Topic Training Buckling lengths for steel

Transcription

1 Tpic Training Buckling lengths fr steel

2 Tpic Training Buckling lengths fr steel All infrmatin in this dcument is subject t mdificatin withut prir ntice. N part f this manual may be reprduced, stred in a database r retrieval system r published, in any frm r in any way, electrnically, mechanically, by print, pht print, micrfilm r any ther means withut prir written permissin frm the publisher. SCIA is nt respnsible fr any direct r indirect damage because f imperfectins in the dcumentatin and/r the sftware. Cpyright 2015 SCIA nv. All rights reserved. 2

3 Table f cntents Table f cntents Intrductin... 5 Buckling factrs and lengths... 6 Autmatic calculatin f buckling ratis... 6 Autmatic placement f buckling supprts Manual placement f buckling supprts Manual input f buckling ratis Buckling curves Buckling check Relative defrmatin Ndal displacements Relative defrmatin References and literature

4 Tpic Training Buckling lengths fr steel 4

5 Intrductin Intrductin This curse will explain the principles and the use f system lengths in SCIA Engineer. The buckling parameters and the related buckling lengths will be discussed, in cmbinatin with the relative defrmatin f 1D elements. Mst f the ptins in the curse can be calculated in SCIA Engineer with the Cncept editin. Fr sme functinality an extra mdule (r editin) is required, but this will always be indicated in thse paragraphs. 5

6 Tpic Training Buckling lengths fr steel Buckling factrs and lengths Autmatic calculatin f buckling ratis By default, the buckling ratis are calculated by SCIA Engineer. Fr this, tw apprximate frmulas are used: ne frmula fr a nn sway structure (resulting in a buckling factr smaller (r equal) than 1) and ne frmula fr a sway structure (resulting in a buckling factr higher (r equal) than 1): Fr a nn sway structure: = Fr a sway structure: = ² + 4 with k L E I C i M i φ i the buckling factr the system length the mdulus f Yung the mment f inertia the stiffness in nde i the mment in nde i the rtatin in nde i 4 + ² = = = The values fr M i and φ i are apprximately determined by the internal frces and the defrmatins, calculated by lad cases which generate defrmatin frms, having an affinity with the buckling frm. The calculatin f the k ratis is autmatically dne when calculating the structure linearly. Fr this, tw additinal lad cases are calculated in the backgrund: Lad case 1: n the beams, the lcal distributed lads qy=1 N/m and qz=-100 N/m are used n the clumns the glbal distributed lads Qx =10000 N/m and Qy =10000 N/m are used. Lad case 2: n the beams, the lcal distributed lads qy=-1 N/m and qz=-100 N/m are used n the clumns the glbal distributed lads Qx = N/m and Qy= N/m are used. 6

7 Buckling factrs and lengths Since these lad cases, and thus the buckling ratis, are calculated during the linear calculatin, it is necessary t always perfrm a linear calculatin f the structure. S when calculating nn linear, the user shuld als perfrm a linear calculatin therwise n buckling factrs are calculated and n steel cde check can be perfrmed. Nte: The used apprach gives gd results fr frame structures with perpendicular rigid r semi-rigid beam cnnectins. Fr ther cases, the user has t evaluate the presented bucking ratis. Since the frmulas are different fr sway and nn sway structure, it is imprtant that the crrect ptins are chsen fr the tw lcal directins: y-y: buckling arund the lcal y-axis (s defrmatin in the directin f the lcal z-axis) z-z: buckling arund the lcal z-axis (s defrmatin in the directin f the lcal y-axis) The ptin Sway r Nn sway can be chsen in the menu Steel > Beams > Steel Setup. These settings apply t the whle structure:

8 Tpic Training Buckling lengths fr steel Example: Buckling Factr.esa In this example, a simple steel frame is used t calculate the buckling ratis. The structure is laded by the tw additinal lad cases as described n the previus page. Cnsider Clumn B1: - L = 4000mm - Set as sway - In nde N1 : My = 0 knm => C 2 = ρ 2 = This nde N1 defines ρ 2 because ρ 2 is always the smaller f the tw. - In nde N2 fr Lad case LC1: M y1 = 79,883 knm φ 1 = fiy = 1,523 mrad C 1 = M y1 / φ 1 = 79,883 knm / 1,523 mrad = 52,451 knm/mrad E = N/mm² Iy = mm 4 ρ 1 = = 5,2451 x Nmm/rad #$ =.! #$ %&&!***++ '() **** % &&, -.***** ++/ = =!1 #1, 23,4 # 3, 1 # 21, 251 # 1, =! -,! *,*23, -,! 3, -,!2*,*25 -,! *,* = 1.0 = 8 3, 3, + 4 = 1, = # 9 -,!,* ; <= = 3² 3² ****?/++² -.***** ++/ = = ; = 3754,8 ; >²²,A-5,!***² This calculated buckling rati can als be fund in SCIA Engineer. Under Steel > Beams > Steel slenderness, the buckling factr k y will be fund: 8

9 Buckling factrs and lengths This can als be displayed in the preview: With the ptin Steel slenderness, all parameters can be shwn graphically and numerically in the preview. Sway y (z): whether this member is cnsidered sway r nt sway. L y (L z ): the system length f the member. This is the distance between the buckling supprts. k y (k z ): the buckling rati. This factr is calculated autmatically by SCIA Engineer r can be inserted manually. l y (l z ): the buckling length. l y = L y * k y Lam y (Lam z): the slenderness f the element l yz : the trsinal buckling length l LTB: the lateral trsinal buckling length

10 Tpic Training Buckling lengths fr steel The type sway r nt sway in the steel setup applies fr the whle structure. It is als pssible t change these (verrule) these settings fr each member (r selectin f members) separately. This can be dne in tw ways with different pririty. Clumn B2 is used. Member Buckling Data. Steel > Beams > Member Check data > Member Buckling Data. The ptin Buckling ky, kz cefficients r buckling lengths has t be set t user input. In the Cefficient menu, the type fr Sway yy and zz can be changed manually. When Member Buckling Data is added t a member, a new label will appear n this member. Since this data is Additinal data, this can be cpied t ther members. Buckling and relative lengths. Prperty windw f the selected member. By clicking n the three dts, the Buckling data windw will pen. After clicking n Edit, the sway type can be changed.

11 Buckling factrs and lengths These settings are stred in the Buckling system BC1. This system can be used fr ther members, if these members have the same amunt f cnstructin ndes. The Member Buckling Data has a higher pririty than the Buckling and relative lengths.

12 Tpic Training Buckling lengths fr steel Example: Several frames.esa In this example, several steel frames are mdeled. In each frame, the same type f clumn is used, but the beams are adapted. The cnnectin between the clumns is fixed. Only in the last frame, this cnnectin is made hinged. Since the structure is cnsidered as sway fr y-y, it is expected t have a k y factr between 1 and 2 fr the clumns. With a smaller beam, the k y factr will be almst 2. With a bigger beam, the k y factr will be almst 1. In the frame with the hinged cnnectin between the beams and the clumns, the k y factr f the clumns will be equal t 2.

13 Buckling factrs and lengths Nte: If the buckling ratis are calculated autmatically, by default a maximum value f 10 is used. This limitatin can be adapted in the Steel setup.

14 Tpic Training Buckling lengths fr steel Autmatic placement f buckling supprts SCIA Engineer will autmatically recgnize every ndal supprt, beam cnnectin, fr the placements f buckling supprts. Example: Buckling supprts.esa In this example, several beams are cnnected t the clumns. A buckling supprt is autmatically placed at every lcatin f a cnnectin between the members. Nte: Buckling supprts can nly be placed in structural ndes. Cnsider clumn B2. This clumn has 3 ndes: N3, N16 and N4. The lcal X directin ges frm the bttm t the tp f the clumn, s internal fr SCIA Engineer N3 is the first nde f this clumn and N4 is the last ne. In the prperties windw f this clumn, the user can chse fr Buckling and relative lengths. With this ptin, the buckling system f the element can be viewed and changed. Default the fllwing ptin will appear: Explanatin f the system lengths: The first nde (accrding t the lcal x-axis) is nde N3, the last ne is nde N4. yy directin: This means arund the lcal y-axis. S the clumn will defrm in the lcal z-directin. Arund the y-axis, nde N3 is supprted. In nde N16 a hrizntal beam in the lcal z- directin can be fund and the clumn will be supprted arund the lcal y-axis (yy) in nde N16. Als in nde N4 a hrizntal beam in the lcal z-directin can be fund and the clumn will als be supprted arund the lcal y-axis (yy) in nde N4. This is indicated with the triangles in this windw: Supprted in nde N3

15 Buckling factrs and lengths zz directins: Supprted in nde N16 Supprted in nde N4 This means arund the lcal z-axis. S the clumn will defrm in the y-directin. Arund the z-axis, nde N3 is supprted. In nde N16 n beam can be fund in the lcal y-directin in this pint, thus clumn B2 is nt supprted arund the z-axis in nde N16. In nde N4 a hrizntal beam in the lcal y-directin can be fund and the clumn will be supprted arund the lcal z-axis (zz) in nde N4. This is indicated with the triangles in this windw: Supprted in nde N3 Nt supprted in nde N16 Supprted in nde N4 The system length will be taken as fllws: Arund the y-axis: the length between nde N3 and nde N16 fr the first part f the clumn (2,5m) and the length between nde N16 and nde N4 fr the secnd part f the clumn (2,5m). Arund the z-axis: the length between nde N3 and nde N4, s 5m. This can als be fund in the menu Steel > Beams > Steel slenderness : In this windw, the user can easily check the system length (L y and L z ), the buckling factrs (k y and k z ) and als the buckling length (l y = k y x L y and l z = k z x L z ) Cmpare clumn B2 and clumns B18 and B19 with each ther. They shuld have exactly the same system lengths. The nly difference between thse clumns is that clumn B2 was inputted as ne element f 5m and clumns B18+B19 are divided int tw parts f 2,5m. SCIA Engineer will cnsider thse tw clumns als as ne buckling system: If the lcal axis are exactly in the same directin. If n hinges has been inputted between the tw clumns. Nte: If members are inserted as a Plyline, the directin f the members may be different. The cmplete plyline is seen as ne buckling system. There is als a graphical representatin f the system lengths. Select clumn B2.

16 Tpic Training Buckling lengths fr steel G t the actins menu and click n Graphical input f system length: Nw the user can chse between the yy and the zz axis:

17 Buckling factrs and lengths Manual placement f buckling supprts Since a buckling supprt (triangle) is placed at every structural nde where there is a ndal supprt r a cnnecting member, it can be necessary t manually change this cnfiguratin. Select clumn B3 and pen the buckling data windw t have a lk at the buckling system. The system lengths are as fllws (as expected, because there is a hrizntal beam in the lcal z-directin n each nde): When lking at the rendered view f the structure, it is clear that beam B17 is t weak t have an influence n the system length f clumn B3. In SCIA Engineer, there is a pssibility t exclude a beam frm a buckling system. This can be dne by inputting Member buckling data t the element. S select beam B17 and g in the Actins menu t Buckling data: In this menu, it is pssible t indicate that beam B17 is a secndary beam and shuld nt be taken int accunt in the system lengths:

18 Tpic Training Buckling lengths fr steel Afterwards, a label will be displayed n beam B17, indicating that this beam cnsists sme buckling data. This buckling data is Additinal data and can be cpied t ther members in the structure. This can be dne by selecting the label, click with the right muse buttn in the screen and chse the ptin Cpy add data BB1. If the additinal data (secndary member) is inserted, the buckling system f clumn B3 can be changed. Select member B3 and change the Buckling and relative lengths back t Default. Afterwards, beam B17 will nt be included in the system lengths:

19 Buckling factrs and lengths It is als pssible t change the buckling supprts using the ptin Buckling and relative lengths in the prperty windw f an element. By clicking n the 3 dts, the Buckling data windw will pen. After clicking n Edit, and using the secnd tab Buckling data, the user can chse whether the ndes shuld be fixed r free by ticking n r ff the ptins fr yy and zz: These settings will be stred in the buckling system BC*. This buckling system can be used fr ther elements, but nly f these elements d have the same amunt f structural ndes.

20 Tpic Training Buckling lengths fr steel The last ptin t change the settings fr fixed r free buckling supprts, is t use the Graphical input f system length in the actin windw: The full red lines are the fixed ndes, the dt lines are the free ndes. By simply clicking n the triangles, the settings fr free and fixed will be changed.

21 Buckling factrs and lengths Manual input f buckling ratis As mentined in a previus chapter, the buckling ratis are autmatically calculated by SCIA Engineer during the linear calculatin. It is als pssible t insert these buckling ratis manually. This can be dne using: Member buckling data. Steel > Beams > Member Check data > Member buckling data. Clumn B4 will be used t explain this ptin. Select member B4 and duble click n Member Buckling data. First f all, the Buckling ky, kz cefficients r buckling lengths has t be set t user input. Next fr the ky factr, there are three pssibilities: Calculate: use the buckling rati calculated by SCIA Engineer Factr: insert manually the buckling factr ky. Length: insert manually the buckling length ly. T be able t insert these factrs manually, the ptin Edit buckling shuld be used: In the next windw, the buckling rati ky r the buckling length ly can be inputted.

22 Tpic Training Buckling lengths fr steel Fr this clumn B4, a ky rati f 3 will be inserted manually. After inputting this value, a new label will appear n this clumn. This Member buckling data is again additinal data which can be cpied t ther elements. Buckling and relative lengths. Prperty windw f the element B4. By clicking n Edit in the Buckling data windw, in the tab Base settings, it is als pssible t chse t insert a buckling rati ky r the buckling length ly manually. In the secnd tab Buckling data, these values can be inserted. With this ptin, it is pssible t insert a different buckling rati fr each part f the clumn. Fr this clumn, a value f 2 will be inserted fr ky fr bth parts f the element. Nte: The tw discussed ptins t insert the buckling ratis (lengths) manually d nt have the same pririty. The values entered by the Member buckling data will have a higher pririty than the values inserted by the Buckling an relative lengths. This can be easily checked by shwing the ky factrs fr clumn B4 in the steel menu: Steel > Beams > Steel slenderness Fr clumn B4, the ky rati f 3 is used:

23 Buckling factrs and lengths

24 Tpic Training Buckling lengths fr steel Buckling curves SCIA Engineer will use the buckling curves accrding t the cde. If the Eurcde is chsen, table 6.2 f EN [1] will be used t determine which buckling curve has t be used.

25 Buckling curves The autmatic use f the crrect buckling curve accrding t the cde is supprted fr the fllwing crss sectin types: Prfile Library Haunch Sheet welded Build-in beams Thin-walled gemetric Fabricated Fr all ther crss sectin types, the buckling curves fr bth directins are by default set t d. This can be changed manually by changing the prperties f the crss sectin. Example: Buckling curves.esa Open the example Buckling curves. In this example, 3 clumns are inserted with a fixed supprt and laded with a pint frce f -100 kn. The fllwing crss sectins are used: Prfile Library > HEA200 Gemetric shape > default buckling curves d Gemetric shape > buckling curves manually changed By default, the buckling curves d are used fr bth directins fr the secnd and third crss sectin. Fr the third crss sectin, this is manually changed int buckling curve b arund the y axis and buckling curve c arund the z axis. This way, the same curves are used as fr the HEA200 prfile. 25

26 Tpic Training Buckling lengths fr steel Nte: There has been made sme changes since SCIA Engineer versin SCIA Engineer r lder. In these versins, it is als pssible t manually change the buckling curves fr each crss sectin type. Hwever, if a crss sectin frm the prfile library is used, the buckling check will always use the buckling curves accrding t table 6.2 f EN [1]. This means that fr these types f crss sectin, the user input fr the buckling curves is neglected in the Steel cde check. SCIA Engineer r newer. The manual mdificatin f the buckling curves in the crss sectin prperties, is always taken int accunt by the buckling check in the steel menu, als fr the crss sectins frm the prfile library.

27 Buckling check Buckling check If the Eurcde is chsen, the flexural buckling check will be executed fllwing EN art [1] The cmpressin member shuld be checked against buckling as fllws: ; C ; D,EC F 1 Where N Ed is the design value f the cmpressin frce. N b,rd is the design buckling resistance f the buckling member. Nte: In SCIA Engineer, a negative value f N Ed means a cmpressin frce. ; D,EC = G H I J K L# ; D,EC = G H MNN I J K L# Fr class 1, 2 r 3 crss sectins Fr class 4 crss sectins The reductin factr χ will be calculated as fllws: O = P2QP²RST, but χ < 1,0 With Φ 0,5 V1 + WXY [ 0,2\ + Y ] Y 8 H I J?^' Fr class 1, 2 r 3 crss-sectins 8 H MNN I J?^' Fr class 4 crss-sectins α Imperfectin depending n the buckling curves: N cr Critical nrmal frce (Euler frce) ; <= = 3² >²² Nte: Fr slenderness Y 2 r fr? _) F 0,04 the buckling effects may be ignred and nly the?^' crss sectinal checks need t be applied.

28 Tpic Training Buckling lengths fr steel Example: Buckling check.esa Open the example Buckling check. In this example, a simple steel hall is mdelled. The structure is laded by the self weight and with a surface lad f -1 kn/m² n the rf. After executing the linear calculatin, the buckling check can be perfrmed in the Steel menu. Steel > Beams > ULS Check > Check. Select clumn B4. In the prperty windw f the ULS check, the fllwing prperties are chsen: The selectin is set t Current t nly see the results f the selected member (clumn B4). The flexural buckling check will be perfrmed in the Stability check and can be shwn in the Detailed utput. Fr lad LC1 (self weight): Fr lad case LC1, the buckling check des nt need t be perfrmed since: Fr lad LC2 (surface lad): ; C ; <= = 3,40 = 0,021 F 0,04 160,24

29 Buckling check Fr this lad case, the buckling check needs t be perfrmed. All the parameters needed t calculate the buckling resistance are shwn in this table. The buckling resistance is calculated fr bth the y and z directin. The smallest f these tw values is used t perfrm the check. The buckling length = system length * buckling factr l y = k y * L y = 4,37 * 5 = 21,847 m This buckling length is used t calculate the critical nrmal frce (Euler frce) ; <= = ² ²² = ²` ² 2, ; = c 3,69 10R c! = 160,2366 ; a`² 21,847² c² Slenderness Y = a` = 21,847c e` 0,082817c = 263,798 Relative slenderness Y = Y Y = Limit slenderness Y 93,3f = 263,79 93,3 = 2,82 The limit slenderness is by default taken frm EN , article Fr flexural buckling, this is a cnstant value f 0,2. The buckling curve b is used, and thus an imperfectin factr α f 0,34. The reductin factr χ will be calculated as fllws: 1 O = Φ + QΦ [ Y And

30 Tpic Training Buckling lengths fr steel Φ = 0,5 V1 + WXY [ 0,2\ + Y ] = 0,5 g1 + 0,34 2,81 [ 0,2 + 2,81 h = 4,89275 Thus O = 1 = Φ + QΦ [ Y Buckling resistance 1 4, Q4,89275 [ 2,81 = 0,1124 iiiiii ; D,EC = O j k` l m = 0,1124 0,00538 c² ;/c² 1 = 142,1073 ; The difference with the result in SCIA Engineer is caused by runding errrs. The buckling check ; C = 13,53 ; D,EC 142,23 = 0,9512 There is als a warning message printed in the utput f the Flexural Buckling Check abut the slenderness f the member. In the steel setup, a maximal slenderness can be inserted. If the real slenderness f the member is higher than this inserted slenderness, this warning message will be printed. In SCIA Engineer, by default the maximal slenderness is set t 200:

31 Relative defrmatin Relative defrmatin Ndal displacements First f all, a simple manual calculatin can be dne t check the ndal displacements in hrizntal vertical directin. The fllwing limits can be checked: h/150 fr hrizntal displacements L/200 fr vertical displacements These values are guidelines. Example: Buckling check.esa Open the example Buckling check. Since this steel hall is nly laded with the self weight f the structure and a vertical surface lad, the ndal displacements in the glbal Y directin are zer. S nly the ndal displacements in the glbal X and Z directins will be checked. T check these values, the lad cmbinatin CO1 is used. Hrizntal defrmatin The maximal ndal displacement in the glbal X directin is 37,1 mm. h/150 = 5000mm/150 = 33,33 mm 37,1 mm > 33,33 mm s this is nt k. Vertical defrmatin The maximal ndal displacement in the glbal Z directin is 223,8 mm. L/200 = 12000/200 = 60 mm 223,8 mm > 60 mm s this is nt k.

32 Tpic Training Buckling lengths fr steel Relative defrmatin Fr the relative defrmatin check, limiting values are inserted in the steel setup fr each type f member. Steel > Beams > Steel setup > Relative defrmatin. With the ptin Steel -> Beams -> SLS Checks - Relative defrmatin, the relative defrmatins can be checked. The relative defrmatins are given as abslute value, relative value related t the span, r as unity check related t the limit fr the relative value t the span. The span is defined in the menu Buckling and relative lengths, and is the distance between tw buckling supprts. Select beam B3. Fr the systems f the relative defrmatin, by default a reference is made t the buckling system yy and zz.

33 Relative defrmatin This can be changed t create a separate system fr the relative defrmatin. In the secnd tab Buckling data, the ndes can be fixed r free fr the relative defrmatin. The same can be dne using the Graphical input f system length.

34 Tpic Training Buckling lengths fr steel The relative defrmatin is always regarded accrding t the lcal axis f the member. Fr the defrmatin in the y directin f the member, there are tw supprting ndes fr member B3. The distance between these ndes is 6,083m. Relative defrmatin in the y directin (arund the z axis). In this directin, there are 2 supprted ndes. The defrmatin at the begin and end nde is 0,0 mm. The maximal defrmatin fr this beam is 11,1 mm.

35 Relative defrmatin Length = 6,083 m Defrmatin uy = 11,1 mm (and 0 mm at the beginning f the beam and 0 mm at the end f the beam) uy relative = 11,1 mm 0.0 mm = 11,1 mm uy relative / Length = 11,1 mm / 6083 mm = 1/546 Check = /!5 /** = 0,37 Relative defrmatin in the z directin (arund the y axis). In this directin, there is ne supprted nde. The defrmatin at the begin nde is 0,0 mm and at the end nde is 105,3 mm. Length = 6,083 m Defrmatin uz = 105,3 mm (and 0 mm at the beginning f the beam) uz relative = 105,3 mm 0.0 mm = 105,3 mm uz relative / Length = 105,3 mm / 6083 mm = 1/58 Check = /5 /** = 3,46

36 Tpic Training Buckling lengths fr steel The relative defrmatin f these members is nw calculated with the length f the beam (distance between the buckling ndes). It is als pssible t perfrm the relative defrmatin check fr the cmplete span f the rf. This can be dne by using plylines. Draw the members as plylines. This can nly be dne if the elements are mdeled using the ptin Member in the Structure menu. Merging elements t a plyline. Select beam B17 and B18. Thrugh the ptin Jin curves int plyline, these 2 beams will becme 1 beam. Since this has an influence n the results, the prject needs t be recalculated. By lking at the buckling system f the new member B18, it is clear that the tw elements are taken as ne fr buckling and relative defrmatin.

37 This results in the fllwing check fr the relative defrmatin. Relative defrmatin

38 Tpic Training Buckling lengths fr steel References and literature [1] Eurcde 3 Design f steel structures Part 1-1 : General rules and rules fr buildings ENV :1992,