Clause 3 5 2 The design axial tensile load M and the design bending moments M and M about the principal x and y axes must satisfy the following inequalities i M 4 4 0 III 20 ON OM ot DM yf M M i eea A 1 0 111 21 OM Moy ON 2 It should be noted from Eq 111 21 that the nominal strength of a member subjected to bending and tension may be greater than that of the same member subjected to the corresponding bending moments only Centre for Advanced Structural Engineering November 1998 The University of Sydney 69 Cold
34. Section button Full and Effective Cross Se Section C 20015 Material 0 4 188E 04 m2 3 361E 06 4 3 049E 07 m4 0 000E 00 m4 0 000 deg 1 052E 05 kPa Fig 16 Display after selecting the Effective Section Nc button Full and Effective Cros Section C 20015 Material G450 5 224E 04 m2 3 196E 06 m4 3 259E 07 m4 1 482E 07 m4 0 000 deg 2 337E 05 kPa Fig 18 Display after selecting the Effective Section Mblx button November 1998 ColdSteel User s Manual Full Section Accurate A 5 552E 04 m2 3 525E 06 m4 3 963E 07 m4 0 000E 00 m4 0 000 deg Fig 13 Display after selecting the Full Section button Full and Effective Cross Sections Section C 20015 Material 6450 2 510E 04 m2 2 225E 06 m4 1 489E 07 m4 0 000E 00 m4 0 000 deg 4 5008 05 kPa Fig 15 Display after selecting the Effective Section Ns button Section C 20015 Material G450 4 659E 04 m2 2 812E 06 m4 2 942E 07 m4 1 737E 07 m4 0 000 deg 4 5008 05 kPa Fig 17 Display after selecting the Effective Section Msx button Centre for Advanced Structural Engineering The University of Sydney 19 Version 0 Full and Effective Cross Sections Section C 20015 Material G450 5 224E 04 m2 3 196E 06 m4 3 259E 07 m4 1 482E 07 m4 0 000 deg 2 337E 05 kPa Fig 20 Display after selecting the Effective Section Mblx button E Full and
35. Steel User s Manual Version 1 0 Appendix IV Error and Warning Codes E Error W Warning E 100 Invalid unit of length E 101 Invalid unit of force E 102 Invalid unit of mass E 110 Invalid axis system E 111 Invalid procedure for calculation of M Clause 3 3 3 2 E 112 Invalid parameter relating to effective widths of unstiffened elements E 113 Invalid parameter for calculation of M Clause 3 3 3 2 E 114 Invalid parameter for calculation of M when C C 1 0 Clause 3 3 3 2 E 115 Invalid parameter for calculation of M Clause 3 3 3 2 E 116 Invalid parameter for calculation of M when C C 1 0 Clause 3 3 3 2 E 117 Invalid parameter for calculation of N E 118 Invalid parameter for calculation of E 119 Invalid option for inclusion of L 1000 eccentricity for angle sections E 120 Invalid R factor option E 121 Invalid option for distortional buckling capacity in compression N a E 122 Invalid option for distortional buckling capacity in bending about x axis Ma3 E 123 Invalid option for distortional buckling capacity in bending about y axis M a E 124 Invalid option for transverse loads for bending about x axis E 125 Invalid option for transverse loads for bending about y axis E 130 Invalid type of cross section E 131 Invalid cross section dimension E 140 Invalid Young s modulus E E 141 Invalid shear modulus G E 142 Invalid yield stress f E 143 Invalid tensile strength f E 144 Invalid material density p E 15
36. The University of Sydney 16 ColdSteel User s Manual Version 1 0 3 5 Designing a Member Clicking on the Design button on the Main form will instruct ColdSteel to perform a design using the currently chosen cross section class design actions and other parameters The cross section designations for the chosen cross section class are ranked in order of mass per unit length and a strength check proceeds from the lightest to heaviest sections until a satisfactory design A 1 0 is attained Fig 12 If the Use Default Material option is checked then the material properties used in conjunction with each cross section for which a design check is performed correspond to those defined in the ColdSteel database the material designation may therefore vary from section to section during the design cycle If the Use Default Material option is unchecked then the currently chosen material is used for all design checks until the lightest satisfactory member is determined Lipped Channel _ 1 0 15316 UNSAFE 0 18841 UNSAFE 0 25042 UNSAFE 0 46920 UNSAFE 0 34187 UNSAFE 0 66542 UNSAFE 1 24988 SAFE 4 6 Abort Close Fig 12 Member design results form 3 5 Visualisation of Full and Effective Sections After a member strength check or design has been performed the full and effective cross sections can be visualised by clicking on the Draw Section button A scaled drawing of the cross section is shown tog
37. ause 3 3 3 2 a Chx Cmy Clause 3 3 3 2 b Cmx Lengths 0000 Lim 2 Lex m Ley m ft Lezim ft Tension Factors gt kt E br m Eile Options Help Section Material Ex 7 6 3 C300 v Design Actions 1st Order N kN pooo mx Nm Poo My kNm 0 025006 Vx kN Vy kN kN Memory Used 324984 Fig 75 Main form pertaining to Example 15 Governing Mode Nominal Capacities and Overload Factors Ex7 6 3 0 31 7185 SAFE CHECK Lipped Channel Governing Load Factor Combined bending and cornpression AS NZS 4600 1996 Clause 3 5 1 a Full Details Fig 76 Output form pertaining to Example 15 Draw Section Centre for Advanced Structural Engineering 47 The University of Sydney ColdSteel User s Manual Version 1 0 Appendix I The ColdSteel Database When ColdSteel is executed a database of available materials and profiles is initialised These components are specified in the initialisation file COLDSTEEL INI This file must reside in the same directory as the executable program ColdSteel exe and can be edited freely using an ordinary text editor An example COLDSTEEL INI file is given at the end of this appendix The various materials comprising the profiles are specified using the Material keyword followed by one line of data for each material defined The various pro
38. between the centroids of the full and effective sections in capacity calculations when a compression force is involved Indeed one of the subtleties in cold formed design is that the nominal column strength N is computed based on the assumption that the design axial compression N acts through the effective section centroid computed for the cross section subjected to a uniform compressive stress f rather than the full section centroid However users of ColdSteel are shielded from the details of effective centroids and associated force eccentricities through the Assumed line of action of compressive N option from within the Options form see Section 3 2 If the compressive force is assumed to act through the effective section centroid then there is no eccentricity and no additional moments are computed internally by ColdSteel If the compressive force is assumed to act through the full section centroid then there may be an eccentricity in which case appropriate additional moments are computed internally by ColdSteel and considered in capacity calculations Design shear forces V and V Design shear forces V and are assumed to act in both the x and y directions respectively but it is not required to distinguish between positive and negative values Design bearing force R A bearing force R is assumed to act in the y direction only with the positive sign convention indicated in Fig 5 The sign convent
39. ction formula are both unity The Main form pertaining to this example is shown in Fig 75 and the Output form obtained upon clicking the Check button is shown in Fig 76 The maximum compressive load which can be applied eccentrically at the intersection of the axis of symmetry and the outer edge of the web of the lipped channel section is therefore N a 31 7 KN Properties of Full Section 0 270562 m Wf Feed width 0 000405843 m2 A full section 0 000405843 m2 A net section 0 0276495 m xc x ordinate of centroid full section Om yc y ordinate of centroid full section 0 0656134 m xo x ordinate of shear centre referred to principal axes Om yo y ordinate of shear centre referred to principal axes 7 12262E 7 m4 Ix full section 3 1562E 7 m4 Iy full section 0 m4 Ixy full section 0 deg Inclination of principal axes full section 0 0418929 m full section radius of gyration 0 0278871 m ry full section radius of gyration O0 0293 995 im Extreme negative x ordinate full section 0 0466005 m Extreme positive x ordinate full section 0 05 m Extreme negative y ordinate full section 0 05 m Extreme positive y ordinate full section 1 42452E 5 m3 Zx Full section modulus yield at extreme positive y ordinate 1 42452E 5 m3 Zx Full section modulus yield at extreme negative y ordinate 6 77288E 6 m3 2 Full section modulus yield at extreme positive x ordinate 1 11136E 5 3
40. d as defined in Tables 3 3 6 1 and 3 3 6 2 then the bearing involves two opposite loads or reactions If 6 gt 1 5d a single load or reaction is assumed to be involved Centre for Advanced Structural Engineering November 1998 The University of Sydney 10 Version 0 Configuration ene Type and Position of Load Single load or reaction 0 gt 1 5 d Single load or reaction c gt 1 5 d Two opposite loads or reactions 0 gt 1 5 d 6 gt 1 5 0 Two opposite loads or reactions c gt 15dy e lt 15d ColdSteel User s Manual Nomenclature End One Flange EOF Interior One Flange AOF End Two Flange ETF Interior Two Flange ITF Fig 6 Definitions of parameters used in bearing capacity calculations Options Form 3 2 The Options form enables the user to set several fundamental options which control the program operation and facilitate access to the more unusual or advanced features The particular options which are available are grouped in the following categories Units This option is used to set the units of length force and mass which pertain to all calculations and reported values The relevant unit of stress is derived from the specified units for length and force If the units are changed then all relevant input values are automatically scaled appropriately and the unit designations updated accordingly Design Actions This option is used to indicate whether the desig
41. d bearing length e E 183 Web too slender for bearing d t gt 200 E 184 Bearing length too long J t gt 210 E 185 Bearing length too long J d gt 3 5 W 186 Bearing equations not valid 7 t gt 6 0 Clause 3 3 6 W 190 Distortional buckling stress f from rational buckling analysis is zero Appendix D was used instead W 191 Distortional buckling stress f from rational buckling analysis is zero Appendix D was used instead W 192 Distortional buckling stress f from rational buckling analysis is zero Appendix D was used instead W 193 Distortional buckling stress f from rational buckling analysis is zero Appendix D was used instead W 194 Distortional buckling stress f from rational buckling analysis is zero Appendix D was used instead E 195 Distortional buckling stress in pure compression f is negative Appendix D E 200 Invalid R factor E 210 Invalid deflection limit for seviceability calculation E 211 Invalid type of beam for serviceability calculation W 220 Unstiffened element too slender b t im 60 Clause 2 1 3 W 221 Stiffened element too slender b 1 200 Clause 2 1 3 W 222 Edge stiffened element too slender Clause 2 1 3 E 223 Circular section too slender d t gt 0 441E f Clause 3 6 1 Centre for Advanced Structural Engineering November 1998 The University of Sydney 71 ColdSteel User s Manual Version 1 0 Appendix V References AISI 1996 Specificati
42. dSteel User s Manual Version 1 0 L L Plain equal Plain unequal Plain Lipped angle angle channel channel Plain Lipped Z section Z section Plain hat with Lipped hat with V stiffener Lipped hat V stiffener Square hollow Rectangular Circular hollow section hollow section section Fig 3 Profile shapes incorporated into ColdSteel Section Classes LILI CC SSIS OO O Fig 4 ColdSteel section class icon palette Section Designation For a particular chosen section class a list of pre defined section designations is available The section designation is chosen from the list box located immediately below the Section Class list box Clicking the arrow on the right hand side of the section designation list box displays the full list of available profiles for the chosen section class It is possible for users to customise their own section designations and this is performed by modifying the ColdSteel database as described in Appendix I Material Grade The Material Grade list box located beside the Material label may be disabled or enabled depending on whether the Use Default Material option is checked or not If the Use Default Material option is checked the Material Grade list box is disabled and the material displayed corresponds to that specified for the current section designation in the ColdSteel database If the Use Default Material option is unchecked the Material Grade list box is enabled and the user can select
43. de Nominal Capacities and Overload Factors CHECK Plain Channel Ex7 6 2 C240 Governing Load Factor 93 4042 SAFE Member capacity flexural or flexural torsional buckling in compression Neft AS NZS 4600 1996 Clause 3 4 1 Fig 64 Output form pertaining to Example 11 Centre for Advanced Structural Engineering The University of Sydney 41 ColdSteel User s Manual Version 1 0 Example 12 Lipped Channel Column Section 7 6 3 of Hancock 1998 Problem Determine the maximum design compressive axial force for the lipped channel section shown in Fig 65 assuming the channel is loaded concentrically through the centroid of the effective section and the effective lengths in flexure L L and torsion L are based on a lateral and torsional restraint in the plane of symmetry at mid height L 2000 mm L 1 1000 mm The nominal yield stress f is 300 MPa Ay TEE All dimensions in mm f y 300 MPa a 1 5 fies 5 Fig 65 Lipped channel section for Example 2 Solution The lipped channel section depicted in Fig 65 and termed Ex 7 6 3 is a specific instance of the LippedChannel section class defined in the ColdSteel database see Appendix I The 300 MPa yield material is defined as C300 in the ColdSteel database In this example the lipped channel is loaded through the centroid of the effective section and hence the maximum design axial compressive force N
44. design moments M and M and shear forces V and the capacity in combined bending and shear is required to be checked independently in a uniaxial sense according to 2 4 2 111 12 OV OM 2 2 ve M 111 13 1 0 lt Vix HM y as given in Clause 3 3 5 of AS NZS 4600 1996 for beams with unstiffened webs Bearing Clause 3 3 6 5 The bearing capacity which is checked in ColdSteel relates to a vertical bearing load for which the corresponding nominal bearing capacity R is defined in Tables 3 3 6 1 or 3 3 6 2 of AS NZS 4600 1996 The corresponding capacity factor gt for bearing is equal to 0 75 The bearing load parameters c and e Centre for Advanced Structural Engineering November 1998 The University of Sydney 67 ColdSteel User s Manual Version 1 0 are supplied as input parameters to ColdSteel If the distance e between opposing bearing loads is less than 1 5 times the web depth d as defined in Tables 3 3 6 1 or 3 3 6 2 then the bearing involves two opposite loads or reactions If 6 gt 1 5d a single load or reaction is assumed to be involved 111 6 Combined Bending and Bearing Clause 3 3 7 For the case of a member subjected to a design moment M and a bearing load the capacity is checked according to M 1 42 11 14 2 1 07 by for shapes having single unstiffened webs Compression Clause 3 4 Members subjected t
45. e A Although the same symbol F is used to indicate both a floating point real variable and the basic dimension of force F the correct interpretation should always be clear from the context Material Specify a list of materials Each material must be defined on a separate line using the following format Format Description Dimension 5 Material name enclosed in quotation marks e g G450 I Unit combination code 0 millimetres newtons kilograms F Young s modulus E F Shear modulus G F Yield stress f F Ultimate tensile strength f F Density p Centre for Advanced Structural Engineering November 1998 The University of Sydney 48 ColdSteel User s Manual Version 1 0 PlainEqualAngle Specify a list of plain unlipped equal angle sections The profile geometry of a plain equal angle section is shown in Fig I 1 Each plain equal angle section must be defined on a separate line using the following format Description Dimension Section name e g 100x100x5 0 EA Section material must be defined in Material e g C450L0 Unit combination code 0 millimetres newtons Thickness f L Overall leg length B Internal corner radius for all corners R L Fig 1 1 PlainEqualAngle definition Format 25 25 Centre for Advanced Structural Engineering November 1998 The University of Sydney 49
46. ect to the x axis of the full section and the summation occurs over all flat elements in the accurate cross section model Corners and lip stiffeners are assumed not to contribute to the shear resistance The shear capacity term V is computed using a slight modification of Eqs 3 3 4 1 to 3 3 4 3 in AS NZS 4600 1996 For eet 1 V 0 64 f bt Ek f bit 5 For 1 lt lt 1415 0 64 Ek f 11 11 Ek f For Fn ais V 0 905Ek 13 b Ek f in which b t and k are length thickness and shear buckling coefficient respectively of the flat element being considered ColdSteel assumes that none of the plate elements are stiffened with transverse stiffeners and with this assumption the shear buckling coefficient is given as k 5 34 in AS NZS 4600 1996 for webs Implicit in the value of k 5 34 however is the assumption that the element is supported on both edges by other plate elements as would be the case with the web of a channel section Since there is no guidance given in AS NZS 4600 1996 as to what values of k should be assumed for unstiffened elements the flanges of an unlipped channel and both legs of an unlipped angle for example the value of k 5 34 has also been used for these elements It should be noted that AS NZS 4600 1996 does not specifically preclude the application of k 5 34 to unstiffened elements in shear H 4 Combined Bending and Shear Clause 3 3 5 For the general case of a member subjected to
47. ed in the ColdSteel database see Appendix I The 240 MPa yield material is defined as C240 in the ColdSteel database In this example the channel is loaded through the centroid of the effective section and hence the maximum design axial compressive force N corresponds to the design compression capacity N which is equal to the computed load factor when a reference load of N 1 is input to ColdSteel The fact that the channel is loaded through the effective centroid rather than the full centroid is indicated by setting the appropriate option in the Options Compression form as shown in Fig 62 The Main and Output forms of ColdSteel pertaining to this example are shown in Figs 63 and 64 respectively from which it can be seen that the maximum design compression force is N a 93 4KN It is interesting to note that if the member is assumed to be loaded through the full section centroid rather than the effective section centroid then the maximum capacity remains at N a 93 4 This is because the section is fully effective under a uniform compressive stress of f and hence the full and effective centroids coincide Centre for Advanced Structural Engineering November 1998 The University of Sydney 40 Version 0 November 1998 ColdSteel User s Manual AS NZS 4600 1996 Options Nonpi Plain Channel amp Principal 2 fon lr Fig 63 Main form pertaining to Example 11 Governing Mo
48. elements or 0 9 if the elements in compression are unstiffened elements The relevant capacity factors are defined appropriately by ColdSteel As far as bending strength governed by lateral buckling is concerned the capacity factor is equal to 0 9 universally Members subjected to a design bending moment M about the principal y axis must satisfy 5 M S My M gt py III 6 in which M is the nominal section capacity based on the initiation of yielding in the effective section and M is the nominal member lateral buckling moment capacity for bending about the y axis 11 3 Shear Clause 3 3 4 Members subjected to design shear forces V and Vy in the x and y axis directions must satisfy 11 7 Vy gt III 8 vx members subjected to shear To circumvent the difficulty associated with the fact that the design shear in which V and V are the corresponding nominal shear capacities and 0 0 9 is the capacity factor for Centre for Advanced Structural Engineering November 1998 The University of Sydney 66 ColdSteel User s Manual Version 1 0 forces V and V are in the axis directions but the capacities of the individual cross section elements to resist shear vary according to their orientation the shear capacities are computed using Va V coso II 9 Flat Elements Vy V jsino 11 10 Flat Elements in which is the orientation of the straight element with resp
49. en tensile and negative when compressive Design moments M and The design bending moments M and M correspond to the maximum moments about the x and y axes caused by the factored nominal loads As discussed above these moments should be derived from first order elastic structural analysis and should therefore not include second order effects Furthermore the sign of the moments may be input as positive or negative with the positive sign convention following the right hand rule as shown in Fig 5 Positive moments M i for example cause compression on the tips of the flanges of the channel section depicted in Fig 5 Where a compressive axial force coexists with bending the design moments M and M 20 input to ColdSteel should be based on the following assumptions e the line of action of the axial force corresponds to the full section centroid e any eccentricity which may exist between the centroid of the full section and the centroid of the effective section subjected to a uniform compressive stress f is ignored Centre for Advanced Structural Engineering November 1998 The University of Sydney ColdSteel User s Manual Version 1 0 Yi T Tension chk C Compression 6 fes Fig 5 Positive sign convention for design moments M and M and bearing force R It should not be interpreted from the second of the above two assumptions that it is always appropriate to ignore the eccentricity
50. ented in Section 3 of this User s Manual C 20015 5 kNm e a eoi o el Fig 2 Lipped channel section beam in uniform bending 5 The Main form comprises the data items described below Section Class The section class data is located in a list box immediately beside the Section label shown at the top left of the Main form Clicking on the arrow on the right hand side of the section class list box reveals the full list of available section classes The sections available in this version of ColdSteel are e Plain unlipped equal angle section e Plain unlipped unequal angle section e Plain unlipped channel section e Lipped channel section e Plain unlipped Z section e Lipped Z section e Plain unlipped hat section e Plain unlipped hat section with an intermediate V stiffener in the top flange e Lipped hat section e Lipped hat section with an intermediate V stiffener in the top flange e Square hollow section e Rectangular hollow section e Circular hollow section The basic profile shapes of these sections are shown in Fig 3 The above section classes are displayed graphically and may be selected from an icon palette as shown in Fig 4 The icon palette is visible if the Options View Icon Palette menu item is checked and is not visible if this item is unchecked The icon palette may be moved and resized as convenient Centre for Advanced Structural Engineering November 1998 The University of Sydney Col
51. ese C coefficients are additional to the C C coefficients described above which are used in elastic lateral buckling moment calculations Centre for Advanced Structural Engineering November 1998 The University of Sydney ColdSteel User s Manual Version 1 0 The values of these C coefficients are defined in Clause 3 5 1 as follows e For compression members in frames subject to joint translation side sway C 0 85 7 e For restrained compression members in frames braced against joint translation and not subjected to transverse loading between their supports in the plane of bending C 0 6 0 4 8 M 2 where M M is the ratio of the smaller to the larger moment at the ends of that portion of the member under consideration which is unbraced in the plane of bending The end moment ratio M M is taken as positive if the member is bent in reverse curvature and negative if it is bent in single curvature e For compression members in frames braced against joint translation in the plane of loading and subject to transverse loading between their supports the value of C may be determined by rational analysis However in lieu of such analysis the following values may be used For members whose ends are restrained C 0 85 0 For members whose ends are unrestrained C 1 0 Bearing Coefficients For all cross section classes included in ColdSteel only a bearing force R in the vertical directi
52. etc Full Details Results of Analysis by ColdSteel 4600 Version 1 0 November 1996 section Class Lipped Channel Section Designation C 20015 Material Grade G450 Governing Load Factor and Mode Governing Load Factor 1 2499 SAFE Member capacity lateral buckling in bending about x axis Mbx AS NZS 4600 1996 Clause 3 3 2 b Length Metres Force Kilonewtons Mass Kilograms Input Parameters d Copy to Clipboard B Print JI Close Fig 25 Full Details form Centre for Advanced Structural Engineering November 1998 The University of Sydney 21 ColdSteel User s Manual Version 1 0 4 Design Examples The following examples are taken from the book Design of Cold Formed Steel Structures 3rd Edition by Gregory J Hancock published by the Australian Institute of Steel Construction Hancock 1998 In this book full working and references to the relevant clauses of AS NZS 4600 1996 are given for all the examples In the application of ColdSteel to all the ensuing examples the following options are set gt Thin walled theory is used for section property calculations e Square corners are assumed for torsional section properties e Design actions are determined from first order analysis e Distortional buckling in compression is ignored It is also assumed that the materials and cross sections referred to in the examples are already defined in the ColdSteel database I
53. ether with a set of axes originating from the centroid of the full section A selection of the cross section properties are also displayed in a smaller moveable window A selection of buttons is available the functions of which are as follows e Full Section button Draws the cross section with the axes located at the full section centroid C The cross section is orientated relative to the principal x y or non principal n p axis system as appropriate The cross sectional properties of area A second moments of area Z I and inclination of principal axes 8 are shown in a smaller window Fig 13 e Simplified Section button Draws the simplified model of the cross section used for determination of torsional section properties with the principal x y axes originating from the full section centroid C The location of the shear centre is also shown and is labelled S The cross sectional properties of area A second moments of area Z J inclination of principal axes 0 shear centre location x y and warping constant are shown in a smaller window Fig 14 e Effective Section buttons A range of effective sections corresponding to different design capacities in compression and bending can be displayed Note that for the purpose of calculating some effective section properties the shape of some elements within the cross section profile may be simplified This is reflected in the graphical depiction of the various ef
54. evant Bending Moment Coefficients based on Cross Sectional Geometry Cross Sectional Geometry Coefficient used for Calculation of Doubly symmetric Singly symmetric about x axis Singly symmetric about y axis Point symmetry No axes of symmetry Centre for Advanced Structural Engineering November 1998 The University of Sydney ColdSteel User s Manual Version 1 0 For calculation of the elastic lateral buckling moment M for a member bent about the principal x axis the following procedures consistent with Clause 3 3 3 2 are used by ColdSteel e Ifthe cross section has an axis of symmetry about the x axis M ox Cy Atgry Soy Soe 1 e If the cross section does not have an axis of symmetry about the x axis Aes CxB2 2 SOF Hra fo C mx 2 In Eq 2 B is the monosymmetry section constant defined by B 7 Q y y 4429 3 where y is the shear centre position relative to the centroid and Cis a coefficient which is equal to 1 depending on the direction of bending about the x axis For the calculation of the elastic lateral buckling moment M for a member bent about the principal y axis the following procedures consistent with Clause 3 3 3 2 are used by ColdSteel e If the cross section has an axis of symmetry about the y axis M y Chy Ar J fox foz 4 e If the cross section does not have an axis of symmetry about the y axis 6 2 Cy fB 2P trOn 5 oy C ny In Eq 5 B
55. ez m 2 8 Bearing ease z Tension Factors Clause 3 3 3 2 b Lb p m 0 1 kt f Cms f cmm f1 Ree 2 br m jo e p m 31 Memory Used 332044 Fig 45 Main form for check of end segment in end span under uplift load Governing Mode Nominal Capacities and Overload Factors CHECK Lipped Z Section Equal Flanges Z 20015 0 Governing Load Factor 2 0503 SAFE Member capacity lateral buckling in bending about n axis bn AS NZS 4600 1996 Clause 3 3 2 b Draw Section Full Details Fig 46 Output form for check of end segment in end span under uplift load AS NZS 4600 1996 Cold Formed Steel Structures _ op x File Options Help Check Design Options Exit 1 A F Axis System Section Lipped Z Section Equal Flanges z Principal xy 220015 5 Material G450 M Use default material Non principal n p Design Actions 1st Order Lengths Ch Cm Factors Mo Cm Factors N M N kN jo L m 7 Clause 3 3 3 2 a Clause 3 5 1 Mn kNm 59 Lex m jo Cbx E Cmn fi Mp kN m po Ley m 2 7 Chy Cmp 1 2 Lez m 2 7 Bearing V jo a Tension Fact Clause 3 3 3 2 b Lb p m jo Vp kN ension Factors kt f Cms f cm pa Rp kN jo e p m p a Memory Used 334088 Fig 47 Main form for check of interior segment in end span under uplift load Centre for Advanced Structural
56. f this is not the case the ColdSteel database file COLDSTEEL INI needs to be modified using a standard text editor to define the required materials and or cross sections The COLDSTEEL INI file supplied with the ColdSteel software contains all the required data to verify the following examples Example 1 Hat Section in Bending Section 4 6 1 of Hancock 1998 Problem Determine the maximum design positive bending moment for bending about a horizontal axis of the hat section shown in Fig 26 The yield stress of the material is 350 MPa Assume the element lies along its centreline and eliminate thickness effects 225 100 Tel 75 All dimensions in mm fy 350 MPa Fig 26 Lipped hat section in bending Solution The material with a yield stress of 350 MPa is termed G350 in the ColdSteel database and is defined in the Material section The hat section shown in Fig 26 is termed Ex 4 6 1 and is a specific instance of the LippedHat section class see Appendix I In the notation of this example a positive bending moment about the horizontal axis is one causing compression in the top flange of the hat section In the notation and terminology of ColdSteel this corresponds to a negative moment M To determine the design moment capacity a reference value of M 1 is input to ColdSteel with all other design actions zero To reflect the fact that a section rather than member capacity is being calcula
57. fective section models The ineffective portions of the cross section are shown highlighted in yellow The origin of the axes is the full section centroid but the labelled centroid C corresponds to the effective section currently displayed The effective area A and second moments of area Zye Ls and the maximum stress fx in the cross section are displayed in a smaller window Centre for Advanced Structural Engineering November 1998 The University of Sydney 17 ColdSteel User s Manual Version 1 0 0 Ns button Displays the effective section corresponding to the section strength in pure compression uniform stress of f Fig 15 Ne button Displays the effective section corresponding to the member flexural or flexural torsional buckling strength in pure compression uniform stress of f Fig 16 Msx button Displays the effective section corresponding to the section strength in pure bending about the positive x axis maximum extreme fibre stress of f Fig 17 Mblx button Displays the effective section corresponding to the member lateral buckling strength in pure bending about the positive x axis maximum extreme fibre compressive stress of f M Z see Clause 3 3 3 3 Fig 18 Msx button Displays the effective section corresponding to the section strength in pure bending about the negative x axis maximum extreme fibre stress of f Fig 19 Mblx button Display the effecti
58. files are defined in the database using a keyword specific to that profile For example standard lipped channel sections are defined using the LippedChannel keyword and standard lipped Z section profiles are defined using the LippedZed keyword The materials must be defined first in the COLDSTEEL INI file The various profiles may then be defined subsequently in any convenient order In addition to defining key dimensions profile definitions may include other cross section specific data such as distortional buckling stresses calculated using a rational elastic buckling analysis of the plate assemblage The profile dimensions are compulsory data but distortional buckling stresses are optional data The data format for each component is described in the following sections The data type of each item is described by the following format characters e S String variable e 1 Integer variable e F Floating point real variable In addition an open square bracket indicates the commencement of an optional block of data and a closing square bracket signifies the end of the optional data It is not possible to include part of the data between the open and closing brackets it must all be provided or none at all To facilitate the use of correct and consistent units in the purlin system database the dimension of each quantity listed in the following tables is given in terms of the fundamental dimensions of length L force F mass M and angl
59. force acts through the centroid of the full section thus producing a possible eccentricity If the member is fix ended at both ends then the effective centroid shift can be followed exactly by the external compression force and thus no additional moments are generated to degrade the strength of the member In this case it is appropriate to assume that the compression force acts through the centroid of the effective section 0 Ina structural analysis program it is usually assumed that all members are connected concentrically through their elastic centroids The axial compression force determined by such an analysis would then be tacitly assumed to act through the full section centroid e Calculation of elastic buckling load The column elastic flexural or flexural torsional buckling load N is required to calculate the column strength Ordinarily N is calculated from the given member effective lengths L L and 7 Alternatively AS NZS 4600 1996 permits the use of a rational elastic buckling analysis to calculate N directly If the latter option is chosen the actual value of N from the rational elastic buckling analysis should be input to ColdSteel e Use L 1000 eccentricity for angle sections This option is only relevant and only becomes operative if the current section is an equal or unequal angle It implements the design provision of Clause 3 4 1 of AS NZS 4600 1996 which states Angle sections shall be designed for
60. form obtained upon clicking the Check button is shown in Fig 46 Assuming the end span of the end segment is governing the maximum uniformly distributed load which can be applied to the purlin system is thus 2 05 kN m This value is slightly greater than the corresponding value of 1 92 kN m reported by Hancock 1998 for the following reasons e In ColdSteel both flanges have been averaged in length whereas in Hancock 1998 it was assumed that the wide flange is in compression e In ColdSteel the elastic lateral buckling moment M is evaluated using Eq 2 whereas in Hancock 1998 the simplified and approximate formula from AS NZS 4600 1996 n Edl a 10 2L for point symmetric Z sections was used In Eq 10 above d is the depth of the section measured between the centrelines of the flanges L is the unbraced length of the member and J is the second moment of area of the compression portion of the full section about the centroidal axis of the full section parallel to the web Interior segment in end span Following the approach of Hancock 1998 the minor axis L and torsional L effective lengths are assumed to be equal to the distance between the central brace and the point of contraflexure in the end span The point of contraflexure has been used to define the end of the segment since sheeting is attached to the top flange by screw fastening and it is therefore assumed to provide lateral restraint to the top compressi
61. gn section capacity in bending of 5 41 kNm Example 1 it can be seen that a bearing load equal to half the design bearing capacity reduces the bending capacity by 11 6 per cent The Main and Output forms of ColdSteel pertaining to the above calculations are shown in Figs 56 and 57 respectively AS NZS 4600 1996 Cold Formed Steel Structures File Options Help Check Design Options Exit November 1998 0 7 Axis System Section lipped Hat Principal x Ex 4 6 1 v Non principal n p Material G350 y M Use default material Design Actions 1st Order Lengths Ch Cm Factors Mo Cm Factors N M N kN jo L m 0 Clause 3 3 3 2 a Clause 3 5 1 Mx kN m 4 784 Lex m jo Cmx j Cmx ft My kN im fo Ley m 0 Chy j Cmy fi Vx kN po Lez m Bearing Tension Factors clause 3 3 3 2 b 196 m 0 05 vy kN ension Factors kt ft Cmx cy m 5 9 023 si brim f ety m 0 15 l Memory Used 212192 Fig 56 Main form pertaining to Example 9 Governing Mode Nominal Capacities and Overload Factors CHECK Lipped Hat Ex4 6 1 0 Governing Load Factor Interaction between bending and bearing about x axis AS NZS 4600 1996 Clause 3 3 7 Draw Section 1 0000 SAFE Full Details Fig 57 Output form pertaining to Example 9 Centre for Advanced Structural Engineering The University of Sydney 38
62. ing Load Factor 1 1056 SAFE Interaction between bending and shear about n axis AS NZS 4600 1996 Clause 3 3 5 Draw Section Full Details Fig 55 Output form pertaining to Example 8 Centre for Advanced Structural Engineering November 1998 The University of Sydney 37 ColdSteel User s Manual Version 1 0 Example 9 Combined Bearing and Bending of Hat Section Section 6 8 2 of Hancock 1998 Problem Determine the design bearing capacity of the hat section in Example 1 for a bearing length of l 50 mm at an interior loading point Determine also the design bending capacity about the x axis with the top flange in compression at the loading point when the load is half of the bearing capacity computed Solution In the terminology of AS NZS 4600 1996 for bearing capacity a single interior loading point is defined by c gt 1 5d and e gt 1 5d Hence we may assume c e 2d 150 mm for ColdSteel calculations An initial ColdSteel analysis using the above parameters indicates that the design bearing capacity of the Ex 4 6 1 LippedHat section is R 18 046 kN Hence in the combined bending and bearing analysis the bearing load Ry should be input as 9 023 kN and the bending moment about the x axis M A negative varied until a load factor of 1 0 is achieved It can quickly be established that when Ry 9 023 KN the maximum design moment is M 4 784 kNm Comparing this result to the desi
63. ing specified as zero Upon reading into ThinWall the interactive data entry screens may be used to modify the data e g the set of assumed buckling half wavelengths if required AS NZS 4600 1996 Options x i Compression Bending Distortional Buckling Units Design Actions Length m zl 1stOrder 2nd Order 000 ThinWall File Theory for calculation of section properties C Thick walled theory Mass kg Thin walled theory M Use square corners for torsional section properties Effective width of unstiffened elements with stress gradient C Clause 2 3 2 2 a and b Appendix Fig 7 General Options e Theory for calculation of section properties Flexural section properties such as second moments of area may be calculated using thick walled or thin walled theory Thick walled calculations include the second moment of area of each element about its own centroidal longitudinal axis whereas thin walled theory neglects such terms For thin sections thick walled theory and thin walled theory give practically identical results It is important to note that irrespective of whether the thick walled or thin walled theory option is chosen torsional section properties such as St Venant torsion constant shear centre warping constant and monosymmetry parameters utilise the thin walled assumption universally e Use square corners for torsional section properties If this option is
64. ions described above for axial forces bearing forces and bending moments are necessary to enable ColdSteel to distinguish between tensile and compressive forces the direction of bearing and the direction of bending the latter being important for non symmetric sections It should be understood however that in the member design checks detailed in Appendix III it is only the magnitude and not the sign of the design actions that is important i e all the design actions are tacitly assumed to be positive when applying the design equations detailed in Appendix 1 Centre for Advanced Structural Engineering November 1998 The University of Sydney ColdSteel User s Manual Version 1 0 Tension Factors Correction factor k The correction factor k is a factor which allows for the effects of eccentric or local end connections on the nominal tensile capacity of a member as governed by fracture though the net section see Clause 3 2 2 of AS NZS 4600 1996 Equivalent removed width b The equivalent removed width b corresponds to the length of the cross section perimeter which is removed due to bolt holes The equivalent removed width b must be input by the user and should incorporate an appropriate allowance for staggered holes if relevant The net area A is then computed by ColdSteel as A A b t in which A is the area of the full section Member Lengths Actual member length L The actual member length L corres
65. is an assumed stress distribution acting over the gross section accurate model including bends From this stress distribution the stresses F and F acting at the ends of the element are determined see Fig II 1 Each of these stresses is calculated at the midline of the element concerned and not at an extreme fibre For calculation purposes it is assumed that 7 and Jy are positive in compression negative in tension and that f gt F Centre for Advanced Structural Engineering November 1998 The University of Sydney 63 ColdSteel User s Manual Version 1 0 Axis of bending 15 tension 15 compression a b b b b f f 1 compression Boo Axis of bending c Fig II 1 Effective widths of stiffened elements subjected to stress gradient and uniform compression and definitions of fi 0 and f For stiffened elements the plate buckling coefficient k is determined using Eq 2 2 3 1 4 of AS NZS 4600 1996 44 2 1 w 2 1 w 1 2 in which the stress ration y is given by I 3 1 For unstiffened elements AS NZS 4600 1996 provides two options for the calculation of the plate buckling coefficient k In line with the AISI Specification AISI 1996 on which AS NZS 4600 1996 is closely based the constant value of k 0 43 1 4 is assumed Alternatively the rationale outlined in Appendix F Table F1 of AS NZS 4600 1996 can be used in which k is expressed as a function of the
66. ith Section 2 of AS NZS 4600 1996 Two geometric models of the cross section are employed in calculations an accurate model and a simplified model The accurate model includes the geometry of the bends exactly and is used for the calculation of all properties which are directly related to section capacities and the torsion constant J In more detail the properties based on the accurate section model include e full and effective cross sectional area for the purposes of determining the nominal tensile capacity N and the nominal compressive capacities N and N e full and effective section moduli for the purposes of determining nominal bending capacities M M sx M M M and M s e the radii of gyration r and r bx e the torsion constant J which is based on the simplified formula bt wt J y 3 II 1 Elements i in which b and t are the midline length and thickness of element i in the cross section In cold formed sections the thickness is constant and ya w in which w denotes the width of the feedstock The simplified cross section models represent the section as an assembly of straight mid line elements and may ignore the bends Generally the simplified model is employed in the calculation of all parameters related to the stability of members These parameters include e the shear centre position x y e the polar radius of gyration of the cross section about the shear centre
67. l e g G450 I Unit combination code 0 millimetres newtons degrees F Thickness f L F Overall depth D L F Overall width of top flange B L F Width of bottom flanges F L F Overall depth of V stiffener V L F Internal corner radius for all bends at flange web junctions R L F Internal corner radius for all bends in V stiffener R L F Angle of webs from the vertical A F Angle of sides of V stiffener from the vertical A 1 2 3 4 5 6 7 8 10 Rf Ry Oy by fodx Fig 1 8 VeePlainHat definition Centre for Advanced Structural Engineering November 1998 The University of Sydney 56 ColdSteel User s Manual Version 1 0 LippedHat Specify a list of lipped hat sections The profile geometry of a lipped hat section is shown in Fig I 9 Each lipped hat section must be defined on a separate line using the following format Format Description Dimension 5 Section name e g 1 11 10010 5 Section material must be defined in Material e g G450 I Unit combination code 0 millimetres newtons degrees F Thickness f L F Overall depth D L F Overall width of top flange B L F Width of bottom flanges F L F Lip stiffener length L L F Internal corner radius for all bends R L F Angle of webs from the vertical A F Angle of bottom flange stiffeners from vertical A 1 203 4 5 6 7 8 9 5 Ow Os foa
68. ld formed steel structural members to the limit states Australian New Zealand Standard AS NZS 4600 1996 SA SNZ 1996 The program runs in a standalone interactive mode under the Windows 95 98 NT operating systems ColdSteel is intended to be used as a cold formed steel design calculator that facilitates the semi automated design of cold formed steel structural members by freeing the engineer from the complex detail of effective section distortional buckling stress and other detailed design computations ColdSteel performs all the relevant member strength calculations for a range of commonly used cold formed profile shapes including angle sections channel sections Z sections hat sections rectangular hollow sections and circular hollow sections The program can run in either a check or design mode For a given set of design actions and other relevant parameters such as effective lengths running ColdSteel in check mode will determine if the member is satisfactorily designed to AS NZS 4600 1996 with respect to all relevant strength limit states The load factor and corresponding governing limit state is also reported In design mode ColdSteel determines the lightest section of a particular cross sectional shape for which the design with respect to the given set of actions and other relevant parameters is satisfactory ColdSteel has extensive reporting and graphical visualisation facilities For any particular check or design C
69. ling stresses are calculated on the fly as part of the member strength check If the rational elastic buckling analysis option is chosen the relevant distortional buckling stresses defined in the ColdSteel database are used in lieu of those calculated according to the simple analytical model It is assumed that the distortional buckling stresses defined in the ColdSteel database have been previously calculated using ThinWall or a similar buckling analysis The distortional buckling options discussed above will only be enabled where they are relevant for the currently chosen cross section Also the format for definition of distortional buckling stresses in the ColdSteel database will vary from profile to profile as outlined in Appendix I Centre for Advanced Structural Engineering November 1998 The University of Sydney 15 ColdSteel User s Manual Version 1 0 AS NZS 4600 1996 Options General Compression Bending Distortional Buckling Distortional buckling stress fodc in compression Calculate ucing Simple ah al vice Moe Use Valle trom rational elastic Buckling analyse Distortional buckling stresses fodx in bending about x axis Calculate using simple analytical mode Use value trom rational elestc buckling analyse Distortional buckling stresses fody in bending about y axis Calculate using simpe ehelytical model Use valle tom rational elacte bucking analyse Distor
70. n the Output form is displayed as shown in Fig 34 As no design actions were input there is no governing failure mode or load factor Clicking on the Full Details button produces a full listing of calculated quantities The effective section properties are reproduced in Fig 35 from which it can be seen that the effective section modulus at yield in bending is Z Z Z 24160 mm Centre for Advanced Structural Engineering November 1998 The University of Sydney 25 ColdSteel User s Manual Version 1 0 AS NZS 4600 1996 Cold Formed Steel Structures _ op x File Options Help Check Design Options Exit 1 5 Axis System Section Lipped Channel z Principal xy i MC 20015 Non principal n p Material G450 M Use default material 1 Design Actions 1st Order Lengths Ch Cm Factors Mo i Factors N M N kN jo Lim 0 Clause 3 3 3 2 a Clause 3 5 1 Mx kN m jo Lex m jo Chx Cmx ft My kN im fo f Cmy ee E ft 0 Lez m op Bearing v jo oa Lb m f1 vy kN po ension Factors kt f cm P cere brim 77 ey im fot Memory Used 265260 Fig 33 Main form pertaining to Example 3 Governing Mode Nominal Capacities and Overload Factors CHECK Lipped Channel MC 20015 0 No failure mode applicable Draw Section Full Details Fig 34 Output form pertaining to Example 3 Properties of Effective Section
71. n actions in particular the moments M and M have been determined using first order or second order elastic analysis In the latter case General Options Compression Options Bending Options Distortional Buckling Options General Options The General Options form is shown in Fig 7 The options which can be set from this form are November 1998 Centre for Advanced Structural Engineering The University of Sydney 11 ColdSteel User s Manual Version 1 0 ColdSteel sets the moment amplification factors C a and C o to be unity in the appropriate member strength interaction equations e ThinWall data file ColdSteel has the capability to generate an input file which can be utilised by the ThinWall software for cross section stress and finite strip buckling analysis developed by the Centre for Advanced Structural Engineering at the University of Sydney CASE 1997b If the input field is non blank a ThinWall input file of the chosen name which must end in dat is generated whenever a member strength check or design is performed by ColdSteel The data written to the ThinWall file relates to the current cross section axis system and design actions For example if it is desired to undertake a ThinWall cross section buckling analysis of a particular profile subjected to pure compression only then a reference value of N of say 1 KN should be used as input to ColdSteel with all other design actions be
72. n the ColdSteel database see Appendix I The 450 MPa yield material is defined as G450 in the ColdSteel database In this example the equal flange variant of the lipped Z section is used see Example 6 Since the combined bending and shear check is essentially a section capacity check all the effective lengths can be input as zero The Main form of ColdSteel with all relevant input parameters is shown in Fig 54 Upon clicking the Check button the Output form is displayed as shown in Fig 55 The load factor of 1 11 indicates that combined bending and shear at the end of the lap is satisfactory and does not control the design of the purlin system AS NZS 4600 1996 Cold Formed Steel Structures _ op x File Options Help Check Design Options Exit Section Lipped Z Section Equal Flanges z z ezon C Principal x y 2005 v gt Non principal n p Material G450 M Use default material Design Actions 1st Order Lengths Ch Cm Factors Mo Cm Factors N M N kN fo tm p Clause 3 3 3 2 a Clause 3 5 1 Mn kNm 744 Lex m D Chx Mpm fo Lev m ehy Vn kN 77 Lez m po Bearing Shee Clause 3 3 3 2 b Lb p m 3 T kt f Cmx cm pa 1 brim f emm 1 Vp kN 8 26 Memory Used 306464 Fig 54 Main form pertaining to Example 8 Governing Mode Nominal Capacities and Overload Factors CHECK Lipped Z Section Equal Flanges Z 20015 0 Govern
73. neral Channels Lipped Channels and Z Sections Simple Lipped Channels or Z Sections in Bending about the Axis Perpendicular to the Web Shear Centre Distance m Torsion Constant J and Warping Constant Z in Compression and Bending D 1 General Channels in Compression D 2 Simple Lipped Channels in Compression D 3 Appendix E Section Properties 1 2 Monosymmetry Section Constants Appendix F Unstiffened Elements with Stress Gradient 3 Program Operation 3 1 Main Form After the initial title screen the Main form of ColdSteel is displayed as shown in Fig 1 The majority of the data that is required to perform a member strength check or design is displayed on the Main form However since some of the design actions may be zero it may not be necessary to enter data for every input parameter At all times the relevant data items are clearly delineated and the unnecessary items are shaded the same colour as the Main form The Options form instigated by clicking on the Options button of the Main form enables a particular combination of length force and mass units to be set together with other parameters relating to calculation of compressive lateral buckling and distortional buckling capacities The Options form is discussed in detail in Section 3 2 It will be observed from Fig that the relevant units are displayed beside each item of data in the Main form If the system of units is changed through the Options form then
74. new effective widths new centroid new stress ratio y new stress f and so on e For unstiffened elements the adoption of 0 43 automatically ensures that effective width calculations are not iterative for those elements Similarly if Appendix F is utilised the values of y and k which should be adopted for each unstiffened element are uniquely determined by the stress gradient y pertaining to the full section This approach is consistent with the philosophy employed in Eurocode 3 CEN 1996 from which Appendix F is drawn As the position of the effective centroid changes from iteration to iteration the stress f used in Eq 11 5 may also change In all cases however f is the maximum compressive stress in the element Therefore it may be stated that effective section calculations in AS NZS 4600 1996 are iterative in principle when the cross section is subjected to a stress gradient The stress ratio yw and plate buckling coefficient k pertaining to a stiffened element may change throughout the iterative process as the effective section changes On the other hand the values of y and k used for an unstiffened element whether based on Eq 11 4 above or Appendix F of AS NZS 4600 1996 are uniquely determined from the initial stress distribution assumed to act over the gross section If the cross section is subjected to a uniform stress distribution effective section calculations entail no iteration Centre for Advanced Structural Enginee
75. o a design compressive force N which acts through the centroid of the effective section must satisfy SN 1 15 N SON III 16 in which N A f with the effective area A calculated at the yield stress f N A f with the effective area A calculated at the inelastic critical stress f The capacity factor gt for concentrically loaded compression members is equal to 0 85 The clauses in AS NZS 4600 1996 relating to distortional buckling are not relevant for any of the sections currently included in ColdSteel It should be noted that in the usual case the design axial force N as computed by the structural analysis is assumed to act through the centroid of the full rather than the effective cross section In this case the member must be designed for the additional design moments resulting from the eccentricity of the axial force from the effective centroid Furthermore for angle sections the effect of the design compressive axial force N acting through an eccentricity e L 1000 causing a moment equal to N L 1000 applied about the minor axis causing compression in the tips of the legs must be considered 11 8 Combined Axial Compressive Load and Bending Clause 3 5 1 The design axial compressive load N and the design bending moments M and M y about the principal x and y axes must satisfy the following two inequalities 4 2210 III 17 ON DM px DM oy N CoM y OM One
76. of the stress gradient across the element and may be used to obtain greater section capacities Compression Options The Compression Options form is shown in Fig 8 The options which can be set from this form are e Assumed line of action of compressive 7 Clause 3 4 1 of AS NZS 4600 1996 relating to concentrically loaded compression members states that This Clause applies to members in which the resultant of all loads acting on the member is an axial load passing through the centroid of the effective section calculated at the critical stress f A corollary of this statement is that if the axial compression force is directed along the line of the full section centroid as indeed should be assumed when determining the design moments M and M H to input to the Main form of ColdSteel then additional bending moments resulting from the eccentricity if it exists of the full and effective section centroids should be considered in the internal design calculations performed by ColdSteel It is up to the judgement of the engineer to ascertain whether it is more appropriate to assume the axial compression force acts through the full section centroid or the effective section centroid however the following points are pertinent If the member is pin ended at both ends then the effective centroid shift in a monosymmetric section has a strength degrading effect and should be considered in design In this case it should be assumed that the compressive
77. oidal axis perpendicular to the web However in ColdSteel Clause 3 3 3 2 b is also deemed appropriate for hat sections bent about the horizontal axis The justification for extending the use of Clause 3 3 3 2 b in this way is due to the caution which should be exercised when applying Clause 3 3 3 2 a to hat sections bent about the horizontal axis refer to the discussion of C C factors in Section 3 1 If it is chosen to calculate M according to Clause 3 3 3 2 b then the elastic lateral buckling moment M may be calculated according to the formulae given in Clause 3 3 3 2 a or b or it may be determined from a rational elastic buckling analysis of the structural system If the latter option is chosen the relevant values of M for positive and negative bending determined from such an analysis must be input to ColdSteel For hat sections bent about the horizontal axis it is recommended that the elastic buckling moments be determined from a rational elastic buckling analysis CASE 1997a Centre for Advanced Structural Engineering November 1998 The University of Sydney 14 ColdSteel User s Manual Version 1 0 AS NZS 4600 1996 Options General Compression Bending Distortional Buckling Member capacity Mbx for lateral buckling Clause 3 3 3 2 Pure bending strength check Calculation of Mcx Clause 3 3 3 2 a d Calculation of Mox Clause 3 3 3 2 8 Mox from rational buckling analysis KN m fo
78. oldSteel irrespective of the given design actions or other input parameters Strictly speaking the Z 20015 section has flanges which are of slightly unequal length When the ColdSteel database is initialised upon program start up two section classes are actually initialised from the cross sections defined in the LippedZed section of the COLDSTEEL INI file These section classes are e Lipped Z Section where the specified flange dimensions which may be unequal are modelled and e Lipped Z Section Equal Flanges where the two given flange dimensions are averaged this giving the section perfect point symmetry For the purposes of this example the Lipped Z Section Equal Flanges section class will be used to avoid the inconvenience of having to distinguish the sense of bending as in the unequal flange model The Main form of ColdSteel with all relevant input parameters is shown in Fig 41 Upon clicking the Check button and display of the Output form clicking on the Full Details button produces a full listing of calculated quantities The effective section properties are reproduced in Fig 42 from which it can be seen that the effective section modulus at yield in bending is Z Z 2 23850 mm er Centre for Advanced Structural Engineering November 1998 The University of Sydney 29 Version 0 at yield at yield at yield at yield fibre fibre fibre fibre ColdSteel User s Manual All dimensions in mm f
79. oldSteel provides a complete list of all cross sectional properties for both the full and effective sections all nominal and design member capacities the load factor against failure for all relevant strength limit states and other miscellaneous parameters such as elastic column buckling stresses elastic beam lateral buckling moments and distortional buckling stresses The graphical capabilities of ColdSteel enable the visualisation of the effective sections in compression and in bending about both axes in both directions 2 Scope of Software ColdSteel is based on the design rules specified in AS NZS 4600 1996 Cold Formed Steel Structures SA SNZ 1996 Specifically the following clauses of AS NZS 4600 1996 are incorporated in the program Section 1 Scope and General 1 6 2 Structural Analysis and Design Section 2 Elements 2 1 Section properties 2 2 Effective Widths of Stiffened Elements 2 3 Effective Widths of Unstiffened Elements 2 4 Effective Widths of Uniformly Compressed Elements with an Edge Stiffener or One Intermediate Stiffener Section 3 Members 3 1 General 3 2 Members Subject to Tension 3 3 Members Subject to Bending 3 4 Concentrically Loaded Compression Members 3 5 Combined Axial Load and Bending 3 6 Cylindrical Tubular Members Centre for Advanced Structural Engineering November 1998 The University of Sydney Version 0 ColdSteel User s Manual Appendix D Distortional Buckling Stresses of Ge
80. on flange between the point of contraflexure and the first interior support As shown in Hancock 1998 the C factor for the interior segment evaluates to C 1 31 The elastic buckling moment is calculated in accordance with Clause 3 3 3 2 a of AS NZS 4600 1996 The effective lengths are given by L L 2700 mm The design moment is M 379 kNm The ColdSteel Main form complete with all the relevant input parameters is shown in Fig 47 and the Output form obtained upon clicking the Check button is shown in Fig 48 Assuming the interior segment of the end span is governing the maximum uniformly distributed load which can be applied to the purlin system is thus 2 11 kN m For the same reasons as outlined previously this value is slightly greater than the corresponding value of 2 02 kN m reported by Hancock 1998 Centre for Advanced Structural Engineering November 1998 The University of Sydney 32 ColdSteel User s Manual Version 1 0 AS NZS 4600 1996 Cold Formed Steel Structures op x File Options Help Check Design Options Exit 2 7 Axis System Section Lipped Z Section Equal Flanges z 220015 Material G450 M Use default material Non principal n p Design Actions 1st Order Lengths Ch Cm Factors Mo Cm Factors N M N kN jo L m 7 Clause 3 3 3 2 a Clause 3 5 1 Mn kNm 9 Lex m p Cbx 1 29 Cmn ft Mp kN m jo Ley m 2 8 Chy ft 9 kN jo L
81. on for the Design of Cold Formed Steel Structural Members 1996 Edition Printed 1 June 1997 Cold Formed Steel Design Manual Part V American Iron and Steel Institute Washington DC CASE 1997a PRFELB A Computer Program for Finite Element Flexural Torsional Buckling Analysis of Plane Frame Version 3 0 Centre for Advanced Structural Engineering Department of Civil Engineering The University of Sydney April 1997 CASE 1997b ThinWall A Computer Program for Cross Section Analysis and Finite Strip Buckling Analysis of Thin Walled Structures User s Manual Version 1 2 Centre for Advanced Structural Engineering Department of Civil Engineering The University of Sydney April 1997 CEN 1996 ENV 1993 1 3 1996 Eurocode 3 Design of Steel Structures Part 1 3 Supplementary rules for cold formed thin gauge members and sheeting edited draft 9 February 1996 European Committee for Standardisation Brussels CCFSS 1992 Four Span Continuous Z Purlin Design Example CCFSS Technical Bulletin Vol 1 No 2 Center for Cold Formed Steel Structures University of Missouri Rolla August Hancock G J 1998 Design of Cold Formed Steel Structures 3rd Edition Australian Institute of Steel Construction Sydney Serette R L amp Pek z T 1995 Distortional Buckling of Thin Walled Beams Panels I Theory Journal of Structural Engineering American Society of Civil Engineers Vol 121 No 4 pp 757 766 SA 199
82. on is considered The corresponding nominal bearing capacity R is defined in Clause 3 3 6 of AS NZS 4600 1996 The capacity factor 6 for bearing is equal to 0 75 The various parameters related to bearing capacity are depicted in Tables 3 3 6 1 and 3 3 6 2 of AS NZS 4600 1996 which have been partly reproduced here as Fig 6 The former table in AS NZS 4600 1996 relates to profiles having single webs e g channel sections and the latter table relates to back to back channel sections and profiles with restraint against web rotation Bearing length 1 The actual length of bearing for a bearing force R is denoted For the case of two equal and opposite concentrated loads distributed over unequal bearing lengths l should correspond to the smaller bearing length Refer to Tables 3 3 6 1 and 3 3 6 2 of AS NZS 4600 1996 or Fig 6 for diagrams depicting bearing length Bearing parameter c The bearing parameter c corresponding to a bearing force R is equal to the edge distance from the end of the beam to the commencement of the first bearing load as depicted in Tables 3 3 6 1 and 3 3 6 2 and Fig 6 Bearing parameter e The bearing parameter e corresponding to two opposing bearing forces R is equal to the interior distance between the two forces as depicted in Tables 3 3 6 1 and 3 3 6 2 and Fig 6 It should be noted that if the distance e between opposing bearing loads is less than 1 5 times the web depth
83. ponds to the physical length of the member between its connection to supports or other members It is provided mainly for reference purposes but is also used to determine the L 1000 eccentricity required for angle sections in compression see Clause 3 4 1 of AS NZS 4600 1996 Effective lengths L L and L ex The flexural L and L and torsional L effective lengths are used for the calculation of the elastic flexural or flexural torsional buckling stress N for the member in compression and for the elastic lateral buckling moments M and M for the member in bending The x and y axes correspond to the principal axes of the cross section C C Factors for Calculation of Elastic Lateral Buckling Moment M The C and C factors are coefficients used in elastic lateral buckling moment M calculations which account for the non uniform distribution of bending moment along the length of the segment see Clause 3 3 3 2 In AS NZS 4600 1996 two methods of calculating M are provided and these are described in Clauses 3 3 3 2 a and 3 3 3 2 b It may be gleaned from the lateral buckling formulae given in Clause 3 3 3 2 that C 1 C but nevertheless AS NZS 4600 1996 requires the use of C in some lateral buckling moment calculations and 6 in others The choice of whether C or C should be used depends on whether or not the cross section has an axis of symmetry in the plane of bending as indicated in Table 1 Table 1 Rel
84. ral Engineering November 1998 The University of Sydney 60 ColdSteel User s Manual Version 1 0 CHS Specify a list of circular hollow sections The assumed profile geometry of a circular hollow section CHS is shown in Fig 1 13 Each circular hollow section must be defined on a separate line using the following format Format Description Dimension 5 Section name e g 100x5 0 CHS 5 Section material must be defined in Material e g G350 I Unit combination code 0 millimetres newtons F Thickness 1 L F Outside diameter D L AY m D x D OMS 12 t D Fig 1 13 CHS definition Centre for Advanced Structural Engineering November 1998 The University of Sydney 61 ColdSteel User s Manual Version 1 0 Sample COLDSTEEL INI File Material G450 O 200000 0 80000 0 450 0 500 0 7 85e 6 G500 O 200000 0 80000 0 500 0 550 0 7 85e 6 G550 O 200000 0 80000 0 550 0 550 0 7 85e 6 LippedChannel C 10010 G450 0 L 0 102 0 910 12 73 2 0 C 10012 G450 0 L 2 102 0 STe A L235 S C 10015 96450 0 L 5 102 0 Sioh TSAS 3 0 C 10019 96450 0 L 9 102 0 Slet MESA 355 0 C 15012 96450 0 2 0 64 0 14 5 5 0 9615015 0450 0 L 5 0 6150 19 0 60 15019 90450 0 LG 0 6250 16050 C 15024 96450 0 2 4 152 0 64 0 18 5 5 0 C 20015 G450 0 L 5 203 0 7650 2 0
85. ring November 1998 The University of Sydney 65 ColdSteel User s Manual Version 1 0 Appendix Ill Summary of Member Design Checks ColdSteel performs design checks for member strength limit states only The notation used in the following is generally the same as that in AS NZS 4600 1996 except with some minor modifications Tension Clause 3 2 Members subjected to a design tension force N positive must satisfy 0 gt III 1 N lt N 1 2 where N A f is the nominal tensile capacity relating to failure by yielding of the gross section N 0 85k A f is the nominal tensile capacity relating to fracture though the net section and 0 0 9 is the capacity factor for members subject to tension The net area A is computed as A A b t in which b is the length of the cross section perimeter which is removed due to bolt holes accounting appropriately for staggers if relevant Bending Clause 3 3 2 Members subjected to a design bending moment M about the principal x axis must satisfy M lt M 11 3 M gt 111 4 in which M is the nominal section capacity based on the initiation of yielding in the effective section and M is the nominal member lateral buckling moment capacity for bending about the x axis As defined in Table 1 6 of AS NZS 4600 1996 the capacity factor 0 for section strength in bending is equal to 0 95 if the elements in compression are stiffened
86. roid of effective section Centroid of full section Calculation of elastic buckling load Noc C Use value from rational elastic buckling analysis Noc from rational buckling analysis kN fo Fig 8 Compression Options Bending Options The Bending Options form is shown in Fig 9 The options which can be set from this form relate to the determination of the lateral buckling moment capacity M Clause 3 3 3 2 of AS NZS 4600 1996 for bending about the principal x axis The lateral buckling moment capacity M is a function of the critical moment M_ and the elastic buckling moment M It may be noted from the Bending Options form that different options are required to be set for the pure bending and the combined bending and compression strength checks The main reason for this is that according to the rules of AS NZS 4600 1996 it is possible to determine M using a rational elastic buckling analysis in the former case but not the latter The critical moment M can be calculated according to Clause 3 3 3 2 a or 3 3 3 2 b Clause 3 3 3 2 a is applicable to all types of cross sections whether doubly singly point or non symmetric If it is chosen to calculate M according to Clause 3 3 3 2 a then the elastic lateral buckling moment must also be calculated according to Clause 3 3 3 2 a According to AS NZS 4600 1996 Clause 3 3 3 2 b is strictly applicable only to channel or Z sections bent about the centr
87. s Exit Section Lipped Channel z pals Sli Principal y i MC 20015 pA Material G450 M Use default material Non principal n p Design Actions 1st Order Lengths Ch Cm Factors Mo Cm Factors N M N kN p L m Clause 3 3 3 2 a Clause 3 5 1 ho Lem POO cx fizo Cmx i mem fo tym B5 cmy cm E Vy kN po Tension Factors Clause 3 3 3 2 b Loy my fat f Eiga cm pa Ry KN p br m jo RED Memory Used 294960 Fig 37 Main form pertaining to Example 4 Governing Mode Nominal Capacities and Overload Factors CHECK Lipped Channel MC 20015 0 Governing Load Factor 5 9933 SAFE Member capacity lateral buckling in bending about x axis Mbx AS NZS 4600 1996 Clause 3 3 2 b Draw Section Full Details Fig 38 Output form pertaining to Example 4 If the R factor method Clause 3 3 3 4 is used in lieu of the lateral buckling method Clause 3 3 3 2 then the strength in bending M is determined by factoring the section capacity in bending M by the reduction factor R which equals 0 85 for this configuration of outwards load and one row of bridging in simple span Hence M px RM 0 85 10 871 9 240kNm 8 Mpx _ 8x0 9x9 240 2 ae 1 36kN m 12 which agrees identically with Hancock 1998 Example 5 Distortional Buckling Stress in Bending for Lipped Channel Section Section 5 8
88. s with a bending moment about the major x axis of M 0 076 kNm The beam is in uniform bending and therefore the moment modification coefficient C used in lateral buckling calculations and C used in the beam column strength interaction formula are both unity The Main form pertaining to this example is shown in Fig 71 and the Output form obtained upon clicking the Check button is shown in Fig 72 The maximum compressive load which can be applied eccentrically at the intersection of the y axis with the extreme fibre of one flange is therefore 43 3 KN AS NZS 4600 1996 Cold Formed Steel Structures op x File Options Help Check Design Options Exit Section Plain Channel z es Sveti p Principal y E Ex 7 6 2 v Non principal n py Material C240 v Use default material Design Actions 1st Order Lengths Ch Cm Factors Mo Cm Factors N M N kN fa L m 1 5 Clause 3 3 3 2 a Clause 3 5 1 Mx kN m jo 076 Lex m 1 5 Cbx ft Cmx ft My kN m jo Ley m 1 5 Cmy ft Cmy fi Vx kN po Lez m 5 Bearing Tension Factors clause 3 3 3 2 b Lb m 0 1 vy kN op ension Fa kt fi Cmx fi cy m 31 Ry kN jo en br m fo 96 m 3 Memory Used 273748 E Fig 71 Main form pertaining to Example 14 CHECK Plain Channel Ex 7 6 2 C240 Governing Load Factor 43 2640 SAFE Combined bending and compression AS NZS 4600 1996 Clause
89. se 3 3 3 2 b 196 m 0 1 vy kN a ension Factors kt ft Cmx fi c y m 3 p br m p ey m 3 Memory Used 271716 Fig 69 Main form pertaining to Example 13 Governing Mode Nominal Capacities and Overload Factors CHECK Plain Channel Ex7 6 2 C240 November 1998 Full Details Fig 70 Output form pertaining to Example 13 17 4881 SAFE Governing Load Factor Combined bending and compression AS NZS 4600 1996 Clause 3 5 1 a Draw Section Centre for Advanced Structural Engineering The University of Sydney 44 ColdSteel User s Manual Version 1 0 Example 14 Unlipped Channel Beam Column Bent about Plane of Symmetry Section 8 5 2 of Hancock 1998 Problem Calculate the maximum design axial compressive load in the unlipped channel shown in Fig 61 assuming the channel is loaded with an axial force on the intersection of the y axis with one flange As in the previous example the effective lengths in flexure L L and torsion L are 1500 mm and the nominal yield stress f is 240 MPa ex Solution The relevant unlipped channel section Ex 7 6 2 is the same as that used in the previous example It can be seen from the Full Details output given in Fig 68 that the dimension from the full section centroid to the extreme fibre in the positive or negative y axis direction is 0 076 m Thus in this example a compressive load of N 1 0kN co exist
90. sion Bending Distortional Buckling gt Member capacity Mbx for lateral buckling Clause 3 3 3 2 Pure bending strength check Calculation of Mcx Clause 3 3 3 2 b bd Calculation of Mox Rational buckling analysis Mox from rational buckling analysis kN m 13 34 Mox from rational buckling analysis kN m 13 34 Combined bending and compression strength check Calculation of Mex Clause 3 3 3 2 a x Clause 3 3 3 2 8 Calculation of Mox Fig 49 Options Bending form for check of purlin system under uplift load using rational elastic buckling analysis Centre for Advanced Structural Engineering November 1998 The University of Sydney 34 ColdSteel User s Manual Version 1 0 AS NZS 4600 1996 Cold Formed Steel Structures _ op x File Options Help Check Design Options Exit Section Lipped Z Section Equal Flanges z 2 aa Principal x y 2005 v gt Non principal n p Material G450 M Use default material Design Actions 1st Order Lengths Ch Cm Factors Mo Cm Factors N M N kN p L m Clause 3 3 3 2 a Clause 3 5 1 Mn kN m 3 79 Lex m DO Che fist Mpr Nm fo lym Phy Cmp Vn kN po Lez m pooo Bearing 0 Tension Factors clause 3 3 3 2 b Lb m 0 1 kt f Cmx f cm pa jibe br m p e p m 3 Memory Used 328456 Fig 50 Main form for check of purlin system under uplift load using rational ela
91. stic buckling analysis Governing Mode Nominal Capacities and Overload Factors CHECK Lipped Z Section Equal Flanges Z 20015 0 Governing Load Factor 1 9991 SAFE Member capacity lateral buckling in bending about n axis bn AS NZS 4600 1996 Clause 3 3 2 b Draw Section Full Details Fig 51 Output form for check of purlin system under uplift load using rational elastic buckling analysis Other design checks In all of the ColdSteel calculations carried out for this example distortional buckling has been checked and found not to govern over lateral buckling Inspection of the bending moment diagram shown in Fig 44 also indicates that distortional buckling will not be critical in the lapped region over the support because the moment there 5 23 kNm is less than half the maximum moment in the unlapped region 3 79 kNm Combined bending and shear should also be checked at critical locations in the beam such as at the end of the lap For brevity the details of these design checks are not included as part of this example Capacity under downwards load End segment in end span Under downwards load the end segment of the end span is in positive bending exclusively so that the top flange is restrained continuously by the sheeting Lateral buckling of this segment is therefore assumed not to occur Interior segment in end span The Center for Cold Formed Steel Structures from the University of Missouri Rolla USA
92. ted all member effective lengths are also input as zero The maximum design moment capacity will then correspond to the relevant design section capacity in bending gt M _ which will also be the computed load factor when a unit design moment M is used Centre for Advanced Structural Engineering November 1998 The University of Sydney 22 ColdSteel User s Manual Version 1 0 The Main form of ColdSteel with all relevant input parameters is shown in Fig 27 Upon clicking the Check button the Output form is displayed as shown in Fig 28 The maximum design bending moment is thus 5 41 kNm AS NZS 4600 1996 Cold Formed Steel Structures _ oy x File Options Help Check Design Options Section fLippedHat H 2 System Principal y S a S Ex 4 6 1 v Material G350 M Use default material Non principal n p Design Actions 1st Order Lengths Ch Cm Factors Mo Cm Factors N M N kN jo L m 0 Clause 3 3 3 2 8 Clause 3 5 1 Mx kN im 1 Lex m 0 Cmx My kN im fo Ley m 0 Chy Lez m Bearing Vx kN jo Sha Tension Factors Clause 3 3 3 2 b Lb y m 3 vy kN ension Fa La kt ft ff ea m 3 Ry kN jo ae br m jo efy m 3 it Memory Used 339924 Fig 27 Main form pertaining to Example 1 Governing Mode Nominal Capacities and Overload Factors CHECK Lipped Hat Ex4 6 1 0 Governing Load
93. teral torsional brace L Ley Lez 3500 mm Ley Lez 3500 mm L 7000 mm M3 7 128 M4 28 Ms 8 Mmax 8 BMD Fig 36 Simply supported purlin with central brace Solution The relevant lipped channel section is termed MC 20015 and is a specific instance of the LippedChannel section class defined in the ColdSteel database see Appendix I In ColdSteel all relevant strength limit states are checked for any given set of input parameters Thus if distortional buckling happens to control over lateral buckling then this is detected automatically by ColdSteel The relevant ColdSteel input parameters to solve this problem using the lateral buckling method are Fig 37 e Reference design moment M 1 kNm e Effective lengths for central brace L L 3 5 m e C factor for uniformly distributed load C 1 299 As can be seen in Fig 38 the load factor A is 5 993 and the governing mode is that of lateral buckling Distortional buckling with a load factor of 8 503 is not critical The maximum uniformly distributed line load is therefore deduced as _ 8AM 8x5 993x1 ai 5 0 978 KN m which agrees almost identically with the result of Hancock 1998 Centre for Advanced Structural Engineering November 1998 The University of Sydney 27 ColdSteel User s Manual Version 1 0 AS NZS 4600 1996 Cold Formed Steel Structures _ op x File Options Help Check Design Option
94. the design axial force N acting simultaneously with a moment equal to N 1 1000 applied about the minor principal axis causing compression in the tips of the angle legs e Check distortional buckling in compression Clause 3 4 6 AS NZS 4600 1996 Clause 3 4 6 suggests that the distortional buckling strength in pure compression should be considered for all sections for which it is a possible mode of buckling However it is stated in the commentary to AS NZS 4600 1996 AS NZS 1998 that it is not normally necessary to check the distortional buckling mode of failure for simple lipped channels subjected to compression as they are already adequately designed for the distortional mode by virtue of Clause 2 4 3 for section capacity On the other hand some singly symmetric sections such as storage rack columns with additional rear flanges are particularly sensitive to distortional buckling and in these cases Clause 3 4 6 is a very important design consideration Due to Centre for Advanced Structural Engineering November 1998 The University of Sydney 13 ColdSteel User s Manual Version 1 0 the degree of subjectivity associated with the distortional buckling strength check in pure compression ColdSteel provides the user with the option of including or excluding it from the member strength calculations AS NZS 4600 1996 Options General Compression Bending Distortional Buckling Assumed line of action of compressive N C Cent
95. ties calculated and all design checks conducted may be obtained by clicking on the Full Details button A scrollable window with an extensive textual report is then displayed as shown in Fig 25 The full report can be printed directly to the printer using the Print button or copied to the clipboard for later pasting into a text editor or word processor using the Copy to Clipboard button The report comprises the following sections e asummary of the cross section class designation and material gt asummary of the governing load factor and the projected mode of failure e the units employed in all calculations e areproduction of all relevant input parameters used for the member strength check design e the overload factors for all strength limit states with irrelevant strength limit states indicated by a dash ale e the nominal capacities for tension compression bending shear and bearing e the design capacities for tension compression bending shear and bearing together with the relevant capacity factors e areproduction of the cross sectional dimensions as provided in the ColdSteel database that correspond to the section analysed e cross sectional properties of the full section e selected effective cross sectional properties for compression and bending capacities and e various miscellaneous parameters such as buckling stresses lateral buckling moments distortional buckling parameters effective centroid shifts
96. tional buckling stresses from ColdSteel database fode fodx fodx fody fody Fig 10 Distortional Buckling Options 3 4 Checking the Strength of a Member Clicking on the Check button from the Main form will instruct ColdSteel to perform a strength check using the currently chosen cross section material design actions and other parameters All relevant strength limit states specified in AS NZS 4600 1996 are examined The result of the strength check is displayed in summarised form in a window Fig 11 which indicates the cross section class designation and material together with the governing load factor and the governing mode of failure The governing load factor is the maximum scalar by which all the given design actions may be multiplied while still complying with all the strength design provisions of AS NZS 4600 1996 That is if the original design actions are represented by S and the design capacity by R then 6R S A value of the load factor A of at least unity indicate that the member has satisfactory strength Governing Mode Nominal Capacities and Overload Factors CHECK Lipped Channel C 20015 0 Governing Load Factor 1 2499 SAFE Member capacity lateral buckling in bending about x axis Mbx ASINZS 4600 1996 Clause 3 3 2 b Draw Section Full Details Fig 11 Member strength check results form Centre for Advanced Structural Engineering November 1998
97. trength interaction equation for combined compression and bending in Section 3 5 1 of AS NZS 4600 1996 function as amplification factors and so it is evident that first order design moments are implied Through the Options General form ColdSteel provides the user with the option of specifying whether the design actions employed have been calculated from first or second order elastic analysis In the latter case ColdSteel sets the moment amplification factors C a and C a to be unity in the appropriate interaction equations This approach seems reasonable Hancock 1998 but it should be noted that further research is required in this area for cold formed members In ColdSteel the design actions comprise the axial force the bending moments about both cross section axes the shear forces parallel to both cross section axes and the bearing force parallel to the vertical axis It should be noted that for any particular member strength check or design some of the design actions may and invariably will be zero The bending moments shear forces and bearing force are defined with respect to the chosen axis system principal or non principal In the following description it will be assumed that the design actions relate to the principal x y axes rather than the non principal n p axes Design axial force N The design axial force N is the maximum axial force in the member caused by the factored nominal loads and is assumed positive wh
98. ty of Sydney 58 ColdSteel User s Manual Version 1 0 SHS Specify a list of square hollow sections The assumed profile geometry of a square hollow section SHS is shown in Fig I 11 Each square hollow section must be defined on a separate line using the following format Format Description Dimension Section name e g 100x100x5 0 SHS Section material must be defined in Material e g G350 Unit combination code 0 millimetres newtons Thickness 1 L Overall depth and width B Internal corner radius for all corners R L 5 25 y ue 213 t B R Fig 1 11 SHS definition Centre for Advanced Structural Engineering November 1998 The University of Sydney 59 ColdSteel User s Manual Version 1 0 RHS Specify a list of rectangular hollow sections The assumed profile geometry of a rectangular hollow section RHS is shown in Fig 1 12 Each rectangular hollow section must be defined on a separate line using the following format Format Description Dimension Section name e g 100x50x5 0 RHS Section material must be defined in Material e g G350 Unit combination code 0 millimetres newtons Thickness f Overall depth D Overall width B Internal corner radius for all corners R 5 N ie A Fig I 12 RHS definition Centre for Advanced Structu
99. uble stiffness in lap Reverse signs 3 42 kNm at 3 76kNmat for uplift loading end of lap end of lap a Bending moment diagram 3 80 kN at end of lap 4 25 KN 2 83 KN at end of lap b Shear force diagram Fig 44 Bending moment and shear force diagrams for three span lapped purlin system Centre for Advanced Structural Engineering November 1998 The University of Sydney 31 ColdSteel User s Manual Version 1 0 Capacity under uplift load End segment in end span Based on a unit uniformly distributed uplift load q the design moment about the horizontal n axis is M gt 3 79 kNm The minor axis and torsional effective lengths are assumed to be equal to the segment length hence L 2800 mm The equivalent moment coefficient C can be determined using the formula Gz 12 5M nax 9 2 5M max 3M 025 4M 0 59 5 in which M absolute value of the maximum moment in the unbraced segment M absolute value of the moment at the quarter point of the unbraced segment 04 absolute value of the moment at the centreline of the unbraced segment M absolute value of the moment at the three quarter point of the unbraced segment As shown in Hancock 1998 the C factor for the end segment evaluates to C 1 29 The elastic buckling moment is calculated in accordance with Clause 3 3 3 2 a of AS NZS 4600 1996 The ColdSteel Main form complete with all the relevant input parameters is shown in Fig 45 and the Output
100. ve section corresponding to the member lateral buckling strength in pure bending about the negative x axis maximum extreme fibre compressive stress of f M Z see Clause 3 3 3 3 Fig 20 Ex Msy button Displays the effective section corresponding to the section strength in pure bending about the positive y axis maximum extreme fibre stress of f Fig 21 Mbly button Displays the effective section corresponding to the member lateral buckling strength in pure bending about the positive y axis maximum extreme fibre compressive stress of f M Z see Clause 3 3 3 3 Fig 22 Mesy button Displays the effective section corresponding to the section strength in pure bending about the negative y axis maximum extreme fibre stress of f Fig 23 0 Mbly button Displays the effective section corresponding to the member lateral buckling strength in pure bending about the negative y axis maximum extreme fibre compressive stress of f M Z see Clause 3 3 3 3 Fig 24 e Print button Prints out the information currently displayed in the window on a single page Centre for Advanced Structural Engineering November 1998 The University of Sydney 18 Version 0 Full and Effective C Section C 20015 Material 6450 Full Section Simple A 5 7008 04 m2 3 678E 06 4 4 221E 07 m4 3 304E 09 m6 0 000 deg 5 240E 02 m 0 000E 00 m Fig 14 Display after selecting the Simplified
101. with a bending moment about the minor y axis of M 0 03869 kNm The beam is in uniform bending and therefore the moment modification coefficients C used in lateral buckling calculations and in the beam column strength interaction formula are both unity The Main form pertaining to this example is shown in Fig 69 and the Output form obtained upon clicking the Check button is shown in Fig 70 The maximum compressive load which can be applied eccentrically at the flange tips of the unlipped channel section is therefore N on 17 5KN Centre for Advanced Structural Engineering November 1998 The University of Sydney 43 ColdSteel User s Manual Properties of Full Section Version 1 0 m Wf Feed width m2 A full section m2 A net section m xc x ordinate of centroid full section m yc y ordinate of centroid full section m xo x ordinate of shear centre referred to principal axes m yo y ordinate of shear centre referred to principal axes m4 Ix full section m4 Iy full section m4 Ixy full section deg Inclination of principal axes full section m rx full section radius of gyration m ry full section radius of gyration m Extreme negative x ordinate full section m Extfeme positive x ordinate full se cti n m Extreme negative y ordinate full section m Extreme positive y ordinate full section m3 Zx Full section modulus yield at extreme positive x ordinate m3 Zx
102. wtons F Thickness f L F Overall depth D L F Overall flange width B L F Internal corner radius for all corners R L 14 Fig 1 5 PlainZed definition Centre for Advanced Structural Engineering November 1998 The University of Sydney 53 ColdSteel User s Manual Version 1 0 LippedZed Specify a list of lipped Z sections The profile geometry of a lipped Z section is shown in Fig I 6 The two flanges of a Z section may be of slightly unequal length to facilitate lapping but not so different that its behaviour differs significantly from one with both flanges of equal and average width In Fig I 6 the bottom flange width is denoted E and the top flange width is denoted F Each lipped Z section must be defined on a separate line using the following format Format Description Dimension 5 Section name e g 10010 5 Section material must be defined in Material e g G450 I Unit combination code 0 millimetres newtons F Thickness t L F Overall depth D L F Overall width of bottom flange E L F Overall width of top flange F L F Overall lip depth L L F Internal corner radius for all corners R L F Distortional buckling stress for bending about positive n axis fa F L F Distortional buckling stress for bending about negative n axis fn F L 1 2 3 4 5 6 7 8 5 ffodn fodn Fig 1 6 LippedZed definition
103. x Fig 1 9 LippedHat definition Centre for Advanced Structural Engineering November 1998 The University of Sydney 57 Version 0 ColdSteel User s Manual VeeLippedHat Specify a list of lipped hat sections with intermediate V stiffener The profile geometry of a lipped hat section with an intermediate V stiffener is shown in Fig I 10 Each lipped hat with an intermediate V stiffener section must be defined on a separate line using the following Dimension lt lt lt lt November 1998 Description Section name e g VLH 10010 Section material must be defined in Material e g G450 Unit combination code 0 millimetres newtons degrees Thickness 1 Overall depth D Overall width of top flange B Width of bottom flanges F Lip stiffener length L Overall depth of V stiffener V Internal corner radius for all bends at flange web junctions R Internal corner radius for all bends in V stiffener R Angle of webs from the vertical Angle of bottom flange stiffeners from vertical Angle of sides of V stiffener from the vertical QR lt 5 E 1 2 3 4 5 6 7 8 9 10 11 12 5 1 EILIV Re Ry Awl Fig 1 10 LippedHat definition format Format 1 Centre for Advanced Structural Engineering The Universi
104. y 450 MPa n 203 2 AS NZS 4600 1996 Cold Formed Steel Structures Help Eile Options Check Design Options Exit E Axis System Section Lipped Z Section Equal Flanges z C Principal x lf 720015 Non principal n p Material G450 M Use default material Design Actions 1st Order Lengths Ch Cm Factors Mo Cm Factors N M N kN bp Lm Clause 3 3 3 2 a Clause 3 5 1 Mn kN m jo Lex m jo Chx ft Cmn ft Mp kNm fo Ley m fo c amp y f Cmp ft Vn kN zz Lez m jo Bearing ane Tension Factors C ause 3 3 3 2 b Lb p m jot kt f Cmx f cm pa Pee br m jo e p m 31 Memory Used 316728 Fig 41 Main form pertaining to Example 6 Properties 05 Effective Section 0 000248469 m2 Ae fy Effective area for uniform stress fy 0 000248469 m2 Ae fn Effective area for uniform stress fn 79356E 6 m4 Ien effective 2nd moment of area n bending extreme 793568 6 m4 Ien effective 2nd moment of area n bending extreme 153678 7 m4 Iep effective 2nd moment of area p bending extreme 153678 7 m4 Iep effective 2nd moment of area p bending extreme 385298 5 m3 Zen effective section modulus at yield n bending POZE M3 AS Gece Selec Lene modulus ak yietd m pending 039228 6 m3 Zept effective section modulus at yield p bending 039228 6 m3 Zep effective section modulus at yield p bending OUNN SP

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