Civil. Engineering. Cross-section stability of structural steel. AISC Faculty Fellowship Progress Report AISC Committee on Research April 2008

Transcription

1 Civil Engineering at JOHNS HOPKINS UNIVERSITY Cross-section stability o structural steel AISC Faculty Fellowship Progress Report AISC Committee on Research April 2008 Schaer, BW

2 Objective: Investigate the application o the Direct Strength Method (DSM) to structural steel shapes, and provide the necessary research advances to make this a viable option or the design o noncompact and slender structural steel shapes

3 Background Direct Strength Method Progress Report 1 talk overview Educational materials on cross-section stability Design approaches or slender cross-sections Progress Report 2 FSM analysis o ALL structural sections (B41+++) Modeling locally slender cross-sections Initiation o nonlinear FE modeling Conclusions

4 wwwcejhuedu/bschaer/aisc

5 apologies The Direct Strength Method - a cold-ormed steel story - remember our goal here is to leverage more than a decade o research into locally slender cold-ormed steel sections in a manner that increases the potential or structural steel so, here s the story

6 Anyone who has ever attempted to design a lightgage member ollowing the [AISI] Speciication provisions probably realized how tedious and complex the process was Alexander Newman 1997, in Metal Building Systems

7 The CFS Stud Edge stiened element with an intermediate stiener, k, I s /I a b e Additional e width reductions on the lip Stiened element under a stress gradient (aka the web) ind k, then e width don t orget to iterate! and that is just or local buckling

8 speciication complication implication Rinchen (1998) - Australia Kesti (2000) - Finland Landolo and Mazzolani (1990) - Italy

9 Speciication complication explained Sections are not doubly-symmetric Element elastic buckling calculation (k s) Eective width eective width = (stress,geometry) stress = (eective properties: eg, A e, I e ) iteration results Web crippling calculations Inclusion o system eects

10 Speciication complication explained Sections are not doubly-symmetric Mechanics / elastic buckling Element elastic buckling calculation (k s) Eective width eective width = (stress,geometry) Direct strength curves stress = (eective properties: eg, A e, I e ) iteration results Web crippling calculations Inclusion o system eects

11 Plate vs cross-section buckling cr cr = 2 π E k 121 ( 2 ν ) t b 2 P = cr A g cr

12 o course this is not just a CFS story

13 Why cross-section buckling? (element interaction) ξ = 3 ξ = 2 ξ = 14 ξ = 1 local buckling inite strip analysis 35 ξ = 3 1 beam 3 k 25 2 ξ = 2, pure bending 2 ξ = ξ = column ξ = web height/lange width

14 How to ind cross-section buckling? Tables and charts essentially limited to two elements (maybe ok or many hot-rolled shapes) not widely available Finite element solutions requires more advanced modeling (plate elements) generality o method is great, but complicates too not widely available Other methods? inite element variant called the inite strip method ree (CUFSM), also available CFS, THINWALL

15 FE vs FSM meshing

16 Finite Strip Analysis b θ1 a v1 u1 θ2 v2 u2 z y x ½ sine wave w1 w2 cubic beam unction

17 CUFSM (Cornell University Finite Strip Method) Free, open source, sotware that allows you to explore the elastic buckling o any cross-section using the inite strip method Mechanics employed are IDENTICAL to the mechanics used to derive the plate buckling coeicient k values in current use

18 Background Direct Strength Method Progress Report 1 talk overview Educational materials on cross-section stability Design approaches or slender cross-sections Progress Report 2 FSM analysis o ALL structural sections (B41+++) Modeling locally slender cross-sections Initiation o nonlinear FE modeling Conclusions

19

20 element node The geometry is deined by nodes and elements, you can change these as you like, here a W36x150 is shown

21 the model is evaluated or many dierent lengths this allows us to explore all the buckling modes, more on this soon

22 go back to the input page when you are done put compression o 1 ksi on ths section, enter 1, uncheck Mxx generate stress should get this distribution

23 note stresses are all 10 now (+ = comp) analyze the section

24 Finite strip analysis results lots to take in here!

25 buckled shape, here we can igure out what type o buckling mode we are looking at, is it local? global? etc hal-wave vs load actor plot here we ind the buckling load and we ind the critical buckling lengths

26 buckled shape at hal-wavelength = 226 and load actor = 487 undeormed shape the little red dot tells you where you are

27 move the little red dot to the minimum on the curve with these controls, then select plot shape and you will get this buckling mode shape result Local buckling

28 How do you know this is local buckling? Where is lange local buckling? Where is web local buckling? In the beginning, looking at the buckled shape in 3D can help a lot

29 select (and be patient) web and lange local buckling is shown remember, applied load is a uniorm compressive stress o 10 ksi

30 let s rotate this section so we can see the buckling rom the end on view

31 Go back to 2D now and see i the shape makes more sense buckled shape at midspan o the hal-wavelength, this is the 2D buckled shape

32 we call this local buckling because the elements which make up the section are distorted/bent in-plane Also, the hal-wavelength is much shorter than typical physical member length, in act the hal-wavelength is less than the largest dimension o the section (this is typical) At what stress or load is this elastic local buckling predicted to occur at?

33 our reerence load o 426 k or, equivalently our reerence stress o 10 ksi everywhere

34 P re = 426 k or re = 10 ksi load actor or local buckling = 4712 P cr,local = 4712 x 426 = 2007 k or cr,local = 4712 x 10 ksi = 4712 ksi

35 change hal-wavelength to ~480 = 40t and plot the shape to get the result shown here try out the 3D shape to better see this mode

36 this is weak axis lexural buckling

37 note that or lexural buckling the crosssection elements do not distort/bend, the ull cross-section translates/rotates rigidly in-plane

38 P re = 426 k or re = 10 ksi load actor or global lexural buckling = 76 at 40 t length P cr = 76 x 426 k = 324 k or cr = 76 x 10 ksi = 76 ksi

39 Column summary A W36x150 under pure compression (a column) has two important cross-section stability elastic buckling modes (1) Local buckling which occurs at a stress o 47 ksi and may repeat along the length o a member every 27 in (it s hal-wavelength) (2) Global lexural buckling, which or a 40 t long member occurs at a stress o 76 ksi (other member lengths may be selected rom the curve provided rom the analysis results) the actual tutorial #1 has ar more detail, and continues on to beams

40 Background Direct Strength Method Progress Report 1 talk overview Educational materials on cross-section stability Design approaches or slender cross-sections Progress Report 2 FSM analysis o ALL structural sections (B41+++) Modeling locally slender cross-sections Initiation o nonlinear FE modeling Conclusions

41 Direct Strength design n

42 Direct strength prediction P n = (P y, P cre, P crd, P crl )? Input Squash load, P y Euler buckling load, P cre Distortional buckling load, P crd Local buckling load, P crl Output Strength, P n

43 Elastic buckling

44 Elastic buckling

45 Direct Strength Curve (university o sydney testing) strength (F u /F y ) or (P u /P y ) channel rack rack+lip hat channel+ web st (d) (a) (b) (c) (e) distortional slenderness (F y /F cr ) 5 or (P y /P cr ) 5

46 Columns Lipped channels Lipped zeds Lipped channels with intermediate web stiener Hat sections Rack post sections Kwon and Hancock (1992), Lau and Hancock (1987), Loughlan (1979), Miller and Peköz (1994), Mulligan (1983), Polyzois et al (1993), Thomasson (1978)

47 267 columns, β = 25, φ = 084

48 Beams Lipped and plain channels Lipped zeds Hats with and without intermediate stiener(s) in the lange Trapezoidal decks with and without intermediate stiener(s) in the web and the lange Cees and Zeds: Cohen 1987, Elliritt et al 1997, LaBoube and Yu 1978, Moreyara 1993, Phung and Yu 1978, Rogers 1995, Schardt and Schrade 1982, Schuster 1992, Shan 1994, Willis and Wallace 1990 Hats and Decks: Acharya 1997, Bernard 1993, Desmond 1977, Höglund 1980, König 1978, Papazian et al 1994

49 569 beams, β=25, φ=09

50 DSM curves 1 08 Elastic buckling Yield Global Local Distortional strength slenderness

51 Direct strength advocacy No eective width, no elements, no iteration Gross properties Element interaction Distortional buckling (less important or now in hot-rolled) Wider applicability and scope Encourage cross-section optimization Your computer perorms analysis that employs undamental mechanics instead o just mimicking old hand calculations DSM integrates known behavior into a straightorward design procedure

52 Background Direct Strength Method Progress Report 1 talk overview Educational materials on cross-section stability Design approaches or slender cross-sections Progress Report 2 FSM analysis o ALL structural sections (B41+++) Modeling locally slender cross-sections Initiation o nonlinear FE modeling Conclusions

53 Educational eorts Objectives: Provide tools, tutorials, and educational aids related to cross-section stability o structural steel shapes so that educators, students, and engineers may explore these concepts more readily Provide educational aids appropriate or courses in steel design using structural steel at the undergraduate and graduate levels

54 Educational work products CUFSM CUFSM Example iles or structural steel shapes (W36x150, W14x120, C5x9, L4x4x1/2, WT 18x150, HSS 4x4x1/2) Tutorials #1 Cross-section stability o a W36x150 using the inite strip method #2 Cross-section stability o a W36x150 exploring higher modes and the interaction o modes #3 Exploring how cross-section changes inluence cross-section stability - an extension to Tutorial #1 Exercises (individual and group hw, rom simple to advanced)

55 Tutorial #1 Learning objectives Identiy all the buckling modes in a W-section For columns explore lexural (Euler) buckling and local buckling For beams explore lateral-torsional buckling and local buckling Predict the buckling stress (load or moment) or identiied buckling modes Learn the interace o a simple program or exploring crosssection stability o any AISC section and learn inite strip method concepts such as hal-wavelength o the bucking mode buckling load actor associated with the applied stresses Let s visit tutorial #1 Go to Tutorial #1

56 Tutorial #2 Learning objectives Understand the role o higher buckling modes in the analysis o a W-section, including how higher buckling modes relate to strong-axis, weak-axis, and torsional buckling in columns what higher buckling modes mean or local buckling when knowledge o higher buckling modes may be useul in design Understand how interaction o modes may be identiied and quantiied using CUFSM or a W-section Go to Tutorial #2

57 Tutorial #3 Learning objectives Study the impact o lange width, web thickness, and lange-to-web illet size on a W-section Learn how to change the cross-section in CUFSM Learn how to compare analysis results to study the impact o changing the cross-section Go to Tutorial #3

58 Homework Tutorial #1 Cross-section stability o a W36x150 using the inite strip method basic checkup questions application question Tutorial #3 Exploring how cross-section changes inluence crosssection stability - an extension to Tutorial #1 basic checkup questions, example: How does the elastic local buckling stress change i the web thickness is increased in a W36x150 to be the same as the lange thickness or the section in pure compression? application questions, example: Determine the elastic local buckling stress and global buckling stress at 40 t or a W14x120 in pure compression Small group homework assignment Optimize a section under constant area, can you increase both the local buckling and the global buckling stress at a given length? Go to homework

59 Background Direct Strength Method Progress Report 1 talk overview Educational materials on cross-section stability Design approaches or slender cross-sections Progress Report 2 FSM analysis o ALL structural sections (B41+++) Modeling locally slender cross-sections Initiation o nonlinear FE modeling Conclusions

60 AISC Q-actor AISI Eective Width AISI Direct Strength Locally slender stub column design expressions comparison o predictions Locally slender long column design expressions comparison o predictions

61 notation (speciication provisions are written in a common notation) crb : Flange elastic critical local buckling stress = crh : Web elastic critical buckling stress = k k ( 2 ν ) 2 2 π E t ( ν ) b 2 2 π E tw w 12 1 h

62 AISC Locally slender stub column > = < < = = y crh g w y crh y crh y crh a y crb y crb y crb y crb y y crb s y g a s n A ht Q Q A Q Q P 2 i i i i i 1 0 c

63 AISI Locally slender stub column < = = < = = + = = y crh y crh y crh y crh h h e y crb y crb y crb y crb b b e w h b e y e n h h b b ht bt A A P 2 2 i i 1 where 2 2 i i 1 where 4 ρ ρ ρ ρ ρ ρ c c

64 AISI DSM Locally slender stub column 1 66 i i < = = = y cr y cr y cr y cr g e y e n A A A P l l l l ρ ρ c

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67 1 AISC AISI - E Width DSM (AISI App 1) P n /P y Stub Column Typical heavy W14 dimensions: ht w /A g =02 2b t /A g =08 crb / crh =08, crb / crlocal = local lange slenderness ( y / crb ) 05

68 1 08 AISC AISI - E Width DSM (AISI App 1) lange becomes partially eective P n /P y Stub Column Typical heavy W36 dimensions: ht w /A g =04 2b t /A g =06 crb / crh =8, crb / crlocal =6 transitioning through AISC Q s equations local web slenderness ( y / crh ) 05

69 AISC 1 determined with 2 i i i i i i i = = = > = < < = < = = a s n g a n crh g w crh crh crh a y crb y crb y crb y crb y y crb s y a s e e y a s e y ) / ( Q Q a s n n g n Q Q ˆ ~ A Q P A ht Q Q Q Q Q Q ) Q Q ( ˆ ˆ A P y e a s

70 modiying the global column curve strength AISI AISC global slenderness

71 AISI < = ρ = ρ < = ρ = ρ + ρ ρ = < = = n crh n crh n crh n crh h h e n crb n crb n crb n crb b b e w h b e y e e y e y ) / ( n n e n h h b b ht bt A ) ( A P y e 2 2 i i 1 where 2 2 i i 1 where i i 0 658

72 DSM 1 66 i i i i < ρ = = ρ < = = n cr n cr n cr n cr g e y e e y e y ) / ( n n e n A A ) ( A P y e l l l l

73 AISC: P n / P y = ( e / y, crb / y, crh / y, ht w / A g ) AISI: P n / P y = ( e / y, crb / y, crh / y, ht w / A g or 2b t / A g ) DSM: P n / P y = ( e / y, cr l/ y )

74 1 Flange local slenderness ( y / crb ) 05 = 01 AISC AISI - E Width DSM (AISI App 1) 1 Flange local slenderness ( y / crb ) 05 = 08 AISC AISI - E Width DSM (AISI App 1) 08 Typical heavy W14 dimensions: ht w /A g =02 2b t /A g =08 08 Typical heavy W14 dimensions: ht w /A g =02 2b t /A g =08 P n /P y 06 crb / crh =08, crb / crlocal =13 P n /P y 06 crb / crh =08, crb / crlocal = global slenderness ( y / e ) global slenderness ( y / e ) 05 (a) compact: lange slenderness o 01, ie crb = 100 y (b) local lange slenderness o 08, ie crb = 156 y 1 Flange local slenderness ( y / crb ) 05 = 13 AISC AISI - E Width DSM (AISI App 1) 1 Flange local slenderness ( y / crb ) 05 = 2 AISC AISI - E Width DSM (AISI App 1) 08 Typical heavy W14 dimensions: ht w /A g =02 2b t /A g =08 08 Typical heavy W14 dimensions: ht w /A g =02 2b t /A g =08 P n /P y 06 crb / crh =08, crb / crlocal =13 P n /P y 06 crb / crh =08, crb / crlocal = global slenderness ( y / e ) global slenderness ( y / e ) 05 (c) local lange slenderness o 13, ie crb = 059 y (b) local lange slenderness o 2, ie crb = 025 y

75 Background Direct Strength Method Progress Report 1 talk overview Educational materials on cross-section stability Design approaches or slender cross-sections Progress Report 2 FSM analysis o ALL structural sections (B41+++) Modeling locally slender cross-sections Initiation o nonlinear FE modeling Conclusions

76 FSM analysis o structural steel sections Objective: investigate web-lange interaction in structural steel shapes and develop a means that this inormation can be used in conventional design All shapes in the AISC shapes database considered (except round pipe) Finite strip analysis perormed or Compression Major-axis bending (positive and negative**) Minor-axis bending (positive and negative**) ** hugely important or singly- and un-symmetric sections

77 1 typical results W-sections lange, k web slenderness h/t w crb = k 2 π E t ( 2 ) 12 1 ν b 2

78 1 FSM results W-sections lange, k web slenderness h/t w 1 k =k w ((h/t w )(2t /b )) -2 k (h/t w )(2t /b )

79 6 W-sections 6 M,S,HP-sections k w k w (h/t w )(2t /b ) (h/t w )(2t /b ) 8 C,MC-sections 05 L-sections k w 5 4 k d (d/t w )(t /b ) d/b

80 Table B41

81 Table B41 on Steroids * Full table * a little baseball humor, ater all opening day was just yesterday

82 Table B41 on HGH * * Full table ** a little more baseball humor

83 Table B41 on HGH * * Full table ** a little more baseball humor

84 Background Direct Strength Method Progress Report 1 talk overview Educational materials on cross-section stability Design approaches or slender cross-sections Progress Report 2 FSM analysis o ALL structural sections (B41+++) Modeling locally slender cross-sections Initiation o nonlinear FE modeling Conclusions

85 Investigating element sensitivity (a) (b) (c) Solid vs plates(shells) ABAQUS library linear vs quadratic reduced integration debates in the literature Mesh density Comparisons with classics like CUFSM Impact o small details like k-zone etc

86 Typical FE eigenbuckling results FSM FSM

87 Initiating nonlinear FE studies Section: W14x233 Stub columns: per SSRC guidelines Material: piece-wise linear elasticplastic with strain hardening (von Mises with isotropic hardening) Element: S4 linear shell Imperections: local mode, magnitude max o b /150 and d/150 (very simplistic) Residual stresses: Galambos and Ketter distribution at 30% y Section slenderness varied by thickness (or now) Engineering Stress (ksi) y = 50 Slope, E =145 Slope, E =29000 u = 65 Slope, E st =720 =0011 Engineering Strain σ t = σ c b t - σ = c y b t + t ( 2 w d t )

88 W14 with reduced lange thickness Force (kips) Displacement (in)

89 1 W14 with reduced lange thickness 08 Pn/Py AISC AISI DSM ABAQUS (y/crb) 05

90 1 W14 with reduced lange thickness and web thickness, in proportion 08 Pn/Py AISC AISI DSM ABAQUS (y/crb) 05

91 Background Direct Strength Method Progress Report 1 talk overview Educational materials on cross-section stability Design approaches or slender cross-sections Progress Report 2 FSM analysis o ALL structural sections (B41+++) Modeling locally slender cross-sections Initiation o nonlinear FE modeling Conclusions

92 Conclusions DSM has something to oer structural steel design potentially simple design expressions or locally slender sections (no elements, no iteration, no eective properties) integrates well with cross-section stability analysis (consistent with DAM or long-term growth o Spec) Q-actor approach in AISC has some limitations (this has been identiied beore), eg, their is good evidence that AISC is overly conservative or unstiened elements FSM o structural steel shapes provides a means to sharpen our pencil on cross-section stability, inal orm could be amenable to conventional design (Table B41 +++) Much work remains, but we are o and running now