讲义分析案例eurocode-1

1、Eurocode 3: Design of Steel StructuresPart-1-5: Design of Plated StructuresWu ChongDepartment of Bridge Engineering Tongji UniversityTel.02165983116-2605 Eurocode同济大学 吴冲 Tongji University, Wu Chong1Ultimate resistance of plates under shearCollapse behaviourPure shear stress Tension field action Plas

2、tic hinge flangea) pure shear stressb) tension field action c) plastic hinge flange mechanismFig. 2.43: Stress states and collapse behaviour of a plate girder subjected to shear a) pure shear stress 同济大学 吴冲 Tongji University, Wu Chong2Ultimate resistance of plates under shearVerification of a girder

3、 subjected to shear readsShear resistanceVbw,Rdresistance from the webVbf,Rdresistance from flangeshwweb heighttwweb thicknesshfactor depending on the steel grade fy 460 N/mm2: h = 1.2 fy 460 N/mm2: h = 1.0 fywweb yield strengthgM1partial safety factor同济大学 吴冲 Tongji University, Wu Chong3Ultimate res

4、istance of plates under shearShear resistance from the webReduction factor for shear non-rigid end postrigid end postfor unstiffened websfor stiffened webs同济大学 吴冲 Tongji University, Wu Chong4Ultimate resistance of plates under shearShear resistance from the web relative slenderness with for transver

5、se stiffeners at supports onlyfor transverse stiffeners at supports, intermediate stiffeners or longitudinal stiffeners or bothkshear buckling coefficient of the web between flangesk,ishear buckling coefficient of sub-panels ihwclear web height between flangeshwiclear height of sub-panels i同济大学 吴冲 T

6、ongji University, Wu Chong5Ultimate resistance of plates under shearShear buckling coefficientfor panels without longitudinal stiffenersfor stiffened panels with one or two longitudinal stiffenersand = a/hw 3.0 or panels with rigid transverse stiffeners only同济大学 吴冲 Tongji University, Wu Chong6Ultima

7、te resistance of plates under shearShear buckling coefficientfor stiffened panels with one or two longitudinal stiffenersand = a/hw 3.0orfor stiffened panels with more than two longitudinal stiffenersor panels with rigid transverse stiffeners onlysecond moment of area Is is determined with an effect

8、ive plate width of 15t on each side of the stiffener web 同济大学 吴冲 Tongji University, Wu Chong7Ultimate resistance of plates under shearShear resistance from the flangesFig. 2.46: Anchorage of the tension field in the flangeswhereAf,1= bf,1tf,1 cross-sectional area of flange 1Af,2 = bf,2tf,2 cross-sec

9、tional area of flange 2fyf,1yield strength of flange 1fyf,2 yield strength of flange 2hf distance between mid-plane of flanges 同济大学 吴冲 Tongji University, Wu Chong8Flange induced buckling Fig. 2.61: Flange induced buckling (case of an elastic bending resistance)同济大学 吴冲 Tongji University, Wu Chong9Fla

10、nge induced bucklingTo express the vertical stress , the following assumptions were madeThe girder has a symmetrical I cross-section Maximum compressive or tensile residual stresses in the flanges are equal to 0.5 fyf , so that at flange yielding: The two identical flanges (area Af) are entirely yie

11、lded when buckling occurs.The bending resistance is elastic. with 同济大学 吴冲 Tongji University, Wu Chong10Flange induced bucklingrelative web slenderness limit with ork = 0.4 if the plastic bending resistance is utilized,k = 0.3 if the plastic rotation is utilized.If the I-girder is initially already c

12、urved in elevation with a radius R, the previous formula should be modified according to EN1993-1-5, Section 8, as follows: 同济大学 吴冲 Tongji University, Wu Chong11同济大学 吴冲 Tongji University, Wu Chong12Stiffeners and detailingTypical cross-sections of stiffeners 同济大学 吴冲 Tongji University, Wu Chong13a) d

13、irect stresses (M, N) Sect. 2.4 torsional stability Sect. 2.9b) shear (buckling coeff. kt) Sect. 2.5c) patch loading (buckling coeff. kF) Sect. 2.6d) direct stresses (transverse bending due to deviation force qdev) Sect. 2.9e) shear (compressive force Nst,ten in intermediate transverse stiffener due

14、 to the tension field action) Sect. 2.9f) shear (introduction of reaction forces and end post details) Sect. 2.9g) external transverse loads (compression force in the transverse stiffener Nst, ex) Sect. 2.9Stiffeners and detailingThe most typical situations where stiffeners are involved in the desig

15、n of plated structures are shown in Fig. 2.62. Fig. 2.62: Typical design situations for longitudinal and transverse stiffeners同济大学 吴冲 Tongji University, Wu Chong14Effective cross-section of stiffenersa) No overlapping of contributing plateb) Overlapping of contributing plateStiffeners and detailing同

16、济大学 吴冲 Tongji University, Wu Chong15Stiffeners and detailingTransverse stiffenersActionsincrease shear resistanceprovide lateral supports to longitudinal stiffenerscarry concentrated transverse forces together with cross-frames or diaphragms reduce distortional deformations of the cross-section. Des

17、ignThey are usually designed as rigid stiffenersTthe panels between two rigid transverse stiffeners may be designed independently without an interaction with adjacent panels. EN 1993-1-5 supports the approach with rigid transverse stiffeners and does not give detailed design rules for the case with

18、flexible transverse stiffeners. 同济大学 吴冲 Tongji University, Wu Chong16Stiffeners and detailingTransverse stiffenersDirect stressesmaximum stress max in the stiffener at the ultimate limit stateadditional lateral deflection w at the ultimate limit state where b is the plate width (see Fig. 2.65). Fig.

19、 2.65: Numerical model for rigid transverse stiffeners同济大学 吴冲 Tongji University, Wu Chong17Stiffeners and detailingTransverse stiffenersDirect stresses: minimum required second moment of area Ist Ist,act is the actual second moment of area of the transverse stiffener, Ist is theminimum required seco

20、nd moment of area of the transverse stiffener to be considered as rigidemax is the maximum distance from the edge of the stiffener to the centroid of the stiffenerNwd is the maximum compressive force of both adjacent panels. It represents the resultant of compression direct stresses and should not b

21、e taken as less than the maximum compressive stress at the edge of the panel times half of the effectivep compressive area of the panel Ac,effscr, scr elastic critical stresses for column- and plate-like buckling同济大学 吴冲 Tongji University, Wu Chong18Stiffeners and detailingTransverse stiffenersDirect

22、 stressesAnother possibility of verifying the requirements (2.95) and (2.96), if transverse stiffeners are not loaded axially but only with deviation forces, is to perform first order elastic analysis on the stiffener loaded laterally with the equivalent uniformly distributed deviation forces is def

23、ined in wel is the elastic deflection of the stiffener. wel may be determined iteratively or it may be taken as the maximum permitted deflection b/300. 同济大学 吴冲 Tongji University, Wu Chong19Stiffeners and detailingTransverse stiffenersShearRigid end posts An inserted hot rolled profilethe section mod

24、ulus of such profiles should not be less than 4hwt2 (for the bending around horizontal axis perpendicular to the web) Two double sided stiffeners 同济大学 吴冲 Tongji University, Wu Chong20Stiffeners and detailingTransverse stiffenersShearRigid end posts A vertical I profile at the endAnother possibility

25、to create rigid end post is to limit length g of the panel at the end support such that the panel resists shear loading for the non-rigid end post conditions 同济大学 吴冲 Tongji University, Wu Chong21Stiffeners and detailingTransverse stiffenersShearNon-rigid end 同济大学 吴冲 Tongji University, Wu Chong22Stif

26、feners and detailingTransverse stiffenersShearIntermediate transverse stiffeners Ist is the second moment of the area of a stiffener for a cross-section, defined in Fig. 2.63, for the axis parallel to the web plate. 同济大学 吴冲 Tongji University, Wu Chong23Stiffeners and detailingTransverse stiffenersSh

27、earIntermediate transverse stiffenersAxial force Nst,ten in the intermediate stiffener imposed by the tension field action (Fig. 2.68) is calculated as: VEd is a design shear force in the adjacent panels. At variable shear forces VEd is taken at the distance 0.5 hw from the edge of the panel with th

28、e largest shear force is a relative slenderness of the panel adjacent to the stiffener 同济大学 吴冲 Tongji University, Wu Chong24Stiffeners and detailingTransverse stiffenersShearIntermediate transverse stiffeners Fig. 2.68: Development of axial force in the intermediate transverse stiffener 同济大学 吴冲 Tong

29、ji University, Wu Chong25Stiffeners and detailingTransverse stiffenersSimultaneous action of direct stresses and shear 同济大学 吴冲 Tongji University, Wu Chong26Stiffeners and detailingTransverse stiffenersSimultaneous action of direct stresses and shear the effect of deviation forces can be transformed

30、into an additional axial force in the stiffener Nst, Ed 同济大学 吴冲 Tongji University, Wu Chong27Stiffeners and detailingTransverse stiffenersSimultaneous action of direct stresses and shear Double sided stiffeners 同济大学 吴冲 Tongji University, Wu Chong28Stiffeners and detailingTransverse stiffenersSimulta

31、neous action of direct stresses and shear Double sided stiffeners w0 equivalent geometric imperfection of the stiffener according to Fig. 2.65Ncr,st Euler elastic critical force of the stiffenerNst,Ed = Nst,ten + Nst,ex (sum of axial forces from the tension field action and from external forces) Nst

32、,Ed = Nst,Ed + Nst,EdAst, Ist cross-section area and second moment of area of the effective cross-section of the stiffeneremax the maximum distance from the edge of the stiffener to the centroid of the stiffener 同济大学 吴冲 Tongji University, Wu Chong29Stiffeners and detailingTransverse stiffenersSimult

33、aneous action of direct stresses and shear Single sided stiffeners Fig. 2.70: Mechanical model for a single sided stiffener 同济大学 吴冲 Tongji University, Wu Chong30Stiffeners and detailingTransverse stiffenersSimultaneous action of direct stresses and shear Single sided stiffeners 同济大学 吴冲 Tongji Univer

34、sity, Wu Chong31Stiffeners and detailingTransverse stiffenersSimultaneous action of direct stresses and shear General casewel may be taken as b/300 (the maximum permitted additional deflection). The actual deflection should be less than b/300. 同济大学 吴冲 Tongji University, Wu Chong32Stiffeners and deta

35、ilingTransverse stiffenersIntroduction of reaction forces and other large transverse forcesThe stiffener should be checked for out of plane bucklingIf both ends are assumed to be supported laterally, the equivalent buckling length may be taken as 0.75 hw At the intermediate transverse stiffeners the

36、 axial force from the tension field action should also be included.In the presence of relevant deviation forces from direct stresses in the plate the design checks should be performedFig. 2.72: Transverse stiffeners loaded by concentrated loads同济大学 吴冲 Tongji University, Wu Chong33Stiffeners and deta

37、ilingLongitudinal stiffenersFig. 2.74: Discontinuity of longitudinal stiffenersFig. 2.73: Position of longitudinal stiffeners同济大学 吴冲 Tongji University, Wu Chong34Stiffeners and detailingStructural detailing related to plate buckling Transverse welds in the plateFig. 2.78: Location of the transverse weld in the plate同济大学 吴冲 Tongji University, Wu Chong35Stiffeners and detailingStructural detailing related to plate buckling Cut-outs in stiffenersLength l and height h of the cut-out should not exceed:l 6 tmin for flat stiffeners in compression,l 8 tmin for other stiffeners in compres