SKILLS Project. October 2013

Transcription

1 SKILLS Project October 2013

2 PORTAL FRAMES IN SINGLE STOREY BUILDINGS

3 LEARNING OUTCOMES Structural elastic analysis including second order effects and imperfections Design procedure of portal frames Design procedure of roof bracing and vertical bracing 3

4 LIST OF CONTENTS Introduction Presentation of industrial steel buildings Examples Global Analysis General Second order effects Frame imperfection Rigidity of joints Design Procedure of portal frames Structural stability of frames Stability of columns and rafters Vertical Bracing Roof Bracing Conclusion 4

5 INTRODUCTION

6 INTRODUCTION Typical design of single storey steel buildings 6

7 INTRODUCTION Purlins 7

8 INTRODUCTION Haunched portal frames 8

9 INTRODUCTION Roof bracing Photo APK 9

10 INTRODUCTION Vertical bracing Photo APK 10

11 INTRODUCTION Photo APK JP Muzeau 11

12 INTRODUCTION 12

13 GLOBAL ANALYSIS

14 GLOBAL ANALYSIS Methods of structural analysis EN Elastic analysis Material is supposed to behave perfectly linear elastic Plastic analysis Material non linearity is taken into account Redistribution of internal forces and moments 14

15 GLOBAL ANALYSIS Effects to be taken into account when significant EN Effects of deformed geometry (2 nd order effects) Imperfections Stiffness of joints Ground-structure interaction 15

16 GLOBAL ANALYSIS First order and second order analysis First order analysis: performed on the non deformed structure Second order analysis: performed including effects of deformed geometry 16

17 GLOBAL ANALYSIS Effects of deformed geometry/second order effects V H I First order analysis of the structure gives: h M I M I I H h H h 3EI 3 17

18 GLOBAL ANALYSIS Effects of deformed geometry/second order effects H V Second order analysis of the structure gives: M II H h V II iterative calculation of II necessary II II n1 II h H h V n 3EI 2 M II 18

19 GLOBAL ANALYSIS Effects of deformed geometry/second order effects H V II M II II n1 Supposing: II II h H h V n 3EI With: n 2 h H h 3EI V II 1 II n And: I H h cr 1 I 2 Vh 1 3EI 3EI h V 1 V cr h 2 3EI 19

20 GLOBAL ANALYSIS Effects of deformed geometry/second order effects H V II I 1 V 1 V cr II M II Substituting: II M II 1 I 1 1 M I cr V cr cr cr V 20

21 GLOBAL ANALYSIS Global and local second order effects Global 2 nd order effects P-D-effects P D Concerns the deformation of the whole structure Local 2 nd order effects P--effects P Concerns the deformation between member ends Generally covered by member checks EN

22 GLOBAL ANALYSIS Summarizing the effects of deformed geometry Taking the deformation of the structure into account generally leads to higher internal forces (shear force) and moments for portal frames. The lesser the rigidity of the structure is, the higher are the deformation and therefore the 2 nd order effects. cr is representative for the influence of 2 nd order effects (high values of cr stand for little influence of 2 nd order effects ) 22

23 GLOBAL ANALYSIS Second order effects in EN First order analysis is permitted if: cr 10 cr 15 for elastic analysis for plastic analysis EN If criterion is not respected 2 nd order effects have to be accounted for 23

24 GLOBAL ANALYSIS Accounting for second order effects in EN cr 10 2 nd order analysis (buckling length = member length) or 1 st order analysis followed by amplification of sway effects (buckling length = member length) or 1 st order analysis (buckling length according to sway buckling mode) cr 3 2 nd order analysis (buckling length = member length) 24

25 GLOBAL ANALYSIS Amplification of sway effects Amplification factor: cr Sway effects: Horizontal loads (e.g. wind) Effects due to imperfection Effects due to geometry of the structure 25

26 GLOBAL ANALYSIS Calculation of cr Simplified formula: cr H V Ed Ed h H,Ed EN (4) V Ed H,Ed h H Ed if roof slop is swallow: < 26 if axial force in the rafter is small: 0,3 Af N y Ed or NEd 0, 09N cr 26

27 GLOBAL ANALYSIS Practical calulation of cr for portal frames h H unit V Ed unit cr H V unit Ed h unit V Ed V Ed 0,5 H unit 0,5 H unit 0,25 H unit 0,5 H unit 0,25 H unit unit mean.column unit mean. column 27

28 IMPERFECTIONS

29 GLOBAL ANALYSIS Structural imperfections Due to: lack of verticality lack of straightness eccentricities in joints residual stresses inhomogeneity of material Physical imperfection are replaced by equivalent geometric imperfection 29

30 GLOBAL ANALYSIS Equivalent geometric imperfection Global initial sway imperfection f f Local bow imperfection e 0 e 0 30

31 GLOBAL ANALYSIS Global sway imperfection f f 0h m EN f 0 : Basic value f 0 1/ 200 h : Reduction factor for the height of the columns 2 2 h but h 1 h 3 m : Reduction factor for the number of columns per row m 1 0,5 1 m m is the number of columns carrying at least 50% of the average vertical load of the column row considered 31

32 GLOBAL ANALYSIS Direction of sway imperfection Every possible direction has to be considered, but only one direction in a time f f f f f f f f 32

33 GLOBAL ANALYSIS System of equivalent forces replacing out-of-plumb f f f 33

34 GLOBAL ANALYSIS System of equivalent forces replacing out-of-plumb f f f f f f 34

35 GLOBAL ANALYSIS Possibility of disregarding global frame imperfection Relatively high horizontal loads H 0 V EN Ed, 15 Frame stability check with equivalent column method (buckling length of columns are based on overall sway buckling mode) Ed EN

36 GLOBAL ANALYSIS Local bow imperfection Local 2 nd order effects are generally included in the member verification formulas of EN Local bow imperfection has to be considered for slender members under high compression axial force 36

37 GLOBAL ANALYSIS If frame is sensitive to 2 nd order effects, local bow imperfection has to be applied on: compressed members that have at least one moment resistant joint and whose reduced slenderness Afy 0,5 EN N is calculated supposing a pin ended column: Ed A f y N cr And N cr L 2 EI 37

38 GLOBAL ANALYSIS Value of local bow imperfection EN e 0 Buckling curve Elastic analysis Plastic analysis e 0 /L e 0 /L a 0 1/350 1/300 a 1/300 1/250 b 1/250 1/200 c 1/200 1/150 d 1/150 1/100 38

39 GLOBAL ANALYSIS System of equivalent forces replacing local bow imperfection 4 e 0,d /L e 0 L 8 e 0,d /L 2 4 e 0,d /L 39

40 GLOBAL ANALYSIS System of equivalent forces replacing local bow imperfection e 0 e 0 4 e 0,d /L 4 e 0,d /L 8 e 0,d /L 2 8 e 0,d /L 2 L 4 e 0,d /L 4 e 0,d /L 40

41 STIFFNESS OF JOINTS

42 GLOBAL ANALYSIS Examples of Joints Rigid joint Nominally pinned joint 42

43 GLOBAL ANALYSIS Classification of joints by stiffness EN M Joint A Joint B Joint C f 43

44 GLOBAL ANALYSIS Classification boundaries EN M Joint A k b EI L beam beam Semi-rigid joints Joint B Rigid joints EI 0,5 L beam beam Joint C f 44 Nominally pinned joints

45 GLOBAL ANALYSIS Value of k b for the classification of joints k b = 8 : k b = 25 : frames where the bracing system reduces the horizontal displacement by at least 80% other frames, provided that in every storey K b /K c 0,1 K b : K c : mean value of I b /L b for all beams at the top of the storey mean value of I c /L c for all columns of the storey I c/b : second moment of area of a column/beam L c/b : height/length of a column/beam 45

46 GLOBAL ANALYSIS Practical comments The designer will probably choose the assumption of rigid rafter-to-column joints. The designer will probably choose the assumption of either pinned or rigid column bases. The assumptions will have to be checked afterwards. 46

47 DESIGN PROCEDURE OF PORTAL FRAMES

48 DESIGN PROCEDURE OF PORTAL FRAMES Structural stability of frames cr 10 : 1 st Method: 1 st order analysis without imperfections Column in-plane stability check using buckling length according to sway buckling mode 2 nd Method: 1 st order analysis with global imperfection EN Column in-plane stability check using member length 48

49 DESIGN PROCEDURE OF PORTAL FRAMES Structural stability of frames cr < 3 : EN Check if introduction of local imperfection is necessary if necessary: 2 nd order analysis with global imperfection if necessary Column in-plane stability check = check of resistance of section 49

50 DESIGN PROCEDURE OF PORTAL FRAMES Structural stability of frames cr < 3 : EN Check if introduction of local imperfection is necessary if not necessary: 2 nd order analysis with global imperfection if necessary Column in-plane stability check using member length 50

51 DESIGN PROCEDURE OF PORTAL FRAMES Structural stability of frames 3 cr < 10 : EN Check if introduction of local imperfection is necessary if necessary: 2 nd order analysis with global imperfection if necessary Column in-plane stability check = check of section resistance 51

52 DESIGN PROCEDURE OF PORTAL FRAMES Structural stability of frames 3 cr < 10 : EN Check if introduction of local imperfection is necessary if not necessary: 1 st Method: 1 st order analysis without imperfections Column in-plane stability check using buckling length according to sway buckling mode Verification of joints and rafters including second order effects (amplification of sway effects) 52

53 DESIGN PROCEDURE OF PORTAL FRAMES Structural stability of frames 3 cr < 10 : EN Check if introduction of local imperfection is necessary if not necessary: 2 nd Method: 1 st order analysis with global imperfection if necessary Amplification of sway effects Column in-plane stability check using member length 53

54 DESIGN PROCEDURE OF PORTAL FRAMES Buckling length = Member length : L cr Buckling length according to sway buckling mode : L cr 54

55 DESIGN PROCEDURE OF PORTAL FRAMES Geometry + Boundary conditions + Loads Calculation of cr cr < 3 3 cr < 10 cr 10 Slide 58 Slide 59 Slide 57 55

56 DESIGN PROCEDURE OF PORTAL FRAMES Geometry + Boundary conditions + Loads Calculation of cr cr 10 Global imperfection 1 st order analysis In plane stability check of columns using member length In plane stability check of columns using buckling length according to global buckling mode 56

57 DESIGN PROCEDURE OF PORTAL FRAMES Geometry + Boundary conditions + Loads Calculation of cr cr < 3 Global imperfection if necessary: EN (4) Local imperfection if necessary: EN (6) Necessary Not necessary 2 nd order analysis In plane stability check of columns = resistance check of section In plane stability check of columns using member length 57

58 DESIGN PROCEDURE OF PORTAL FRAMES Geometry + Boundary conditions + Loads Calculation of cr 3 cr < 10 Local imperfection if necessary: EN (6) Necessary Not necessary Global imperfection if necessary: EN (4) Necessary Not necessary 2 nd order analysis Amplification of sway effects 1 st order analysis In plane stability check of columns = resistance check of section In plane stability check of columns using member length In plane stability check of columns using buckling length according to sway buckling mode 58

59 STABILITY OF COLUMNS AND RAFTERS

60 DESIGN PROCEDURE OF PORTAL FRAMES Stability of columns and rafters Columns and rafters are subjected to axial forces and moments Use of interaction formula EN N N y Ed M1 Rk k yy M y, Ed LT DM M y, Rk M1 y, Ed k yz M z, Ed M DM z, Rk M1 z, Ed 1 N zn Ed Rk M1 k zy M y, Ed LT DM M y, Rk M1 y, Ed k zz M z, Ed M DM z, Rk M1 z, Ed 1 60

61 DESIGN PROCEDURE OF PORTAL FRAMES Simplification for common frames Columns and rafters are not subjected to out-of-plane moments Columns and rafters are usually double symmetric sections N N y Ed M1 Rk k yy M LT y, Ed M y, Rk M1 1 N zn Ed Rk M1 k zy M LT y, Ed M y, Rk M1 1 61

62 ROOF BRACING

63 ROOF BRACING Photo APK 63

64 ROOF BRACING Rafters Roof bracing Purlins transmitting horizontal loads to roof bracing 64

65 ROOF BRACING Ground view of roof bracing Roof bracing 6 Rafters Purlins transmitting horizontal loads to roof bracing 65

66 ROOF BRACING Idealisation of roof bracing F exterior m rafters whose flanges are subjected to the axial force (including rafters acting as upper and lower flange of roof bracing) Horizontal loads transmitted by purlins Roof bracing 66

67 ROOF BRACING Imperfection for roof bracing EN F exterior e 0 e 0 e 0 m rafters whose flanges are subjected to the axial force and that are subjected to imperfection e 0 e 0 Horizontal loads due to imperfection e 0 and axial forces and to F exterior Roof bracing 67

68 ROOF BRACING Imperfection for roof bracing F exterior e 0 e 0 N Ed M h Rafter,Ed Section A upflange A Section N Rafter,Ed e 0 e 0 m L 500 m 0,5 1 1 m e 0 Horizontal loads due to imperfection e 0 and axial forces and to F exterior Roof bracing 68

69 ROOF BRACING Calculation of roof bracing F exterior e 0 Use of geometric imperfection and 2 nd order analysis e 0 e 0 Use of equivalent forces and 1 st order analysis e 0 69

70 ROOF BRACING Equivalent load concept q d L/8 q d L/4 q d L/4 q d L/4 q d L/8 q d L/2 q d L/2 L F exterior q d q d NEd8 e g : deflection of the roof bracing due to exterior load F exterior and equivalent load q d iterative calculation of q d 1 or 2 iterations sufficient 0 L 2 g 70

71 VERTICAL BRACING

72 VERTICAL BRACING Photo APK 72

73 VERTICAL BRACING Design procedure Calculation of cr 1 st order or 2 nd order theory Determination of horizontal loads Wind Loads due to global imperfection if necessary Calculation of internal forces and moments Verification of stability in bracing plane Verification of out of bracing plane stability as before 73

74 VERTICAL BRACING Calculation of cr for vertical bracings V total H unit V V V V h cr H V unit total h mean 74

75 VERTICAL BRACING In-plane loads on vertical bracing N tot f + H V V N tot : Sum of axial forces of all columns stabilized by bracing H: External horizontal loads V: Vertical loads on columns N tot f f: Sway imperfection 75

76 CONCLUSION

77 CONCLUSION Generally 2 nd order effects and imperfections have to be accounted for in the design of portal frames. Depending on the value of cr different calculation methods can be adopted. For portal frames it is convenient to account for global imperfection and global 2 nd order effects in the global analysis. 77

78 CONCLUSION Local 2 nd order effects are generally included in the member verification formulas of EN Physical imperfections are replaced by either equivalent geometric imperfections or equivalent loads. Bracing systems are subjected to external horizontal loads and loads due to their function as stabilizing elements. 78

79 SKILLS training modules have been developed by a consortium of organisations whose logos appear at the bottom of this slide. The material is under a creative commons license The project was funded with support from the European Commission. This module reflects only the views of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein.